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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> glob_iolevel,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> glob_large_float,
> glob_hmin,
> glob_clock_sec,
> days_in_year,
> min_in_hour,
> glob_current_iter,
> glob_look_poles,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_display_flag,
> glob_dump,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_initial_pass,
> sec_in_min,
> glob_warned2,
> glob_optimal_done,
> djd_debug2,
> glob_log10normmin,
> glob_start,
> glob_relerr,
> years_in_century,
> hours_in_day,
> djd_debug,
> glob_html_log,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_warned,
> glob_abserr,
> glob_h,
> glob_almost_1,
> glob_orig_start_sec,
> glob_small_float,
> glob_dump_analytic,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_no_eqs,
> glob_max_hours,
> glob_hmax,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_norms,
> array_type_pole,
> array_y_init,
> array_m1,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_iolevel, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_max_terms,
glob_iter, glob_max_rel_trunc_err, glob_last_good_h, glob_large_float,
glob_hmin, glob_clock_sec, days_in_year, min_in_hour, glob_current_iter,
glob_look_poles, glob_hmin_init, glob_clock_start_sec, glob_display_flag,
glob_dump, MAX_UNCHANGED, glob_smallish_float, glob_optimal_clock_start_sec,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_warned2,
glob_optimal_done, djd_debug2, glob_log10normmin, glob_start, glob_relerr,
years_in_century, hours_in_day, djd_debug, glob_html_log,
glob_subiter_method, glob_max_minutes, glob_log10relerr, glob_log10abserr,
glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter,
glob_optimal_expect_sec, glob_normmax, glob_max_sec, glob_warned,
glob_abserr, glob_h, glob_almost_1, glob_orig_start_sec, glob_small_float,
glob_dump_analytic, glob_curr_iter_when_opt, glob_optimal_start,
glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr,
glob_not_yet_start_msg, centuries_in_millinium, glob_no_eqs, glob_max_hours,
glob_hmax, glob_disp_incr, glob_not_yet_finished, glob_percent_done,
array_const_3D0, array_const_0D0, array_const_1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_pole,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_norms,
array_type_pole, array_y_init, array_m1, array_poles, array_y_higher_work2,
array_y_higher_work, array_real_pole, array_complex_pole,
array_y_set_initial, array_y_higher, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> glob_iolevel,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> glob_large_float,
> glob_hmin,
> glob_clock_sec,
> days_in_year,
> min_in_hour,
> glob_current_iter,
> glob_look_poles,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_display_flag,
> glob_dump,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_initial_pass,
> sec_in_min,
> glob_warned2,
> glob_optimal_done,
> djd_debug2,
> glob_log10normmin,
> glob_start,
> glob_relerr,
> years_in_century,
> hours_in_day,
> djd_debug,
> glob_html_log,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_warned,
> glob_abserr,
> glob_h,
> glob_almost_1,
> glob_orig_start_sec,
> glob_small_float,
> glob_dump_analytic,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_no_eqs,
> glob_max_hours,
> glob_hmax,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_norms,
> array_type_pole,
> array_y_init,
> array_m1,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_iolevel, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_max_terms,
glob_iter, glob_max_rel_trunc_err, glob_last_good_h, glob_large_float,
glob_hmin, glob_clock_sec, days_in_year, min_in_hour, glob_current_iter,
glob_look_poles, glob_hmin_init, glob_clock_start_sec, glob_display_flag,
glob_dump, MAX_UNCHANGED, glob_smallish_float, glob_optimal_clock_start_sec,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_warned2,
glob_optimal_done, djd_debug2, glob_log10normmin, glob_start, glob_relerr,
years_in_century, hours_in_day, djd_debug, glob_html_log,
glob_subiter_method, glob_max_minutes, glob_log10relerr, glob_log10abserr,
glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter,
glob_optimal_expect_sec, glob_normmax, glob_max_sec, glob_warned,
glob_abserr, glob_h, glob_almost_1, glob_orig_start_sec, glob_small_float,
glob_dump_analytic, glob_curr_iter_when_opt, glob_optimal_start,
glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr,
glob_not_yet_start_msg, centuries_in_millinium, glob_no_eqs, glob_max_hours,
glob_hmax, glob_disp_incr, glob_not_yet_finished, glob_percent_done,
array_const_3D0, array_const_0D0, array_const_1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_pole,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_norms,
array_type_pole, array_y_init, array_m1, array_poles, array_y_higher_work2,
array_y_higher_work, array_real_pole, array_complex_pole,
array_y_set_initial, array_y_higher, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> glob_iolevel,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> glob_large_float,
> glob_hmin,
> glob_clock_sec,
> days_in_year,
> min_in_hour,
> glob_current_iter,
> glob_look_poles,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_display_flag,
> glob_dump,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_initial_pass,
> sec_in_min,
> glob_warned2,
> glob_optimal_done,
> djd_debug2,
> glob_log10normmin,
> glob_start,
> glob_relerr,
> years_in_century,
> hours_in_day,
> djd_debug,
> glob_html_log,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_warned,
> glob_abserr,
> glob_h,
> glob_almost_1,
> glob_orig_start_sec,
> glob_small_float,
> glob_dump_analytic,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_no_eqs,
> glob_max_hours,
> glob_hmax,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_norms,
> array_type_pole,
> array_y_init,
> array_m1,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_iolevel, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_max_terms,
glob_iter, glob_max_rel_trunc_err, glob_last_good_h, glob_large_float,
glob_hmin, glob_clock_sec, days_in_year, min_in_hour, glob_current_iter,
glob_look_poles, glob_hmin_init, glob_clock_start_sec, glob_display_flag,
glob_dump, MAX_UNCHANGED, glob_smallish_float, glob_optimal_clock_start_sec,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_warned2,
glob_optimal_done, djd_debug2, glob_log10normmin, glob_start, glob_relerr,
years_in_century, hours_in_day, djd_debug, glob_html_log,
glob_subiter_method, glob_max_minutes, glob_log10relerr, glob_log10abserr,
glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter,
glob_optimal_expect_sec, glob_normmax, glob_max_sec, glob_warned,
glob_abserr, glob_h, glob_almost_1, glob_orig_start_sec, glob_small_float,
glob_dump_analytic, glob_curr_iter_when_opt, glob_optimal_start,
glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr,
glob_not_yet_start_msg, centuries_in_millinium, glob_no_eqs, glob_max_hours,
glob_hmax, glob_disp_incr, glob_not_yet_finished, glob_percent_done,
array_const_3D0, array_const_0D0, array_const_1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_pole,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_norms,
array_type_pole, array_y_init, array_m1, array_poles, array_y_higher_work2,
array_y_higher_work, array_real_pole, array_complex_pole,
array_y_set_initial, array_y_higher, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> glob_iolevel,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> glob_large_float,
> glob_hmin,
> glob_clock_sec,
> days_in_year,
> min_in_hour,
> glob_current_iter,
> glob_look_poles,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_display_flag,
> glob_dump,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_initial_pass,
> sec_in_min,
> glob_warned2,
> glob_optimal_done,
> djd_debug2,
> glob_log10normmin,
> glob_start,
> glob_relerr,
> years_in_century,
> hours_in_day,
> djd_debug,
> glob_html_log,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_warned,
> glob_abserr,
> glob_h,
> glob_almost_1,
> glob_orig_start_sec,
> glob_small_float,
> glob_dump_analytic,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_no_eqs,
> glob_max_hours,
> glob_hmax,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_norms,
> array_type_pole,
> array_y_init,
> array_m1,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global glob_iolevel, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_max_terms,
glob_iter, glob_max_rel_trunc_err, glob_last_good_h, glob_large_float,
glob_hmin, glob_clock_sec, days_in_year, min_in_hour, glob_current_iter,
glob_look_poles, glob_hmin_init, glob_clock_start_sec, glob_display_flag,
glob_dump, MAX_UNCHANGED, glob_smallish_float, glob_optimal_clock_start_sec,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_warned2,
glob_optimal_done, djd_debug2, glob_log10normmin, glob_start, glob_relerr,
years_in_century, hours_in_day, djd_debug, glob_html_log,
glob_subiter_method, glob_max_minutes, glob_log10relerr, glob_log10abserr,
glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter,
glob_optimal_expect_sec, glob_normmax, glob_max_sec, glob_warned,
glob_abserr, glob_h, glob_almost_1, glob_orig_start_sec, glob_small_float,
glob_dump_analytic, glob_curr_iter_when_opt, glob_optimal_start,
glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr,
glob_not_yet_start_msg, centuries_in_millinium, glob_no_eqs, glob_max_hours,
glob_hmax, glob_disp_incr, glob_not_yet_finished, glob_percent_done,
array_const_3D0, array_const_0D0, array_const_1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_pole,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_norms,
array_type_pole, array_y_init, array_m1, array_poles, array_y_higher_work2,
array_y_higher_work, array_real_pole, array_complex_pole,
array_y_set_initial, array_y_higher, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> glob_iolevel,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> glob_large_float,
> glob_hmin,
> glob_clock_sec,
> days_in_year,
> min_in_hour,
> glob_current_iter,
> glob_look_poles,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_display_flag,
> glob_dump,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_initial_pass,
> sec_in_min,
> glob_warned2,
> glob_optimal_done,
> djd_debug2,
> glob_log10normmin,
> glob_start,
> glob_relerr,
> years_in_century,
> hours_in_day,
> djd_debug,
> glob_html_log,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_warned,
> glob_abserr,
> glob_h,
> glob_almost_1,
> glob_orig_start_sec,
> glob_small_float,
> glob_dump_analytic,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_no_eqs,
> glob_max_hours,
> glob_hmax,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_norms,
> array_type_pole,
> array_y_init,
> array_m1,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global glob_iolevel, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_max_terms,
glob_iter, glob_max_rel_trunc_err, glob_last_good_h, glob_large_float,
glob_hmin, glob_clock_sec, days_in_year, min_in_hour, glob_current_iter,
glob_look_poles, glob_hmin_init, glob_clock_start_sec, glob_display_flag,
glob_dump, MAX_UNCHANGED, glob_smallish_float, glob_optimal_clock_start_sec,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_warned2,
glob_optimal_done, djd_debug2, glob_log10normmin, glob_start, glob_relerr,
years_in_century, hours_in_day, djd_debug, glob_html_log,
glob_subiter_method, glob_max_minutes, glob_log10relerr, glob_log10abserr,
glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter,
glob_optimal_expect_sec, glob_normmax, glob_max_sec, glob_warned,
glob_abserr, glob_h, glob_almost_1, glob_orig_start_sec, glob_small_float,
glob_dump_analytic, glob_curr_iter_when_opt, glob_optimal_start,
glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr,
glob_not_yet_start_msg, centuries_in_millinium, glob_no_eqs, glob_max_hours,
glob_hmax, glob_disp_incr, glob_not_yet_finished, glob_percent_done,
array_const_3D0, array_const_0D0, array_const_1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_pole,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_norms,
array_type_pole, array_y_init, array_m1, array_poles, array_y_higher_work2,
array_y_higher_work, array_real_pole, array_complex_pole,
array_y_set_initial, array_y_higher, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> glob_iolevel,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> glob_large_float,
> glob_hmin,
> glob_clock_sec,
> days_in_year,
> min_in_hour,
> glob_current_iter,
> glob_look_poles,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_display_flag,
> glob_dump,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_initial_pass,
> sec_in_min,
> glob_warned2,
> glob_optimal_done,
> djd_debug2,
> glob_log10normmin,
> glob_start,
> glob_relerr,
> years_in_century,
> hours_in_day,
> djd_debug,
> glob_html_log,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_warned,
> glob_abserr,
> glob_h,
> glob_almost_1,
> glob_orig_start_sec,
> glob_small_float,
> glob_dump_analytic,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_no_eqs,
> glob_max_hours,
> glob_hmax,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_norms,
> array_type_pole,
> array_y_init,
> array_m1,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult $eq_no = 1 i = 1
> array_tmp1[1] := (array_m1[1] * (array_const_3D0[1]));
> #emit pre div $eq_no = 1 i = 1
> array_tmp2[1] := (array_tmp1[1] / (array_x[1]));
> #emit pre div $eq_no = 1 i = 1
> array_tmp3[1] := (array_tmp2[1] / (array_x[1]));
> #emit pre div $eq_no = 1 i = 1
> array_tmp4[1] := (array_tmp3[1] / (array_x[1]));
> #emit pre div $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp4[1] / (array_x[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> # emit pre mult $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_m1,array_const_3D0,1);
> #emit pre div $eq_no = 1 i = 2
> array_tmp2[2] := ((array_tmp1[2] - ats(2,array_x,array_tmp2,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 2
> array_tmp3[2] := ((array_tmp2[2] - ats(2,array_x,array_tmp3,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 2
> array_tmp4[2] := ((array_tmp3[2] - ats(2,array_x,array_tmp4,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 2
> array_tmp5[2] := ((array_tmp4[2] - ats(2,array_x,array_tmp5,2))/array_x[1]);
> #emit pre add $eq_no = 1 i = 2
> array_tmp6[2] := array_const_0D0[2] + array_tmp5[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_tmp6[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> # emit pre mult $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_m1,array_const_3D0,1);
> #emit pre div $eq_no = 1 i = 3
> array_tmp2[3] := ((array_tmp1[3] - ats(3,array_x,array_tmp2,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 3
> array_tmp3[3] := ((array_tmp2[3] - ats(3,array_x,array_tmp3,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 3
> array_tmp4[3] := ((array_tmp3[3] - ats(3,array_x,array_tmp4,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 3
> array_tmp5[3] := ((array_tmp4[3] - ats(3,array_x,array_tmp5,2))/array_x[1]);
> #emit pre add $eq_no = 1 i = 3
> array_tmp6[3] := array_const_0D0[3] + array_tmp5[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_tmp6[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> # emit pre mult $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_m1,array_const_3D0,1);
> #emit pre div $eq_no = 1 i = 4
> array_tmp2[4] := ((array_tmp1[4] - ats(4,array_x,array_tmp2,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 4
> array_tmp3[4] := ((array_tmp2[4] - ats(4,array_x,array_tmp3,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 4
> array_tmp4[4] := ((array_tmp3[4] - ats(4,array_x,array_tmp4,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 4
> array_tmp5[4] := ((array_tmp4[4] - ats(4,array_x,array_tmp5,2))/array_x[1]);
> #emit pre add $eq_no = 1 i = 4
> array_tmp6[4] := array_const_0D0[4] + array_tmp5[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_tmp6[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> # emit pre mult $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_m1,array_const_3D0,1);
> #emit pre div $eq_no = 1 i = 5
> array_tmp2[5] := ((array_tmp1[5] - ats(5,array_x,array_tmp2,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 5
> array_tmp3[5] := ((array_tmp2[5] - ats(5,array_x,array_tmp3,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 5
> array_tmp4[5] := ((array_tmp3[5] - ats(5,array_x,array_tmp4,2))/array_x[1]);
> #emit pre div $eq_no = 1 i = 5
> array_tmp5[5] := ((array_tmp4[5] - ats(5,array_x,array_tmp5,2))/array_x[1]);
> #emit pre add $eq_no = 1 i = 5
> array_tmp6[5] := array_const_0D0[5] + array_tmp5[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_tmp6[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_m1,array_const_3D0,1);
> #emit div $eq_no = 1
> array_tmp2[kkk] := ((array_tmp1[kkk] - ats(kkk,array_x,array_tmp2,2))/array_x[1]);
> #emit div $eq_no = 1
> array_tmp3[kkk] := ((array_tmp2[kkk] - ats(kkk,array_x,array_tmp3,2))/array_x[1]);
> #emit div $eq_no = 1
> array_tmp4[kkk] := ((array_tmp3[kkk] - ats(kkk,array_x,array_tmp4,2))/array_x[1]);
> #emit div $eq_no = 1
> array_tmp5[kkk] := ((array_tmp4[kkk] - ats(kkk,array_x,array_tmp5,2))/array_x[1]);
> #emit add $eq_no = 1
> array_tmp6[kkk] := array_const_0D0[kkk] + array_tmp5[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_tmp6[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global glob_iolevel, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_max_terms,
glob_iter, glob_max_rel_trunc_err, glob_last_good_h, glob_large_float,
glob_hmin, glob_clock_sec, days_in_year, min_in_hour, glob_current_iter,
glob_look_poles, glob_hmin_init, glob_clock_start_sec, glob_display_flag,
glob_dump, MAX_UNCHANGED, glob_smallish_float, glob_optimal_clock_start_sec,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_warned2,
glob_optimal_done, djd_debug2, glob_log10normmin, glob_start, glob_relerr,
years_in_century, hours_in_day, djd_debug, glob_html_log,
glob_subiter_method, glob_max_minutes, glob_log10relerr, glob_log10abserr,
glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter,
glob_optimal_expect_sec, glob_normmax, glob_max_sec, glob_warned,
glob_abserr, glob_h, glob_almost_1, glob_orig_start_sec, glob_small_float,
glob_dump_analytic, glob_curr_iter_when_opt, glob_optimal_start,
glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr,
glob_not_yet_start_msg, centuries_in_millinium, glob_no_eqs, glob_max_hours,
glob_hmax, glob_disp_incr, glob_not_yet_finished, glob_percent_done,
array_const_3D0, array_const_0D0, array_const_1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_pole,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_norms,
array_type_pole, array_y_init, array_m1, array_poles, array_y_higher_work2,
array_y_higher_work, array_real_pole, array_complex_pole,
array_y_set_initial, array_y_higher, glob_last;
array_tmp1[1] := array_m1[1]*array_const_3D0[1];
array_tmp2[1] := array_tmp1[1]/array_x[1];
array_tmp3[1] := array_tmp2[1]/array_x[1];
array_tmp4[1] := array_tmp3[1]/array_x[1];
array_tmp5[1] := array_tmp4[1]/array_x[1];
array_tmp6[1] := array_const_0D0[1] + array_tmp5[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp6[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_m1, array_const_3D0, 1);
array_tmp2[2] :=
(array_tmp1[2] - ats(2, array_x, array_tmp2, 2))/array_x[1];
array_tmp3[2] :=
(array_tmp2[2] - ats(2, array_x, array_tmp3, 2))/array_x[1];
array_tmp4[2] :=
(array_tmp3[2] - ats(2, array_x, array_tmp4, 2))/array_x[1];
array_tmp5[2] :=
(array_tmp4[2] - ats(2, array_x, array_tmp5, 2))/array_x[1];
array_tmp6[2] := array_const_0D0[2] + array_tmp5[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp6[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_m1, array_const_3D0, 1);
array_tmp2[3] :=
(array_tmp1[3] - ats(3, array_x, array_tmp2, 2))/array_x[1];
array_tmp3[3] :=
(array_tmp2[3] - ats(3, array_x, array_tmp3, 2))/array_x[1];
array_tmp4[3] :=
(array_tmp3[3] - ats(3, array_x, array_tmp4, 2))/array_x[1];
array_tmp5[3] :=
(array_tmp4[3] - ats(3, array_x, array_tmp5, 2))/array_x[1];
array_tmp6[3] := array_const_0D0[3] + array_tmp5[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp6[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_m1, array_const_3D0, 1);
array_tmp2[4] :=
(array_tmp1[4] - ats(4, array_x, array_tmp2, 2))/array_x[1];
array_tmp3[4] :=
(array_tmp2[4] - ats(4, array_x, array_tmp3, 2))/array_x[1];
array_tmp4[4] :=
(array_tmp3[4] - ats(4, array_x, array_tmp4, 2))/array_x[1];
array_tmp5[4] :=
(array_tmp4[4] - ats(4, array_x, array_tmp5, 2))/array_x[1];
array_tmp6[4] := array_const_0D0[4] + array_tmp5[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp6[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_m1, array_const_3D0, 1);
array_tmp2[5] :=
(array_tmp1[5] - ats(5, array_x, array_tmp2, 2))/array_x[1];
array_tmp3[5] :=
(array_tmp2[5] - ats(5, array_x, array_tmp3, 2))/array_x[1];
array_tmp4[5] :=
(array_tmp3[5] - ats(5, array_x, array_tmp4, 2))/array_x[1];
array_tmp5[5] :=
(array_tmp4[5] - ats(5, array_x, array_tmp5, 2))/array_x[1];
array_tmp6[5] := array_const_0D0[5] + array_tmp5[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp6[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_m1, array_const_3D0, 1);
array_tmp2[kkk] :=
(array_tmp1[kkk] - ats(kkk, array_x, array_tmp2, 2))/array_x[1]
;
array_tmp3[kkk] :=
(array_tmp2[kkk] - ats(kkk, array_x, array_tmp3, 2))/array_x[1]
;
array_tmp4[kkk] :=
(array_tmp3[kkk] - ats(kkk, array_x, array_tmp4, 2))/array_x[1]
;
array_tmp5[kkk] :=
(array_tmp4[kkk] - ats(kkk, array_x, array_tmp5, 2))/array_x[1]
;
array_tmp6[kkk] := array_const_0D0[kkk] + array_tmp5[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_tmp6[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 1.0/x/x/x;
> end;
exact_soln_y := proc(x) 1.0/(x*x*x) end proc
>
>
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> glob_iolevel,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_max_rel_trunc_err,
> glob_last_good_h,
> glob_large_float,
> glob_hmin,
> glob_clock_sec,
> days_in_year,
> min_in_hour,
> glob_current_iter,
> glob_look_poles,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_display_flag,
> glob_dump,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_initial_pass,
> sec_in_min,
> glob_warned2,
> glob_optimal_done,
> djd_debug2,
> glob_log10normmin,
> glob_start,
> glob_relerr,
> years_in_century,
> hours_in_day,
> djd_debug,
> glob_html_log,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_warned,
> glob_abserr,
> glob_h,
> glob_almost_1,
> glob_orig_start_sec,
> glob_small_float,
> glob_dump_analytic,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_no_eqs,
> glob_max_hours,
> glob_hmax,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_norms,
> array_type_pole,
> array_y_init,
> array_m1,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_iolevel := 5;
> INFO := 2;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> DEBUGL := 3;
> glob_max_terms := 30;
> glob_iter := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_large_float := 9.0e100;
> glob_hmin := 0.00000000001;
> glob_clock_sec := 0.0;
> days_in_year := 365.0;
> min_in_hour := 60.0;
> glob_current_iter := 0;
> glob_look_poles := false;
> glob_hmin_init := 0.001;
> glob_clock_start_sec := 0.0;
> glob_display_flag := true;
> glob_dump := false;
> MAX_UNCHANGED := 10;
> glob_smallish_float := 0.1e-100;
> glob_optimal_clock_start_sec := 0.0;
> glob_reached_optimal_h := false;
> glob_initial_pass := true;
> sec_in_min := 60.0;
> glob_warned2 := false;
> glob_optimal_done := false;
> djd_debug2 := true;
> glob_log10normmin := 0.1;
> glob_start := 0;
> glob_relerr := 0.1e-10;
> years_in_century := 100.0;
> hours_in_day := 24.0;
> djd_debug := true;
> glob_html_log := true;
> glob_subiter_method := 3;
> glob_max_minutes := 0.0;
> glob_log10relerr := 0.0;
> glob_log10abserr := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_max_iter := 1000;
> glob_max_opt_iter := 10;
> glob_optimal_expect_sec := 0.1;
> glob_normmax := 0.0;
> glob_max_sec := 10000.0;
> glob_warned := false;
> glob_abserr := 0.1e-10;
> glob_h := 0.1;
> glob_almost_1 := 0.9990;
> glob_orig_start_sec := 0.0;
> glob_small_float := 0.1e-50;
> glob_dump_analytic := false;
> glob_curr_iter_when_opt := 0;
> glob_optimal_start := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_not_yet_start_msg := true;
> centuries_in_millinium := 10.0;
> glob_no_eqs := 0;
> glob_max_hours := 0.0;
> glob_hmax := 1.0;
> glob_disp_incr := 0.1;
> glob_not_yet_finished := true;
> glob_percent_done := 0.0;
> #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/sing5postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -1.0;");
> omniout_str(ALWAYS,"x_end := -0.7;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> 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/x/x/x;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> 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_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_tmp5:= Array(1..(max_terms + 1),[]);
> array_tmp6:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp6[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_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[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
> ;
> 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_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0[1] := 3.0;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -1.0;
> x_end := -0.7;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-13T04:11:06-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing5")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"sing5 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing5 maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp;
global glob_iolevel, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_max_terms,
glob_iter, glob_max_rel_trunc_err, glob_last_good_h, glob_large_float,
glob_hmin, glob_clock_sec, days_in_year, min_in_hour, glob_current_iter,
glob_look_poles, glob_hmin_init, glob_clock_start_sec, glob_display_flag,
glob_dump, MAX_UNCHANGED, glob_smallish_float, glob_optimal_clock_start_sec,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_warned2,
glob_optimal_done, djd_debug2, glob_log10normmin, glob_start, glob_relerr,
years_in_century, hours_in_day, djd_debug, glob_html_log,
glob_subiter_method, glob_max_minutes, glob_log10relerr, glob_log10abserr,
glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter,
glob_optimal_expect_sec, glob_normmax, glob_max_sec, glob_warned,
glob_abserr, glob_h, glob_almost_1, glob_orig_start_sec, glob_small_float,
glob_dump_analytic, glob_curr_iter_when_opt, glob_optimal_start,
glob_max_trunc_err, glob_log10_relerr, glob_log10_abserr,
glob_not_yet_start_msg, centuries_in_millinium, glob_no_eqs, glob_max_hours,
glob_hmax, glob_disp_incr, glob_not_yet_finished, glob_percent_done,
array_const_3D0, array_const_0D0, array_const_1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_pole,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_norms,
array_type_pole, array_y_init, array_m1, array_poles, array_y_higher_work2,
array_y_higher_work, array_real_pole, array_complex_pole,
array_y_set_initial, array_y_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_iolevel := 5;
INFO := 2;
ALWAYS := 1;
DEBUGMASSIVE := 4;
DEBUGL := 3;
glob_max_terms := 30;
glob_iter := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_large_float := 0.90*10^101;
glob_hmin := 0.1*10^(-10);
glob_clock_sec := 0.;
days_in_year := 365.0;
min_in_hour := 60.0;
glob_current_iter := 0;
glob_look_poles := false;
glob_hmin_init := 0.001;
glob_clock_start_sec := 0.;
glob_display_flag := true;
glob_dump := false;
MAX_UNCHANGED := 10;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_clock_start_sec := 0.;
glob_reached_optimal_h := false;
glob_initial_pass := true;
sec_in_min := 60.0;
glob_warned2 := false;
glob_optimal_done := false;
djd_debug2 := true;
glob_log10normmin := 0.1;
glob_start := 0;
glob_relerr := 0.1*10^(-10);
years_in_century := 100.0;
hours_in_day := 24.0;
djd_debug := true;
glob_html_log := true;
glob_subiter_method := 3;
glob_max_minutes := 0.;
glob_log10relerr := 0.;
glob_log10abserr := 0.;
glob_unchanged_h_cnt := 0;
glob_max_iter := 1000;
glob_max_opt_iter := 10;
glob_optimal_expect_sec := 0.1;
glob_normmax := 0.;
glob_max_sec := 10000.0;
glob_warned := false;
glob_abserr := 0.1*10^(-10);
glob_h := 0.1;
glob_almost_1 := 0.9990;
glob_orig_start_sec := 0.;
glob_small_float := 0.1*10^(-50);
glob_dump_analytic := false;
glob_curr_iter_when_opt := 0;
glob_optimal_start := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_not_yet_start_msg := true;
centuries_in_millinium := 10.0;
glob_no_eqs := 0;
glob_max_hours := 0.;
glob_hmax := 1.0;
glob_disp_incr := 0.1;
glob_not_yet_finished := true;
glob_percent_done := 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/sing5postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -1.0;");
omniout_str(ALWAYS, "x_end := -0.7;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
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/x/x/x;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
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_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_tmp5 := Array(1 .. max_terms + 1, []);
array_tmp6 := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[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_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := -1.0;
x_end := -0.7;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-13T04:11:06-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sing5");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 090 | ");
logitem_str(html_log_file,
"sing5 diffeq.mxt");
logitem_str(html_log_file,
"sing5 maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/sing5postode.ode#################
diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.0;
x_end := -0.7;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
1.0/x/x/x;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = -1
y[1] (analytic) = -1
y[1] (numeric) = -1
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.011
Order of pole = 5.626
x[1] = -0.9999
y[1] (analytic) = -1.0003000600100015002100280036005
y[1] (numeric) = -1.0003000600100015002110081764288
absolute error = 9.801728283e-22
relative error = 9.7987880585571467617169999999995e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.011
Order of pole = 5.626
x[1] = -0.9998
y[1] (analytic) = -1.0006002400800240067217924609153
y[1] (numeric) = -1.000600240080024006723753689186
absolute error = 1.9612282707e-21
relative error = 1.9600517690692826578343999999999e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.011
Order of pole = 5.626
x[1] = -0.9997
y[1] (analytic) = -1.0009005402701215510504198761535
y[1] (numeric) = -1.000900540270121551053363043364
absolute error = 2.9431672105e-21
relative error = 2.9405191545862313203165000000001e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.011
Order of pole = 5.626
x[1] = -0.9996
y[1] (analytic) = -1.0012009606403842151547470119056
y[1] (numeric) = -1.0012009606403842151586730024372
absolute error = 3.9259905316e-21
relative error = 3.9212812271862717739776000000001e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.011
Order of pole = 5.626
x[1] = -0.9995
y[1] (analytic) = -1.0015015012509381566877814258887
y[1] (numeric) = -1.0015015012509381566926911250079
absolute error = 4.9096991192e-21
relative error = 4.9023382521818270101000000000002e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.011
Order of pole = 5.626
x[1] = -0.9994
y[1] (analytic) = -1.0018021621619456342673765259818
y[1] (numeric) = -1.0018021621619456342732708198412
absolute error = 5.8942938594e-21
relative error = 5.8836904950172806783696000000004e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.011
Order of pole = 5.626
x[1] = -0.9993
y[1] (analytic) = -1.0021029434336050327671393511817
y[1] (numeric) = -1.0021029434336050327740191268209
absolute error = 6.8797756392e-21
relative error = 6.8653382212681065797544000000004e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.011
Order of pole = 5.626
x[1] = -0.9992
y[1] (analytic) = -1.0024038451261508886275893043363
y[1] (numeric) = -1.0024038451261508886354554496828
absolute error = 7.8661453465e-21
relative error = 7.8472816966399988625919999999998e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 5.626
x[1] = -0.9991
y[1] (analytic) = -1.0027048672998539151875860807557
y[1] (numeric) = -1.0027048672998539151964394846262
absolute error = 8.8534038705e-21
relative error = 8.8295211873669238934054999999992e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 5.626
x[1] = -0.999
y[1] (analytic) = -1.0030060100150210280360450550661
y[1] (numeric) = -1.0030060100150210280458866071674
absolute error = 9.8415521013e-21
relative error = 9.8120569598108517986999999999998e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 5.626
x[1] = -0.9989
y[1] (analytic) = -1.003307273331995370383958406955
y[1] (numeric) = -1.0033072733319953703947889978847
absolute error = 1.08305909297e-20
relative error = 1.0794889280261548283569300000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 5.626
x[1] = -0.9988
y[1] (analytic) = -1.0036086573111563384567402847603
y[1] (numeric) = -1.0036086573111563384685608060081
absolute error = 1.18205212478e-20
relative error = 1.1778018415533849779801600000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.1MB, time=0.51
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 5.626
x[1] = -0.9987
y[1] (analytic) = -1.0039101620129196069069143241831
y[1] (numeric) = -1.0039101620129196069197256681314
absolute error = 1.28113439483e-20
relative error = 1.2761444632268925226584900000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 5.626
x[1] = -0.9986
y[1] (analytic) = -1.004211787497737154247161857745
y[1] (numeric) = -1.0042117874977371542609649176702
absolute error = 1.38030599252e-20
relative error = 1.3745168197630923741251200000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 5.626
x[1] = -0.9985
y[1] (analytic) = -1.0045135338260972883037491689787
y[1] (numeric) = -1.0045135338260972883185448390522
absolute error = 1.47956700735e-20
relative error = 1.4729189379006859626937500000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 5.626
x[1] = -0.9984
y[1] (analytic) = -1.004815401058524671690352163725
y[1] (numeric) = -1.004815401058524671706141339014
absolute error = 1.57891752890e-20
relative error = 1.5713508443806557536255999999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 5.626
x[1] = -0.9983
y[1] (analytic) = -1.0051173892555803473022968493139
y[1] (numeric) = -1.0051173892555803473190804257827
absolute error = 1.67835764688e-20
relative error = 1.6698125659959393304785600000002e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 5.626
x[1] = -0.9982
y[1] (analytic) = -1.0054194984778617638312340308354
y[1] (numeric) = -1.0054194984778617638490129053458
absolute error = 1.77788745104e-20
relative error = 1.7683041295017684943347200000002e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 5.626
x[1] = -0.9981
y[1] (analytic) = -1.005721728786002801300266652148
y[1] (numeric) = -1.0057217287860028013190417224607
absolute error = 1.87750703127e-20
relative error = 1.8668255617150889266190699999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 5.626
x[1] = -0.998
y[1] (analytic) = -1.0060240802406737966195482277442
y[1] (numeric) = -1.0060240802406737966393203925201
absolute error = 1.97721647759e-20
relative error = 1.9653768895044592592799999999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 5.626
x[1] = -0.9979
y[1] (analytic) = -1.0063265529025815691623708300762
y[1] (numeric) = -1.0063265529025815691831409888768
absolute error = 2.07701588006e-20
relative error = 2.0639581397004711285643399999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 5.626
x[1] = -0.9978
y[1] (analytic) = -1.0066291468324694463617611154506
y[1] (numeric) = -1.0066291468324694463835301687394
absolute error = 2.17690532888e-20
relative error = 2.1625693391950793956857600000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 5.626
x[1] = -0.9977
y[1] (analytic) = -1.006931862091117289327602890133
y[1] (numeric) = -1.0069318620911172893503717392761
absolute error = 2.27688491431e-20
relative error = 2.2612105148619923472902300000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 5.626
x[1] = -0.9976
y[1] (analytic) = -1.0072346987393415184843047368464
y[1] (numeric) = -1.0072346987393415185080742841139
absolute error = 2.37695472675e-20
relative error = 2.3598816936360560974080000000002e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 5.626
x[1] = -0.9975
y[1] (analytic) = -1.0075376568379951392290312404211
y[1] (numeric) = -1.0075376568379951392538023889876
absolute error = 2.47711485665e-20
relative error = 2.4585829024237675523437499999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 5.626
x[1] = -0.9974
y[1] (analytic) = -1.0078407364479677676105163699359
y[1] (numeric) = -1.0078407364479677676362900238823
absolute error = 2.57736539464e-20
relative error = 2.5573141682322371230073600000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 5.626
x[1] = -0.9973
y[1] (analytic) = -1.0081439376301856560284775933093
y[1] (numeric) = -1.008143937630185656055254657623
absolute error = 2.67770643137e-20
relative error = 2.6560755180102613732442900000002e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 5.626
x[1] = -0.9972
y[1] (analytic) = -1.0084472604456117189536493189175
y[1] (numeric) = -1.0084472604456117189814306994936
absolute error = 2.77813805761e-20
relative error = 2.7548669787475043465452799999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 5.626
x[1] = -0.9971
y[1] (analytic) = -1.0087507049552455586684542774776
y[1] (numeric) = -1.0087507049552455586972408811204
absolute error = 2.87866036428e-20
relative error = 2.8536885775041071599750799999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 5.626
x[1] = -0.997
y[1] (analytic) = -1.0090542712201234910283314761
y[1] (numeric) = -1.0090542712201234910581242105234
absolute error = 2.97927344234e-20
relative error = 2.9525403413015002368200000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 5.626
x[1] = -0.9969
y[1] (analytic) = -1.0093579593013185712437393751045
y[1] (numeric) = -1.0093579593013185712745391489333
absolute error = 3.07997738288e-20
relative error = 3.0514222972115582170219200000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.1MB, time=1.14
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 5.626
x[1] = -0.9968
y[1] (analytic) = -1.0096617692599406196828529569112
y[1] (numeric) = -1.009661769259940619714660679682
absolute error = 3.18077227708e-20
relative error = 3.1503344723168379222425600000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 5.626
x[1] = -0.9967
y[1] (analytic) = -1.0099657011571362476949733750471
y[1] (numeric) = -1.0099657011571362477277899572093
absolute error = 3.28165821622e-20
relative error = 3.2492768937203945911018599999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 5.626
x[1] = -0.9966
y[1] (analytic) = -1.0102697550540888834546688900638
y[1] (numeric) = -1.0102697550540888834884952429808
absolute error = 3.38263529170e-20
relative error = 3.3482495885654786510232000000002e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 5.626
x[1] = -0.9965
y[1] (analytic) = -1.0105739310120187978266658179378
y[1] (numeric) = -1.0105739310120187978615028538877
absolute error = 3.48370359499e-20
relative error = 3.4472525839859292473037500000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 5.626
x[1] = -0.9964
y[1] (analytic) = -1.0108782290921831302515082353155
y[1] (numeric) = -1.0108782290921831302873568674923
absolute error = 3.58486321768e-20
relative error = 3.5462859071555811143219200000003e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 5.626
x[1] = -0.9963
y[1] (analytic) = -1.0111826493558759146520052047874
y[1] (numeric) = -1.0111826493558759146888663473019
absolute error = 3.68611425145e-20
relative error = 3.6453495852584668728031500000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 5.626
x[1] = -0.9962
y[1] (analytic) = -1.0114871918644281053604843022057
y[1] (numeric) = -1.0114871918644281053983588700867
absolute error = 3.78745678810e-20
relative error = 3.7444436455183916153767999999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 5.626
x[1] = -0.9961
y[1] (analytic) = -1.0117918566792076030668702469233
y[1] (numeric) = -1.0117918566792076031057591561186
absolute error = 3.88889091953e-20
relative error = 3.8435681151790366982999300000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 5.626
x[1] = -0.996
y[1] (analytic) = -1.0120966438616192807876074547054
y[1] (numeric) = -1.0120966438616192808275116220827
absolute error = 3.99041673773e-20
relative error = 3.9427230214939798252800000000005e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 5.626
x[1] = -0.9959
y[1] (analytic) = -1.0124015534731050098554453519673
y[1] (numeric) = -1.0124015534731050098963656953149
absolute error = 4.09203433476e-20
relative error = 4.0419083917068555608060399999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 5.626
x[1] = -0.9958
y[1] (analytic) = -1.012706585575143685930105308909
y[1] (numeric) = -1.0127065855751436859720427469376
absolute error = 4.19374380286e-20
relative error = 4.1411242531599204849083199999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 5.626
x[1] = -0.9957
y[1] (analytic) = -1.0130117402292512550298480680638
y[1] (numeric) = -1.0130117402292512550728035204069
absolute error = 4.29554523431e-20
relative error = 4.2403706331556332314148300000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 5.626
x[1] = -0.9956
y[1] (analytic) = -1.0133170174969807395839605637318
y[1] (numeric) = -1.0133170174969807396279349509468
absolute error = 4.39743872150e-20
relative error = 4.3396475590257246677440000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 5.626
x[1] = -0.9955
y[1] (analytic) = -1.0136224174399222645061810467584
y[1] (numeric) = -1.0136224174399222645511752903278
absolute error = 4.49942435694e-20
relative error = 4.4389550581409495788425000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 5.626
x[1] = -0.9954
y[1] (analytic) = -1.0139279401197030832890814481198
y[1] (numeric) = -1.0139279401197030833350964704521
absolute error = 4.60150223323e-20
relative error = 4.5382931578813700667247199999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 5.626
x[1] = -0.9953
y[1] (analytic) = -1.0142335855979876041194259338012
y[1] (numeric) = -1.014233585597987604166462658232
absolute error = 4.70367244308e-20
relative error = 4.6376618856559908537051599999996e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 5.626
x[1] = -0.9952
y[1] (analytic) = -1.0145393539364774160145246225004
y[1] (numeric) = -1.0145393539364774160625839732935
absolute error = 4.80593507931e-20
relative error = 4.7370612689026456161484800000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.006
Order of pole = 5.626
x[1] = -0.9951
y[1] (analytic) = -1.0148452451969113149796014567565
y[1] (numeric) = -1.0148452451969113150286843591046
absolute error = 4.90829023481e-20
relative error = 4.8364913350484685291383100000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.006
Order of pole = 5.626
x[1] = -0.995
y[1] (analytic) = -1.0151512594410653301861952371894
y[1] (numeric) = -1.0151512594410653302363026172155
absolute error = 5.01073800261e-20
relative error = 4.9359521115787954237500000000003e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.006
Order of pole = 5.626
x[1] = -0.9949
y[1] (analytic) = -1.0154573967307527501716128486483
y[1] (numeric) = -1.0154573967307527502227456334065
absolute error = 5.11327847582e-20
relative error = 5.0354436259779191386011800000003e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.3MB, time=1.77
Real estimate of pole used
Radius of convergence = 1.006
Order of pole = 5.626
x[1] = -0.9948
y[1] (analytic) = -1.0157636571278241490594537261941
y[1] (numeric) = -1.0157636571278241491116128436705
absolute error = 5.21591174764e-20
relative error = 5.1349659057388655446348799999996e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.006
Order of pole = 5.626
x[1] = -0.9947
y[1] (analytic) = -1.0160700406941674128012246279937
y[1] (numeric) = -1.016070040694167412854411007108
absolute error = 5.31863791143e-20
relative error = 5.2345189784322028661358899999996e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.006
Order of pole = 5.626
x[1] = -0.9946
y[1] (analytic) = -1.0163765474917077654390638013777
y[1] (numeric) = -1.0163765474917077654932783719838
absolute error = 5.42145706061e-20
relative error = 5.3341028716074655709069600000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.006
Order of pole = 5.626
x[1] = -0.9945
y[1] (analytic) = -1.0166831775824077953895936475039
y[1] (numeric) = -1.0166831775824077954448373403908
absolute error = 5.52436928869e-20
relative error = 5.4337176128226232117012500000003e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.006
Order of pole = 5.626
x[1] = -0.9944
y[1] (analytic) = -1.016989931028267481748921009286
y[1] (numeric) = -1.016989931028267481805194756179
absolute error = 5.62737468930e-20
relative error = 5.5333632296734959078911999999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.006
Order of pole = 5.626
x[1] = -0.9943
y[1] (analytic) = -1.0172968078913242206188042264831
y[1] (numeric) = -1.0172968078913242206761089600452
absolute error = 5.73047335621e-20
relative error = 5.6330397498132865321014700000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 5.626
x[1] = -0.9942
y[1] (analytic) = -1.0176038082336528514540061211035
y[1] (numeric) = -1.0176038082336528515123427749358
absolute error = 5.83366538323e-20
relative error = 5.7327472008541533188282400000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 5.626
x[1] = -0.9941
y[1] (analytic) = -1.0179109321173656834308520955519
y[1] (numeric) = -1.0179109321173656834902216041951
absolute error = 5.93695086432e-20
relative error = 5.8324856104752653744227200000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 5.626
x[1] = -0.994
y[1] (analytic) = -1.0182181796046125218370125452544
y[1] (numeric) = -1.0182181796046125218974158441896
absolute error = 6.04032989352e-20
relative error = 5.9322550063538831596800000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 5.626
x[1] = -0.9939
y[1] (analytic) = -1.0185255507575806944825288068129
y[1] (numeric) = -1.0185255507575806945439668324627
absolute error = 6.14380256498e-20
relative error = 6.0320554161947447156746199999997e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 5.626
x[1] = -0.9938
y[1] (analytic) = -1.0188330456384950781321018820853
y[1] (numeric) = -1.0188330456384950781945755718151
absolute error = 6.24736897298e-20
relative error = 6.1318868677495834612225600000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 5.626
x[1] = -0.9937
y[1] (analytic) = -1.0191406643096181249586631979532
y[1] (numeric) = -1.0191406643096181250221734900717
absolute error = 6.35102921185e-20
relative error = 6.2317493887384886440430499999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 5.626
x[1] = -0.9936
y[1] (analytic) = -1.0194484068332498890182466809207
y[1] (numeric) = -1.0194484068332498890827945146815
absolute error = 6.45478337608e-20
relative error = 6.3316430069577833712844800000005e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 5.626
x[1] = -0.9935
y[1] (analytic) = -1.0197562732717280527461814451014
y[1] (numeric) = -1.0197562732717280528117677607035
absolute error = 6.55863156021e-20
relative error = 6.4315677501719693948287499999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 5.626
x[1] = -0.9934
y[1] (analytic) = -1.0200642636874279534746244115717
y[1] (numeric) = -1.0200642636874279535412501501611
absolute error = 6.66257385894e-20
relative error = 6.5315236462215401293857599999996e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 5.626
x[1] = -0.9933
y[1] (analytic) = -1.0203723781427626099714521965267
y[1] (numeric) = -1.0203723781427626100391183001973
absolute error = 6.76661036706e-20
relative error = 6.6315107229541921421332200000004e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 5.626
x[1] = -0.9932
y[1] (analytic) = -1.020680616700182749000531625141
y[1] (numeric) = -1.0206806167001827490692390369352
absolute error = 6.87074117942e-20
relative error = 6.7315290081953506150105600000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 5.626
x[1] = -0.9931
y[1] (analytic) = -1.0209889794221768319033882475307
y[1] (numeric) = -1.020988979422176831973137911441
absolute error = 6.97496639103e-20
relative error = 6.8315785298460756640257299999997e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 5.626
x[1] = -0.993
y[1] (analytic) = -1.0212974663712710812022922527324
y[1] (numeric) = -1.0212974663712710812730851137024
absolute error = 7.07928609700e-20
relative error = 6.9316593158241277290000000000005e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 5.626
memory used=15.2MB, alloc=4.3MB, time=2.42
x[1] = -0.9929
y[1] (analytic) = -1.0216060776100295072247811961462
y[1] (numeric) = -1.0216060776100295072966182000713
absolute error = 7.18370039251e-20
relative error = 7.0317713940345051036533900000006e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 5.626
x[1] = -0.9928
y[1] (analytic) = -1.0219148132010539347496389754494
y[1] (numeric) = -1.0219148132010539348225210691781
absolute error = 7.28820937287e-20
relative error = 7.1319147924281047374182400000007e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 5.626
x[1] = -0.9927
y[1] (analytic) = -1.0222236732069840296743505095705
y[1] (numeric) = -1.0222236732069840297482786409052
absolute error = 7.39281313347e-20
relative error = 7.2320895389526681058010099999996e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 5.626
x[1] = -0.9926
y[1] (analytic) = -1.0225326576904973257040515949096
y[1] (numeric) = -1.0225326576904973257790267126083
absolute error = 7.49751176987e-20
relative error = 7.3322956616407308097991199999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 5.626
x[1] = -0.9925
y[1] (analytic) = -1.0228417667143092510619934326208
y[1] (numeric) = -1.0228417667143092511380164863974
absolute error = 7.60230537766e-20
relative error = 7.4325331884725489246874999999992e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 5.626
x[1] = -0.9924
y[1] (analytic) = -1.0231510003411731552215413404092
y[1] (numeric) = -1.0231510003411731552986132809353
absolute error = 7.70719405261e-20
relative error = 7.5328021475227118222726400000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 5.626
x[1] = -0.9923
y[1] (analytic) = -1.023460358633880335659727181972
y[1] (numeric) = -1.0234603586338803357378489608771
absolute error = 7.81217789051e-20
relative error = 7.6331025668035951254981699999994e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 5.626
x[1] = -0.9922
y[1] (analytic) = -1.0237698416552600646323750668909
y[1] (numeric) = -1.0237698416552600647115476367643
absolute error = 7.91725698734e-20
relative error = 7.7334344744314354406283199999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 5.626
x[1] = -0.9921
y[1] (analytic) = -1.0240794494681796159708198935044
y[1] (numeric) = -1.0240794494681796160510442078957
absolute error = 8.02243143913e-20
relative error = 7.8337978984893929926839300000005e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 5.626
x[1] = -0.992
y[1] (analytic) = -1.0243891821355442919002383270116
y[1] (numeric) = -1.0243891821355442919815153404317
absolute error = 8.12770134201e-20
relative error = 7.9341928670763388108799999999993e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 5.626
x[1] = -0.9919
y[1] (analytic) = -1.0246990397202974498796118248184
y[1] (numeric) = -1.0246990397202974499619424927413
absolute error = 8.23306679229e-20
relative error = 8.0346194083848302793101100000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 5.626
x[1] = -0.9918
y[1] (analytic) = -1.0250090222854205294633413409148
y[1] (numeric) = -1.0250090222854205295467266197778
absolute error = 8.33852788630e-20
relative error = 8.1350775505448008225416000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 5.626
x[1] = -0.9917
y[1] (analytic) = -1.0253191298939330791845333608626
y[1] (numeric) = -1.0253191298939330792689742080679
absolute error = 8.44408472053e-20
relative error = 8.2355673217601248374128899999997e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 5.626
x[1] = -0.9916
y[1] (analytic) = -1.0256293626088927834599769388015
y[1] (numeric) = -1.0256293626088927835454743127173
absolute error = 8.54973739158e-20
relative error = 8.3360887502596827153676800000005e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 5.626
x[1] = -0.9915
y[1] (analytic) = -1.025939720493395489516831427719
y[1] (numeric) = -1.02593972049339548960338628768
absolute error = 8.65548599610e-20
relative error = 8.4366418642387673200874999999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 5.626
x[1] = -0.9914
y[1] (analytic) = -1.026250203610575234341044614092
y[1] (numeric) = -1.0262502036105752344286579204013
absolute error = 8.76133063093e-20
relative error = 8.5372266919954809615879200000006e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 5.626
x[1] = -0.9913
y[1] (analytic) = -1.026560812023604271647520987901
y[1] (numeric) = -1.0265608120236042717361937018303
absolute error = 8.86727139293e-20
relative error = 8.6378432617649055565162100000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 5.626
x[1] = -0.9912
y[1] (analytic) = -1.0268715457956930988720598989161
y[1] (numeric) = -1.0268715457956930989617929827075
absolute error = 8.97330837914e-20
relative error = 8.7384916018749380555059199999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 5.626
x[1] = -0.9911
y[1] (analytic) = -1.0271824049900904841850833700943
y[1] (numeric) = -1.0271824049900904842758777869612
absolute error = 9.07944168669e-20
relative error = 8.8391717406584587205373900000002e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 5.626
x[1] = -0.991
y[1] (analytic) = -1.0274933896700834935271733588728
y[1] (numeric) = -1.0274933896700834936190300730005
absolute error = 9.18567141277e-20
relative error = 8.9398837064240532006699999999994e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=3.08
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 5.626
x[1] = -0.9909
y[1] (analytic) = -1.0278044998989975176664382771198
y[1] (numeric) = -1.0278044998989975177593582536673
absolute error = 9.29199765475e-20
relative error = 9.0406275275727298548877499999995e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 5.626
x[1] = -0.9908
y[1] (analytic) = -1.0281157357401962992777286005036
y[1] (numeric) = -1.0281157357401962993717128056043
absolute error = 9.39842051007e-20
relative error = 9.1414032324907148290118399999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 5.626
x[1] = -0.9907
y[1] (analytic) = -1.028427097257081960043721418055
y[1] (numeric) = -1.0284270972570819601387708188177
absolute error = 9.50494007627e-20
relative error = 9.2422108495785718485916100000002e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 5.626
x[1] = -0.9906
y[1] (analytic) = -1.028738584513095027777893792743
y[1] (numeric) = -1.028738584513095027874009357253
absolute error = 9.61155645100e-20
relative error = 9.3430504072608277826159999999992e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 5.626
x[1] = -0.9905
y[1] (analytic) = -1.0290501975717144635694048239448
y[1] (numeric) = -1.0290501975717144636665875212654
absolute error = 9.71826973206e-20
relative error = 9.4439219340247337200575000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 5.626
x[1] = -0.9904
y[1] (analytic) = -1.0293619364964576889499063227803
y[1] (numeric) = -1.0293619364964576890481571229532
absolute error = 9.82508001729e-20
relative error = 9.5448254583132341621145599999997e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 5.626
x[1] = -0.9903
y[1] (analytic) = -1.0296738013508806130823020313827
y[1] (numeric) = -1.0296738013508806131816219054297
absolute error = 9.93198740470e-20
relative error = 9.6457610086512140592368999999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.001
Order of pole = 5.626
x[1] = -0.9902
y[1] (analytic) = -1.0299857921985776599714753373157
y[1] (numeric) = -1.0299857921985776600718652572395
absolute error = 1.003899199238e-19
relative error = 9.7467286135579212334830400000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.001
Order of pole = 5.626
x[1] = -0.9901
y[1] (analytic) = -1.0302979091031817956970054544934
y[1] (numeric) = -1.0302979091031817957984663932787
absolute error = 1.014609387853e-19
relative error = 9.8477283015760189321195299999997e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.001
Order of pole = 5.626
x[1] = -0.99
y[1] (analytic) = -1.0306101521283645556678920621376
y[1] (numeric) = -1.0306101521283645557704249937523
absolute error = 1.025329316147e-19
relative error = 9.9487601012811795299999999999995e-18 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;
Iterations = 100
Total Elapsed Time = 3 Seconds
Elapsed Time(since restart) = 3 Seconds
Expected Time Remaining = 1 Minutes 34 Seconds
Optimized Time Remaining = 1 Minutes 34 Seconds
Time to Timeout = 14 Minutes 56 Seconds
Percent Done = 3.367 %
> quit
memory used=20.9MB, alloc=4.3MB, time=3.38