|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_relerr,
> glob_html_log,
> glob_log10normmin,
> glob_start,
> glob_max_sec,
> glob_optimal_start,
> glob_large_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_h,
> glob_clock_start_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_sec,
> glob_dump,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_hmax,
> glob_initial_pass,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_warned,
> glob_max_hours,
> centuries_in_millinium,
> glob_display_flag,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_reached_optimal_h,
> min_in_hour,
> glob_small_float,
> glob_last_good_h,
> glob_not_yet_finished,
> years_in_century,
> glob_log10_relerr,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_type_pole,
> array_y_init,
> array_pole,
> array_complex_pole,
> array_y_higher_work2,
> array_y_higher,
> array_y_higher_work,
> array_real_pole,
> array_poles,
> array_y_set_initial,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, ALWAYS, glob_iolevel,
glob_log10abserr, glob_current_iter, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, glob_no_eqs, glob_max_trunc_err, glob_relerr,
glob_html_log, glob_log10normmin, glob_start, glob_max_sec,
glob_optimal_start, glob_large_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, sec_in_min, glob_subiter_method,
glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_log10_abserr,
glob_dump_analytic, glob_h, glob_clock_start_sec, glob_normmax, glob_iter,
glob_warned2, glob_abserr, glob_look_poles, glob_hmin, hours_in_day,
djd_debug2, glob_hmin_init, glob_optimal_done, glob_clock_sec, glob_dump,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_hmax,
glob_initial_pass, days_in_year, djd_debug, glob_max_opt_iter, glob_warned,
glob_max_hours, centuries_in_millinium, glob_display_flag,
glob_orig_start_sec, glob_smallish_float, glob_reached_optimal_h,
min_in_hour, glob_small_float, glob_last_good_h, glob_not_yet_finished,
years_in_century, glob_log10_relerr, glob_percent_done,
glob_max_rel_trunc_err, glob_max_iter, array_const_2D0, array_const_1,
array_const_0D0, array_const_1D0, array_1st_rel_error, array_norms, array_y,
array_x, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_m1, array_type_pole, array_y_init, array_pole,
array_complex_pole, array_y_higher_work2, array_y_higher,
array_y_higher_work, array_real_pole, array_poles, array_y_set_initial,
glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_relerr,
> glob_html_log,
> glob_log10normmin,
> glob_start,
> glob_max_sec,
> glob_optimal_start,
> glob_large_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_h,
> glob_clock_start_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_sec,
> glob_dump,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_hmax,
> glob_initial_pass,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_warned,
> glob_max_hours,
> centuries_in_millinium,
> glob_display_flag,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_reached_optimal_h,
> min_in_hour,
> glob_small_float,
> glob_last_good_h,
> glob_not_yet_finished,
> years_in_century,
> glob_log10_relerr,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_type_pole,
> array_y_init,
> array_pole,
> array_complex_pole,
> array_y_higher_work2,
> array_y_higher,
> array_y_higher_work,
> array_real_pole,
> array_poles,
> array_y_set_initial,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, ALWAYS, glob_iolevel,
glob_log10abserr, glob_current_iter, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, glob_no_eqs, glob_max_trunc_err, glob_relerr,
glob_html_log, glob_log10normmin, glob_start, glob_max_sec,
glob_optimal_start, glob_large_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, sec_in_min, glob_subiter_method,
glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_log10_abserr,
glob_dump_analytic, glob_h, glob_clock_start_sec, glob_normmax, glob_iter,
glob_warned2, glob_abserr, glob_look_poles, glob_hmin, hours_in_day,
djd_debug2, glob_hmin_init, glob_optimal_done, glob_clock_sec, glob_dump,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_hmax,
glob_initial_pass, days_in_year, djd_debug, glob_max_opt_iter, glob_warned,
glob_max_hours, centuries_in_millinium, glob_display_flag,
glob_orig_start_sec, glob_smallish_float, glob_reached_optimal_h,
min_in_hour, glob_small_float, glob_last_good_h, glob_not_yet_finished,
years_in_century, glob_log10_relerr, glob_percent_done,
glob_max_rel_trunc_err, glob_max_iter, array_const_2D0, array_const_1,
array_const_0D0, array_const_1D0, array_1st_rel_error, array_norms, array_y,
array_x, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_m1, array_type_pole, array_y_init, array_pole,
array_complex_pole, array_y_higher_work2, array_y_higher,
array_y_higher_work, array_real_pole, array_poles, array_y_set_initial,
glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_relerr,
> glob_html_log,
> glob_log10normmin,
> glob_start,
> glob_max_sec,
> glob_optimal_start,
> glob_large_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_h,
> glob_clock_start_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_sec,
> glob_dump,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_hmax,
> glob_initial_pass,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_warned,
> glob_max_hours,
> centuries_in_millinium,
> glob_display_flag,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_reached_optimal_h,
> min_in_hour,
> glob_small_float,
> glob_last_good_h,
> glob_not_yet_finished,
> years_in_century,
> glob_log10_relerr,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_type_pole,
> array_y_init,
> array_pole,
> array_complex_pole,
> array_y_higher_work2,
> array_y_higher,
> array_y_higher_work,
> array_real_pole,
> array_poles,
> array_y_set_initial,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, ALWAYS, glob_iolevel,
glob_log10abserr, glob_current_iter, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, glob_no_eqs, glob_max_trunc_err, glob_relerr,
glob_html_log, glob_log10normmin, glob_start, glob_max_sec,
glob_optimal_start, glob_large_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, sec_in_min, glob_subiter_method,
glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_log10_abserr,
glob_dump_analytic, glob_h, glob_clock_start_sec, glob_normmax, glob_iter,
glob_warned2, glob_abserr, glob_look_poles, glob_hmin, hours_in_day,
djd_debug2, glob_hmin_init, glob_optimal_done, glob_clock_sec, glob_dump,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_hmax,
glob_initial_pass, days_in_year, djd_debug, glob_max_opt_iter, glob_warned,
glob_max_hours, centuries_in_millinium, glob_display_flag,
glob_orig_start_sec, glob_smallish_float, glob_reached_optimal_h,
min_in_hour, glob_small_float, glob_last_good_h, glob_not_yet_finished,
years_in_century, glob_log10_relerr, glob_percent_done,
glob_max_rel_trunc_err, glob_max_iter, array_const_2D0, array_const_1,
array_const_0D0, array_const_1D0, array_1st_rel_error, array_norms, array_y,
array_x, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_m1, array_type_pole, array_y_init, array_pole,
array_complex_pole, array_y_higher_work2, array_y_higher,
array_y_higher_work, array_real_pole, array_poles, array_y_set_initial,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_relerr,
> glob_html_log,
> glob_log10normmin,
> glob_start,
> glob_max_sec,
> glob_optimal_start,
> glob_large_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_h,
> glob_clock_start_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_sec,
> glob_dump,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_hmax,
> glob_initial_pass,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_warned,
> glob_max_hours,
> centuries_in_millinium,
> glob_display_flag,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_reached_optimal_h,
> min_in_hour,
> glob_small_float,
> glob_last_good_h,
> glob_not_yet_finished,
> years_in_century,
> glob_log10_relerr,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_type_pole,
> array_y_init,
> array_pole,
> array_complex_pole,
> array_y_higher_work2,
> array_y_higher,
> array_y_higher_work,
> array_real_pole,
> array_poles,
> array_y_set_initial,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, ALWAYS, glob_iolevel,
glob_log10abserr, glob_current_iter, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, glob_no_eqs, glob_max_trunc_err, glob_relerr,
glob_html_log, glob_log10normmin, glob_start, glob_max_sec,
glob_optimal_start, glob_large_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, sec_in_min, glob_subiter_method,
glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_log10_abserr,
glob_dump_analytic, glob_h, glob_clock_start_sec, glob_normmax, glob_iter,
glob_warned2, glob_abserr, glob_look_poles, glob_hmin, hours_in_day,
djd_debug2, glob_hmin_init, glob_optimal_done, glob_clock_sec, glob_dump,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_hmax,
glob_initial_pass, days_in_year, djd_debug, glob_max_opt_iter, glob_warned,
glob_max_hours, centuries_in_millinium, glob_display_flag,
glob_orig_start_sec, glob_smallish_float, glob_reached_optimal_h,
min_in_hour, glob_small_float, glob_last_good_h, glob_not_yet_finished,
years_in_century, glob_log10_relerr, glob_percent_done,
glob_max_rel_trunc_err, glob_max_iter, array_const_2D0, array_const_1,
array_const_0D0, array_const_1D0, array_1st_rel_error, array_norms, array_y,
array_x, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_m1, array_type_pole, array_y_init, array_pole,
array_complex_pole, array_y_higher_work2, array_y_higher,
array_y_higher_work, array_real_pole, array_poles, array_y_set_initial,
glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_relerr,
> glob_html_log,
> glob_log10normmin,
> glob_start,
> glob_max_sec,
> glob_optimal_start,
> glob_large_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_h,
> glob_clock_start_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_sec,
> glob_dump,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_hmax,
> glob_initial_pass,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_warned,
> glob_max_hours,
> centuries_in_millinium,
> glob_display_flag,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_reached_optimal_h,
> min_in_hour,
> glob_small_float,
> glob_last_good_h,
> glob_not_yet_finished,
> years_in_century,
> glob_log10_relerr,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_type_pole,
> array_y_init,
> array_pole,
> array_complex_pole,
> array_y_higher_work2,
> array_y_higher,
> array_y_higher_work,
> array_real_pole,
> array_poles,
> array_y_set_initial,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, ALWAYS, glob_iolevel,
glob_log10abserr, glob_current_iter, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, glob_no_eqs, glob_max_trunc_err, glob_relerr,
glob_html_log, glob_log10normmin, glob_start, glob_max_sec,
glob_optimal_start, glob_large_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, sec_in_min, glob_subiter_method,
glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_log10_abserr,
glob_dump_analytic, glob_h, glob_clock_start_sec, glob_normmax, glob_iter,
glob_warned2, glob_abserr, glob_look_poles, glob_hmin, hours_in_day,
djd_debug2, glob_hmin_init, glob_optimal_done, glob_clock_sec, glob_dump,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_hmax,
glob_initial_pass, days_in_year, djd_debug, glob_max_opt_iter, glob_warned,
glob_max_hours, centuries_in_millinium, glob_display_flag,
glob_orig_start_sec, glob_smallish_float, glob_reached_optimal_h,
min_in_hour, glob_small_float, glob_last_good_h, glob_not_yet_finished,
years_in_century, glob_log10_relerr, glob_percent_done,
glob_max_rel_trunc_err, glob_max_iter, array_const_2D0, array_const_1,
array_const_0D0, array_const_1D0, array_1st_rel_error, array_norms, array_y,
array_x, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_m1, array_type_pole, array_y_init, array_pole,
array_complex_pole, array_y_higher_work2, array_y_higher,
array_y_higher_work, array_real_pole, array_poles, array_y_set_initial,
glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_relerr,
> glob_html_log,
> glob_log10normmin,
> glob_start,
> glob_max_sec,
> glob_optimal_start,
> glob_large_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_h,
> glob_clock_start_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_sec,
> glob_dump,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_hmax,
> glob_initial_pass,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_warned,
> glob_max_hours,
> centuries_in_millinium,
> glob_display_flag,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_reached_optimal_h,
> min_in_hour,
> glob_small_float,
> glob_last_good_h,
> glob_not_yet_finished,
> years_in_century,
> glob_log10_relerr,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_type_pole,
> array_y_init,
> array_pole,
> array_complex_pole,
> array_y_higher_work2,
> array_y_higher,
> array_y_higher_work,
> array_real_pole,
> array_poles,
> array_y_set_initial,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult $eq_no = 1 i = 1
> array_tmp1[1] := (array_m1[1] * (array_const_2D0[1]));
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_tmp1[1] * (array_x[1]));
> # emit pre mult $eq_no = 1 i = 1
> array_tmp3[1] := (array_x[1] * (array_x[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_1D0[1];
> #emit pre div $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp2[1] / (array_tmp4[1]));
> # emit pre mult $eq_no = 1 i = 1
> array_tmp6[1] := (array_x[1] * (array_x[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp6[1] + array_const_1D0[1];
> #emit pre div $eq_no = 1 i = 1
> array_tmp8[1] := (array_tmp5[1] / (array_tmp7[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp9[1] := array_const_0D0[1] + array_tmp8[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_tmp9[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_2D0,1);
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_tmp1,array_x,1);
> # emit pre mult $eq_no = 1 i = 2
> array_tmp3[2] := ats(2,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2] + array_const_1D0[2];
> #emit pre div $eq_no = 1 i = 2
> array_tmp5[2] := ((array_tmp2[2] - ats(2,array_tmp4,array_tmp5,2))/array_tmp4[1]);
> # emit pre mult $eq_no = 1 i = 2
> array_tmp6[2] := ats(2,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp6[2] + array_const_1D0[2];
> #emit pre div $eq_no = 1 i = 2
> array_tmp8[2] := ((array_tmp5[2] - ats(2,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add $eq_no = 1 i = 2
> array_tmp9[2] := array_const_0D0[2] + array_tmp8[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_tmp9[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_2D0,1);
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_tmp1,array_x,1);
> # emit pre mult $eq_no = 1 i = 3
> array_tmp3[3] := ats(3,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3] + array_const_1D0[3];
> #emit pre div $eq_no = 1 i = 3
> array_tmp5[3] := ((array_tmp2[3] - ats(3,array_tmp4,array_tmp5,2))/array_tmp4[1]);
> # emit pre mult $eq_no = 1 i = 3
> array_tmp6[3] := ats(3,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp6[3] + array_const_1D0[3];
> #emit pre div $eq_no = 1 i = 3
> array_tmp8[3] := ((array_tmp5[3] - ats(3,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add $eq_no = 1 i = 3
> array_tmp9[3] := array_const_0D0[3] + array_tmp8[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_tmp9[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_2D0,1);
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_tmp1,array_x,1);
> # emit pre mult $eq_no = 1 i = 4
> array_tmp3[4] := ats(4,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4] + array_const_1D0[4];
> #emit pre div $eq_no = 1 i = 4
> array_tmp5[4] := ((array_tmp2[4] - ats(4,array_tmp4,array_tmp5,2))/array_tmp4[1]);
> # emit pre mult $eq_no = 1 i = 4
> array_tmp6[4] := ats(4,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp6[4] + array_const_1D0[4];
> #emit pre div $eq_no = 1 i = 4
> array_tmp8[4] := ((array_tmp5[4] - ats(4,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add $eq_no = 1 i = 4
> array_tmp9[4] := array_const_0D0[4] + array_tmp8[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_tmp9[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_2D0,1);
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_tmp1,array_x,1);
> # emit pre mult $eq_no = 1 i = 5
> array_tmp3[5] := ats(5,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5] + array_const_1D0[5];
> #emit pre div $eq_no = 1 i = 5
> array_tmp5[5] := ((array_tmp2[5] - ats(5,array_tmp4,array_tmp5,2))/array_tmp4[1]);
> # emit pre mult $eq_no = 1 i = 5
> array_tmp6[5] := ats(5,array_x,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp6[5] + array_const_1D0[5];
> #emit pre div $eq_no = 1 i = 5
> array_tmp8[5] := ((array_tmp5[5] - ats(5,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add $eq_no = 1 i = 5
> array_tmp9[5] := array_const_0D0[5] + array_tmp8[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_tmp9[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_2D0,1);
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_tmp1,array_x,1);
> #emit mult $eq_no = 1
> array_tmp3[kkk] := ats(kkk,array_x,array_x,1);
> #emit add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk] + array_const_1D0[kkk];
> #emit div $eq_no = 1
> array_tmp5[kkk] := ((array_tmp2[kkk] - ats(kkk,array_tmp4,array_tmp5,2))/array_tmp4[1]);
> #emit mult $eq_no = 1
> array_tmp6[kkk] := ats(kkk,array_x,array_x,1);
> #emit add $eq_no = 1
> array_tmp7[kkk] := array_tmp6[kkk] + array_const_1D0[kkk];
> #emit div $eq_no = 1
> array_tmp8[kkk] := ((array_tmp5[kkk] - ats(kkk,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit add $eq_no = 1
> array_tmp9[kkk] := array_const_0D0[kkk] + array_tmp8[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_tmp9[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, ALWAYS, glob_iolevel,
glob_log10abserr, glob_current_iter, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, glob_no_eqs, glob_max_trunc_err, glob_relerr,
glob_html_log, glob_log10normmin, glob_start, glob_max_sec,
glob_optimal_start, glob_large_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, sec_in_min, glob_subiter_method,
glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_log10_abserr,
glob_dump_analytic, glob_h, glob_clock_start_sec, glob_normmax, glob_iter,
glob_warned2, glob_abserr, glob_look_poles, glob_hmin, hours_in_day,
djd_debug2, glob_hmin_init, glob_optimal_done, glob_clock_sec, glob_dump,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_hmax,
glob_initial_pass, days_in_year, djd_debug, glob_max_opt_iter, glob_warned,
glob_max_hours, centuries_in_millinium, glob_display_flag,
glob_orig_start_sec, glob_smallish_float, glob_reached_optimal_h,
min_in_hour, glob_small_float, glob_last_good_h, glob_not_yet_finished,
years_in_century, glob_log10_relerr, glob_percent_done,
glob_max_rel_trunc_err, glob_max_iter, array_const_2D0, array_const_1,
array_const_0D0, array_const_1D0, array_1st_rel_error, array_norms, array_y,
array_x, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_m1, array_type_pole, array_y_init, array_pole,
array_complex_pole, array_y_higher_work2, array_y_higher,
array_y_higher_work, array_real_pole, array_poles, array_y_set_initial,
glob_last;
array_tmp1[1] := array_m1[1]*array_const_2D0[1];
array_tmp2[1] := array_tmp1[1]*array_x[1];
array_tmp3[1] := array_x[1]*array_x[1];
array_tmp4[1] := array_tmp3[1] + array_const_1D0[1];
array_tmp5[1] := array_tmp2[1]/array_tmp4[1];
array_tmp6[1] := array_x[1]*array_x[1];
array_tmp7[1] := array_tmp6[1] + array_const_1D0[1];
array_tmp8[1] := array_tmp5[1]/array_tmp7[1];
array_tmp9[1] := array_const_0D0[1] + array_tmp8[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp9[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_2D0, 1);
array_tmp2[2] := ats(2, array_tmp1, array_x, 1);
array_tmp3[2] := ats(2, array_x, array_x, 1);
array_tmp4[2] := array_tmp3[2] + array_const_1D0[2];
array_tmp5[2] :=
(array_tmp2[2] - ats(2, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp6[2] := ats(2, array_x, array_x, 1);
array_tmp7[2] := array_tmp6[2] + array_const_1D0[2];
array_tmp8[2] :=
(array_tmp5[2] - ats(2, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[2] := array_const_0D0[2] + array_tmp8[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp9[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_2D0, 1);
array_tmp2[3] := ats(3, array_tmp1, array_x, 1);
array_tmp3[3] := ats(3, array_x, array_x, 1);
array_tmp4[3] := array_tmp3[3] + array_const_1D0[3];
array_tmp5[3] :=
(array_tmp2[3] - ats(3, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp6[3] := ats(3, array_x, array_x, 1);
array_tmp7[3] := array_tmp6[3] + array_const_1D0[3];
array_tmp8[3] :=
(array_tmp5[3] - ats(3, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[3] := array_const_0D0[3] + array_tmp8[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp9[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_2D0, 1);
array_tmp2[4] := ats(4, array_tmp1, array_x, 1);
array_tmp3[4] := ats(4, array_x, array_x, 1);
array_tmp4[4] := array_tmp3[4] + array_const_1D0[4];
array_tmp5[4] :=
(array_tmp2[4] - ats(4, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp6[4] := ats(4, array_x, array_x, 1);
array_tmp7[4] := array_tmp6[4] + array_const_1D0[4];
array_tmp8[4] :=
(array_tmp5[4] - ats(4, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[4] := array_const_0D0[4] + array_tmp8[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp9[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_2D0, 1);
array_tmp2[5] := ats(5, array_tmp1, array_x, 1);
array_tmp3[5] := ats(5, array_x, array_x, 1);
array_tmp4[5] := array_tmp3[5] + array_const_1D0[5];
array_tmp5[5] :=
(array_tmp2[5] - ats(5, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp6[5] := ats(5, array_x, array_x, 1);
array_tmp7[5] := array_tmp6[5] + array_const_1D0[5];
array_tmp8[5] :=
(array_tmp5[5] - ats(5, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[5] := array_const_0D0[5] + array_tmp8[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp9[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_2D0, 1);
array_tmp2[kkk] := ats(kkk, array_tmp1, array_x, 1);
array_tmp3[kkk] := ats(kkk, array_x, array_x, 1);
array_tmp4[kkk] := array_tmp3[kkk] + array_const_1D0[kkk];
array_tmp5[kkk] := (
array_tmp2[kkk] - ats(kkk, array_tmp4, array_tmp5, 2))/
array_tmp4[1];
array_tmp6[kkk] := ats(kkk, array_x, array_x, 1);
array_tmp7[kkk] := array_tmp6[kkk] + array_const_1D0[kkk];
array_tmp8[kkk] := (
array_tmp5[kkk] - ats(kkk, array_tmp7, array_tmp8, 2))/
array_tmp7[1];
array_tmp9[kkk] := array_const_0D0[kkk] + array_tmp8[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_tmp9[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 + 1.0);
> end;
exact_soln_y := proc(x) 1.0/(x*x + 1.0) 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
> DEBUGMASSIVE,
> glob_max_terms,
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_relerr,
> glob_html_log,
> glob_log10normmin,
> glob_start,
> glob_max_sec,
> glob_optimal_start,
> glob_large_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_h,
> glob_clock_start_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_sec,
> glob_dump,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_hmax,
> glob_initial_pass,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_warned,
> glob_max_hours,
> centuries_in_millinium,
> glob_display_flag,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_reached_optimal_h,
> min_in_hour,
> glob_small_float,
> glob_last_good_h,
> glob_not_yet_finished,
> years_in_century,
> glob_log10_relerr,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_1st_rel_error,
> array_norms,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_type_pole,
> array_y_init,
> array_pole,
> array_complex_pole,
> array_y_higher_work2,
> array_y_higher,
> array_y_higher_work,
> array_real_pole,
> array_poles,
> array_y_set_initial,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> glob_max_terms := 30;
> DEBUGL := 3;
> INFO := 2;
> ALWAYS := 1;
> glob_iolevel := 5;
> glob_log10abserr := 0.0;
> glob_current_iter := 0;
> glob_unchanged_h_cnt := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_no_eqs := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_html_log := true;
> glob_log10normmin := 0.1;
> glob_start := 0;
> glob_max_sec := 10000.0;
> glob_optimal_start := 0.0;
> glob_large_float := 9.0e100;
> glob_disp_incr := 0.1;
> glob_not_yet_start_msg := true;
> glob_almost_1 := 0.9990;
> sec_in_min := 60.0;
> glob_subiter_method := 3;
> glob_max_minutes := 0.0;
> glob_log10relerr := 0.0;
> MAX_UNCHANGED := 10;
> glob_log10_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_h := 0.1;
> glob_clock_start_sec := 0.0;
> glob_normmax := 0.0;
> glob_iter := 0;
> glob_warned2 := false;
> glob_abserr := 0.1e-10;
> glob_look_poles := false;
> glob_hmin := 0.00000000001;
> hours_in_day := 24.0;
> djd_debug2 := true;
> glob_hmin_init := 0.001;
> glob_optimal_done := false;
> glob_clock_sec := 0.0;
> glob_dump := false;
> glob_optimal_expect_sec := 0.1;
> glob_curr_iter_when_opt := 0;
> glob_hmax := 1.0;
> glob_initial_pass := true;
> days_in_year := 365.0;
> djd_debug := true;
> glob_max_opt_iter := 10;
> glob_warned := false;
> glob_max_hours := 0.0;
> centuries_in_millinium := 10.0;
> glob_display_flag := true;
> glob_orig_start_sec := 0.0;
> glob_smallish_float := 0.1e-100;
> glob_reached_optimal_h := false;
> min_in_hour := 60.0;
> glob_small_float := 0.1e-50;
> glob_last_good_h := 0.1;
> glob_not_yet_finished := true;
> years_in_century := 100.0;
> glob_log10_relerr := 0.1e-10;
> glob_percent_done := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_iter := 1000;
> #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/sing4postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 50;");
> 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 := -2.0;");
> omniout_str(ALWAYS,"x_end := 1.0;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.1;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 50;");
> 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 + 1.0);");
> 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 := 50;
> 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_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_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_tmp7:= Array(1..(max_terms + 1),[]);
> array_tmp8:= Array(1..(max_terms + 1),[]);
> array_tmp9:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher := 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_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_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_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_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_pole[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_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_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_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_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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_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_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0[1] := 2.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1D0[1] := 1.0;
> array_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 := -2.0;
> x_end := 1.0;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.1;
> glob_look_poles := true;
> glob_max_iter := 50;
> #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 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-13T04:07:44-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing4")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"sing4 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing4 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 DEBUGMASSIVE, glob_max_terms, DEBUGL, INFO, ALWAYS, glob_iolevel,
glob_log10abserr, glob_current_iter, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, glob_no_eqs, glob_max_trunc_err, glob_relerr,
glob_html_log, glob_log10normmin, glob_start, glob_max_sec,
glob_optimal_start, glob_large_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, sec_in_min, glob_subiter_method,
glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_log10_abserr,
glob_dump_analytic, glob_h, glob_clock_start_sec, glob_normmax, glob_iter,
glob_warned2, glob_abserr, glob_look_poles, glob_hmin, hours_in_day,
djd_debug2, glob_hmin_init, glob_optimal_done, glob_clock_sec, glob_dump,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_hmax,
glob_initial_pass, days_in_year, djd_debug, glob_max_opt_iter, glob_warned,
glob_max_hours, centuries_in_millinium, glob_display_flag,
glob_orig_start_sec, glob_smallish_float, glob_reached_optimal_h,
min_in_hour, glob_small_float, glob_last_good_h, glob_not_yet_finished,
years_in_century, glob_log10_relerr, glob_percent_done,
glob_max_rel_trunc_err, glob_max_iter, array_const_2D0, array_const_1,
array_const_0D0, array_const_1D0, array_1st_rel_error, array_norms, array_y,
array_x, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_m1, array_type_pole, array_y_init, array_pole,
array_complex_pole, array_y_higher_work2, array_y_higher,
array_y_higher_work, array_real_pole, array_poles, array_y_set_initial,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
glob_max_terms := 30;
DEBUGL := 3;
INFO := 2;
ALWAYS := 1;
glob_iolevel := 5;
glob_log10abserr := 0.;
glob_current_iter := 0;
glob_unchanged_h_cnt := 0;
glob_optimal_clock_start_sec := 0.;
glob_no_eqs := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_html_log := true;
glob_log10normmin := 0.1;
glob_start := 0;
glob_max_sec := 10000.0;
glob_optimal_start := 0.;
glob_large_float := 0.90*10^101;
glob_disp_incr := 0.1;
glob_not_yet_start_msg := true;
glob_almost_1 := 0.9990;
sec_in_min := 60.0;
glob_subiter_method := 3;
glob_max_minutes := 0.;
glob_log10relerr := 0.;
MAX_UNCHANGED := 10;
glob_log10_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_h := 0.1;
glob_clock_start_sec := 0.;
glob_normmax := 0.;
glob_iter := 0;
glob_warned2 := false;
glob_abserr := 0.1*10^(-10);
glob_look_poles := false;
glob_hmin := 0.1*10^(-10);
hours_in_day := 24.0;
djd_debug2 := true;
glob_hmin_init := 0.001;
glob_optimal_done := false;
glob_clock_sec := 0.;
glob_dump := false;
glob_optimal_expect_sec := 0.1;
glob_curr_iter_when_opt := 0;
glob_hmax := 1.0;
glob_initial_pass := true;
days_in_year := 365.0;
djd_debug := true;
glob_max_opt_iter := 10;
glob_warned := false;
glob_max_hours := 0.;
centuries_in_millinium := 10.0;
glob_display_flag := true;
glob_orig_start_sec := 0.;
glob_smallish_float := 0.1*10^(-100);
glob_reached_optimal_h := false;
min_in_hour := 60.0;
glob_small_float := 0.1*10^(-50);
glob_last_good_h := 0.1;
glob_not_yet_finished := true;
years_in_century := 100.0;
glob_log10_relerr := 0.1*10^(-10);
glob_percent_done := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_iter := 1000;
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/sing4postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.\
0) /( x * x + 1.0);");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 50;");
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 := -2.0;");
omniout_str(ALWAYS, "x_end := 1.0;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.1;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 50;");
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 + 1.0);");
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 := 50;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_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_tmp7 := Array(1 .. max_terms + 1, []);
array_tmp8 := Array(1 .. max_terms + 1, []);
array_tmp9 := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher := 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_poles := Array(1 .. 2, 1 .. 4, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_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_pole[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_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_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_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_tmp9 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 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_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_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 1.0;
array_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 := -2.0;
x_end := 1.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.1;
glob_look_poles := true;
glob_max_iter := 50;
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 * 2.0 * x / (x * x + 1.0)\
/( x * x + 1.0);");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-13T04:07:44-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sing4");
logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / (\
x * x + 1.0) /( x * x + 1.0);");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 090 | ");
logitem_str(html_log_file,
"sing4 diffeq.mxt");
logitem_str(html_log_file,
"sing4 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/sing4postode.ode#################
diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);
!
#BEGIN FIRST INPUT BLOCK
Digits := 50;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -2.0;
x_end := 1.0;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.1;
glob_look_poles := true;
glob_max_iter := 50;
#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 + 1.0);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = -2
y[1] (analytic) = 0.2
y[1] (numeric) = 0.2
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.259
Order of pole = 3.572
x[1] = -1.9999
y[1] (analytic) = 0.20001600088003840131202815962871
y[1] (numeric) = 0.20001600088003840131202814663258
absolute error = 1.299612915477496758365330e-26
relative error = 6.4975447452174219478982714516533e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.259
Order of pole = 3.572
x[1] = -1.9998
y[1] (analytic) = 0.20003200352030722099290109623219
y[1] (numeric) = 0.20003200352030722099290107021885
absolute error = 2.601334060465285245783901e-26
relative error = 1.3004589339131416419334287710556e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.259
Order of pole = 3.572
x[1] = -1.9997
y[1] (analytic) = 0.20004800792103690627884260920704
y[1] (numeric) = 0.2000480079210369062788425701554
absolute error = 3.905164638857162913662054e-26
relative error = 1.9521137348184003469958537764785e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.259
Order of pole = 3.571
x[1] = -1.9996
y[1] (analytic) = 0.20006401408245793590083431815511
y[1] (numeric) = 0.20006401408245793590083426604405
absolute error = 5.211105855110177982476668e-26
relative error = 2.6047192339959650445239854527467e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.259
Order of pole = 3.571
x[1] = -1.9995
y[1] (analytic) = 0.2000800220048008200879941932776
y[1] (numeric) = 0.20008002200480082008799412808601
absolute error = 6.519158914244863325265478e-26
relative error = 3.2582757883185555460892690360370e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.259
Order of pole = 3.571
x[1] = -1.9994
y[1] (analytic) = 0.20009603168829610057095481720351
y[1] (numeric) = 0.20009603168829610057095473891026
absolute error = 7.829325021845470432994178e-26
relative error = 3.9127837547731930900301059850704e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
x[1] = -1.9993
y[1] (analytic) = 0.20011204313317435058524137781792
y[1] (numeric) = 0.20011204313317435058524128640187
absolute error = 9.141605384060203461817128e-26
relative error = 4.5682434904612286928892248331993e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
x[1] = -1.9992
y[1] (analytic) = 0.20012805633966617487464939165554
y[1] (numeric) = 0.20012805633966617487464928709553
absolute error = 1.0456001207601453362248512e-25
relative error = 5.2246553525983715025413516600648e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
x[1] = -1.9991
y[1] (analytic) = 0.20014407130800220969462215742456
y[1] (numeric) = 0.20014407130800220969462203969942
absolute error = 1.1772513699746032090260748e-25
relative error = 5.8820196985147171530064794418406e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
x[1] = -1.999
y[1] (analytic) = 0.20016008803841312281562793922579
y[1] (numeric) = 0.20016008803841312281562780831435
absolute error = 1.3091144068335406900326967e-25
relative error = 6.5403368856547761209440427458967e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
memory used=3.8MB, alloc=3.1MB, time=0.51
x[1] = -1.9989
y[1] (analytic) = 0.20017610653112961352653687903162
y[1] (numeric) = 0.20017610653112961352653673491269
absolute error = 1.4411893521775934720424370e-25
relative error = 7.1996072715775020838232994485488e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
x[1] = -1.9988
y[1] (analytic) = 0.20019212678638241263799763798915
y[1] (numeric) = 0.20019212678638241263799748064152
absolute error = 1.5734763269039096609015244e-25
relative error = 7.8598312139563202797652063810751e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
x[1] = -1.9987
y[1] (analytic) = 0.2002081488044022824858137661117
y[1] (numeric) = 0.20020814880440228248581359551416
absolute error = 1.7059754519661732294022435e-25
relative error = 8.5210090705791558690510835235915e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
x[1] = -1.9986
y[1] (analytic) = 0.20022417258542001693431979992255
y[1] (numeric) = 0.20022417258542001693431961605387
absolute error = 1.8386868483746274793816051e-25
relative error = 9.1831411993484622972933480993860e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
x[1] = -1.9985
y[1] (analytic) = 0.20024019812966644137975708761445
y[1] (numeric) = 0.20024019812966644137975689045338
absolute error = 1.9716106371960985120228160e-25
relative error = 9.8462279582812496602635951553360e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
x[1] = -1.9984
y[1] (analytic) = 0.20025622543737241275364934128839
y[1] (numeric) = 0.20025622543737241275364913081369
absolute error = 2.1047469395540187063612257e-25
relative error = 1.0510269705509113070373304940258e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.258
Order of pole = 3.571
x[1] = -1.9983
y[1] (analytic) = 0.2002722545087688195261779158347
y[1] (numeric) = 0.20027225450876881952617769202511
absolute error = 2.2380958766284502059964243e-25
relative error = 1.1175266799278261024802441144426e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
x[1] = -1.9982
y[1] (analytic) = 0.20028828534408658170955681401937
y[1] (numeric) = 0.20028828534408658170955657685362
absolute error = 2.3716575696561084140121657e-25
relative error = 1.1841219597949543775271202306377e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
x[1] = -1.9981
y[1] (analytic) = 0.2003043179435566508614074173382
y[1] (numeric) = 0.20030431794355665086140716679498
absolute error = 2.5054321399303854961057924e-25
relative error = 1.2508128459998481699450198919671e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
x[1] = -1.998
y[1] (analytic) = 0.20032035230741001008813294220117
y[1] (numeric) = 0.2003203523074100100881326782592
absolute error = 2.6394197088013738919288308e-25
relative error = 1.3175993744015293674004291068923e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
x[1] = -1.9979
y[1] (analytic) = 0.2003363884358776740482926210092
y[1] (numeric) = 0.20033638843587767404829234364716
absolute error = 2.7736203976758898346404324e-25
relative error = 1.3844815808704925449265353132147e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
x[1] = -1.9978
y[1] (analytic) = 0.20035242632919068895597560768514
y[1] (numeric) = 0.2003524263291906889559753168817
absolute error = 2.9080343280174968786753309e-25
relative error = 1.4514595012887078025529204376682e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
x[1] = -1.9977
y[1] (analytic) = 0.20036846598758013258417460722055
y[1] (numeric) = 0.20036846598758013258417430295439
absolute error = 3.0426616213465294357279853e-25
relative error = 1.5185331715496236030971944036282e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
x[1] = -1.9976
y[1] (analytic) = 0.20038450741127711426815922879986
y[1] (numeric) = 0.20038450741127711426815891104962
absolute error = 3.1775023992401163189545786e-25
relative error = 1.5857026275581696101180926223813e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
x[1] = -1.9975
y[1] (analytic) = 0.2004005506005127749088490620628
y[1] (numeric) = 0.20040055060051277490884873080712
absolute error = 3.3125567833322042953945420e-25
relative error = 1.6529679052307595260295610795888e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
x[1] = -1.9974
y[1] (analytic) = 0.2004165955555182869761864760661
y[1] (numeric) = 0.20041659555551828697618613128361
absolute error = 3.4478248953135816466132707e-25
relative error = 1.7203290404952939303753506590430e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
x[1] = -1.9973
y[1] (analytic) = 0.20043264227652485451250914050516
y[1] (numeric) = 0.20043264227652485451250878217448
absolute error = 3.5833068569319017375676998e-25
relative error = 1.7877860692911631182636434710692e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.257
Order of pole = 3.571
memory used=7.6MB, alloc=4.1MB, time=1.17
x[1] = -1.9972
y[1] (analytic) = 0.2004486907637637131359222687559
y[1] (numeric) = 0.20044869076376371313592189685562
absolute error = 3.7190027899917065936964062e-25
relative error = 1.8553390275692499389612325830385e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.256
Order of pole = 3.57
x[1] = -1.9971
y[1] (analytic) = 0.20046474101746613004367058229701
y[1] (numeric) = 0.20046474101746613004367019680573
absolute error = 3.8549128163544504862359010e-25
relative error = 1.9229879512919326346467757792327e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.256
Order of pole = 3.57
x[1] = -1.997
y[1] (analytic) = 0.20048079303786340401550999607258
y[1] (numeric) = 0.20048079303786340401550959696888
absolute error = 3.9910370579385235257647786e-25
relative error = 1.9907328764330876793226447539807e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.256
Order of pole = 3.57
x[1] = -1.9969
y[1] (analytic) = 0.20049684682518686541707902435451
y[1] (numeric) = 0.20049684682518686541707861161695
absolute error = 4.1273756367192752639773846e-25
relative error = 2.0585738389780926178848890253626e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.256
Order of pole = 3.57
x[1] = -1.9968
y[1] (analytic) = 0.20051290237966787620326990666429
y[1] (numeric) = 0.20051290237966787620326948027142
absolute error = 4.2639286747290383036886665e-25
relative error = 2.1265108749238289053508347340745e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.256
Order of pole = 3.57
x[1] = -1.9967
y[1] (analytic) = 0.20052895970153782992159945331314
y[1] (numeric) = 0.20052895970153782992159901324351
absolute error = 4.4006962940571519170718688e-25
relative error = 2.1945440202786847462438372244491e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.256
Order of pole = 3.57
x[1] = -1.9966
y[1] (analytic) = 0.20054501879102815171557961011947
y[1] (numeric) = 0.2005450187910281517155791563516
absolute error = 4.5376786168499856721307336e-25
relative error = 2.2626733110625579341347059854320e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.256
Order of pole = 3.57
x[1] = -1.9965
y[1] (analytic) = 0.20056107964837029832808774186225
y[1] (numeric) = 0.20056107964837029832808727437467
absolute error = 4.6748757653109630674078668e-25
relative error = 2.3308987833068586913393199611168e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.256
Order of pole = 3.57
x[1] = -1.9964
y[1] (analytic) = 0.20057714227379575810473663402865
y[1] (numeric) = 0.20057714227379575810473615279986
absolute error = 4.8122878617005851749309308e-25
relative error = 2.3992204730545125087719515701343e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.256
Order of pole = 3.57
x[1] = -1.9963
y[1] (analytic) = 0.20059320666753605099724421241409
y[1] (numeric) = 0.20059320666753605099724371742259
absolute error = 4.9499150283364542913983202e-25
relative error = 2.4676384163599629859538155104044e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.256
Order of pole = 3.57
x[1] = -1.9962
y[1] (analytic) = 0.2006092728298227285668029801326
y[1] (numeric) = 0.20060927282982272856680247135686
absolute error = 5.0877573875932975976059803e-25
relative error = 2.5361526492891746711763600029796e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.9961
y[1] (analytic) = 0.200625340760887373987449171595
y[1] (numeric) = 0.20062534076088737398744864901349
absolute error = 5.2258150619029908261170229e-25
relative error = 2.6047632079196359018188154182678e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.996
y[1] (analytic) = 0.20064141046096160204943162301245
y[1] (numeric) = 0.20064141046096160204943108660363
absolute error = 5.3640881737545819371757995e-25
relative error = 2.6734701283403616448195179520792e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.9959
y[1] (analytic) = 0.2006574819302770591625803589823
y[1] (numeric) = 0.20065748193027705916257980872461
absolute error = 5.5025768456943148028680822e-25
relative error = 2.7422734466518963373005210664382e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.9958
y[1] (analytic) = 0.20067355516906542335967489471321
y[1] (numeric) = 0.20067355516906542335967433058509
absolute error = 5.6412812003256528995290107e-25
relative error = 2.8111731989663167273450113811989e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.9957
y[1] (analytic) = 0.20068963017755840429981225344614
y[1] (numeric) = 0.20068963017755840429981167542601
absolute error = 5.7802013603093030084004566e-25
relative error = 2.8801694214072347149270420470923e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.9956
y[1] (analytic) = 0.20070570695598774327177469862754
y[1] (numeric) = 0.20070570695598774327177410669379
absolute error = 5.9193374483632389245394584e-25
relative error = 2.9492621501098001929930976616075e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.9955
y[1] (analytic) = 0.20072178550458521319739718039083
y[1] (numeric) = 0.20072178550458521319739657452187
absolute error = 6.0586895872627251739793795e-25
relative error = 3.0184514212207038886950041751435e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.3MB, time=1.83
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.9954
y[1] (analytic) = 0.20073786582358261863493449590213
y[1] (numeric) = 0.20073786582358261863493387607634
absolute error = 6.1982578998403407391454390e-25
relative error = 3.0877372708981802047736959239889e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.9953
y[1] (analytic) = 0.20075394791321179578242816312573
y[1] (numeric) = 0.20075394791321179578242752932148
absolute error = 6.3380425089860027925262664e-25
relative error = 3.1571197353120100610933525096905e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.9952
y[1] (analytic) = 0.20077003177370461248107300756463
y[1] (numeric) = 0.20077003177370461248107235976028
absolute error = 6.4780435376469904386031284e-25
relative error = 3.2265988506435237363254167350798e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.255
Order of pole = 3.57
x[1] = -1.9951
y[1] (analytic) = 0.20078611740529296821858346153142
y[1] (numeric) = 0.20078611740529296821858279970531
absolute error = 6.6182611088279684640384774e-25
relative error = 3.2961746530856037097820054406802e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.57
x[1] = -1.995
y[1] (analytic) = 0.20080220480820879413255957550414
y[1] (numeric) = 0.2008022048082087941325588996346
absolute error = 6.7586953455910110961254681e-25
relative error = 3.3658471788426875033982234274702e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.57
x[1] = -1.9949
y[1] (analytic) = 0.20081829398268405301385274112182
y[1] (numeric) = 0.20081829398268405301385205118718
absolute error = 6.8993463710556257695000887e-25
relative error = 3.4356164641307705238628906387827e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.57
x[1] = -1.9948
y[1] (analytic) = 0.20083438492895073930993112537403
y[1] (numeric) = 0.2008343849289507393099304213526
absolute error = 7.0402143083987769011175536e-25
relative error = 3.5054825451774089048971929103769e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.569
x[1] = -1.9947
y[1] (analytic) = 0.20085047764724087912824481553851
y[1] (numeric) = 0.20085047764724087912824409740858
absolute error = 7.1812992808549096734946010e-25
relative error = 3.5754454582217223496807647922142e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.569
x[1] = -1.9946
y[1] (analytic) = 0.20086657213778653023959067442068
y[1] (numeric) = 0.20086657213778653023958994216054
absolute error = 7.3226014117159738262193405e-25
relative error = 3.6455052395143969734247137301169e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.569
x[1] = -1.9945
y[1] (analytic) = 0.2008826684008197820814769054487
y[1] (numeric) = 0.20088266840081978208147615903661
absolute error = 7.4641208243314474557302929e-25
relative error = 3.7156619253176881460910933897560e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.569
x[1] = -1.9944
y[1] (analytic) = 0.20089876643657275576148732717724
y[1] (numeric) = 0.20089876643657275576148656659147
absolute error = 7.6058576421083608233662651e-25
relative error = 3.7859155519054233352583341927834e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.569
x[1] = -1.9943
y[1] (analytic) = 0.20091486624527760406064535675327
y[1] (numeric) = 0.20091486624527760406064458197207
absolute error = 7.7478119885113201716887009e-25
relative error = 3.8562661555630049491321380285372e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.569
x[1] = -1.9942
y[1] (analytic) = 0.20093096782716651143677770189642
y[1] (numeric) = 0.20093096782716651143677691289802
absolute error = 7.8899839870625315490781486e-25
relative error = 3.9267137725874131797013440941399e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.569
x[1] = -1.9941
y[1] (analytic) = 0.2009470711824716940278777609467
y[1] (numeric) = 0.20094707118247169402787695770932
absolute error = 8.0323737613418246426064842e-25
relative error = 3.9972584392872088460382717104595e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.254
Order of pole = 3.569
x[1] = -1.994
y[1] (analytic) = 0.20096317631142539965546873053169
y[1] (numeric) = 0.20096317631142539965546791303355
absolute error = 8.1749814349866766191865303e-25
relative error = 4.0679001919825362377430465487891e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.9939
y[1] (analytic) = 0.20097928321425990782796642040548
y[1] (numeric) = 0.20097928321425990782796558862476
absolute error = 8.3178071316922359750007062e-25
relative error = 4.1386390670051259585314143544998e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.9938
y[1] (analytic) = 0.20099539189120752974404177501089
y[1] (numeric) = 0.20099539189120752974404092892579
absolute error = 8.4608509752113463932103491e-25
relative error = 4.2094751006982977699655483848139e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.3MB, time=2.51
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.9937
y[1] (analytic) = 0.20101150234250060829598310131678
y[1] (numeric) = 0.20101150234250060829598224090547
absolute error = 8.6041130893545706099473389e-25
relative error = 4.2804083294169634353273530369601e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.9936
y[1] (analytic) = 0.20102761456837151807305800248155
y[1] (numeric) = 0.20102761456837151807305712772219
absolute error = 8.7475935979902142885896652e-25
relative error = 4.3514387895276295636337691203567e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.9935
y[1] (analytic) = 0.20104372856905266536487501689396
y[1] (numeric) = 0.20104372856905266536487412776469
absolute error = 8.8912926250443499023225677e-25
relative error = 4.4225665174084004537935824868285e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.9934
y[1] (analytic) = 0.201059844344776488164744962142
y[1] (numeric) = 0.20105984434477648816474405862097
absolute error = 9.0352102945008406249868860e-25
relative error = 4.4937915494489809389052400638354e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.9933
y[1] (analytic) = 0.20107596189577545617304198346042
y[1] (numeric) = 0.20107596189577545617304106552575
absolute error = 9.1793467304013642302162483e-25
relative error = 4.5651139220506792306951740452946e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.9932
y[1] (analytic) = 0.20109208122228207080056430620706
y[1] (numeric) = 0.20109208122228207080056337383686
absolute error = 9.3237020568454369988647335e-25
relative error = 4.6365336716264097640961374254077e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.9931
y[1] (analytic) = 0.20110820232452886517189469191813
y[1] (numeric) = 0.20110820232452886517189374509049
absolute error = 9.4682763979904376347266356e-25
relative error = 4.7080508346006960419650512192561e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.993
y[1] (analytic) = 0.2011243252027484041287605974921
y[1] (numeric) = 0.20112432520274840412875963618511
absolute error = 9.6130698780516311885499595e-25
relative error = 4.7796654474096734799398637582016e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.253
Order of pole = 3.569
x[1] = -1.9929
y[1] (analytic) = 0.20114044985717328423339403705177
y[1] (numeric) = 0.20114044985717328423339306124351
absolute error = 9.7580826213021929903452794e-25
relative error = 4.8513775465010922514349234370575e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.252
Order of pole = 3.569
x[1] = -1.9928
y[1] (analytic) = 0.20115657628803613377189114603375
y[1] (numeric) = 0.20115657628803613377189015570228
absolute error = 9.9033147520732325899915847e-25
relative error = 4.9231871683343201327743631024391e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.252
Order of pole = 3.569
x[1] = -1.9927
y[1] (analytic) = 0.20117270449556961275757144705431
y[1] (numeric) = 0.20117270449556961275757044217768
absolute error = 1.00487663947538177061407437e-24
relative error = 4.9950943493803453484629969024192e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.252
Order of pole = 3.569
x[1] = -1.9926
y[1] (analytic) = 0.20118883448000641293433681710041
y[1] (numeric) = 0.20118883448000641293433579765665
absolute error = 1.01944376737909981834222080e-24
relative error = 5.0670991261217794165942266843310e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.252
Order of pole = 3.569
x[1] = -1.9925
y[1] (analytic) = 0.20120496624157925778003015559432
y[1] (numeric) = 0.20120496624157925778002912156144
absolute error = 1.03403287136898299579495849e-24
relative error = 5.1392015350528599943944571617151e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.252
Order of pole = 3.569
x[1] = -1.9924
y[1] (analytic) = 0.20122109978052090250979375288008
y[1] (numeric) = 0.20122109978052090250979270423611
absolute error = 1.04864396390133990311307012e-24
relative error = 5.2114016126794537239035170792821e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.252
Order of pole = 3.569
x[1] = -1.9923
y[1] (analytic) = 0.20123723509706413407942735867985
y[1] (numeric) = 0.20123723509706413407942629540279
absolute error = 1.06327705743828454517827819e-24
relative error = 5.2836993955190590777905836018619e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.252
Order of pole = 3.568
x[1] = -1.9922
y[1] (analytic) = 0.2012533721914417711887459500677
y[1] (numeric) = 0.20125337219144177118874487213554
absolute error = 1.07793216444773873065543671e-24
relative error = 5.3560949201008092053051070014174e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.252
Order of pole = 3.568
x[1] = -1.9921
y[1] (analytic) = 0.20126951106388666428493719850846
y[1] (numeric) = 0.20126951106388666428493610589916
absolute error = 1.09260929740343447186555862e-24
relative error = 5.4285882229654747783622305771215e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.252
Order of pole = 3.568
x[1] = -1.992
y[1] (analytic) = 0.20128565171463169556591863550872
y[1] (numeric) = 0.20128565171463169556591752820025
absolute error = 1.10730846878491638548984136e-24
relative error = 5.5011793406654668377622032263270e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=3.18
Complex estimate of poles used
Radius of convergence = 2.252
Order of pole = 3.568
x[1] = -1.9919
y[1] (analytic) = 0.201301794143909778983694516427
y[1] (numeric) = 0.20130179414390977898369339439731
absolute error = 1.12202969107754409410485219e-24
relative error = 5.5738683097648396395432779583962e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.9918
y[1] (analytic) = 0.20131793835195386024771238198974
y[1] (numeric) = 0.20131793835195386024771124521676
absolute error = 1.13677297677249462854903542e-24
relative error = 5.6466551668392935014675923753656e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.9917
y[1] (analytic) = 0.20133408433899691682821931705952
y[1] (numeric) = 0.20133408433899691682821816552119
absolute error = 1.15153833836676483112070317e-24
relative error = 5.7195399484761776496395244099974e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.9916
y[1] (analytic) = 0.20135023210527195795961790620178
y[1] (numeric) = 0.201350232105271957959616739876
absolute error = 1.16632578836317375960767143e-24
relative error = 5.7925226912744930652560173072481e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.9915
y[1] (analytic) = 0.2013663816510120246438218855958
y[1] (numeric) = 0.20136638165101202464382070446047
absolute error = 1.18113533927036509214870301e-24
relative error = 5.8656034318448953314883668914525e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.9914
y[1] (analytic) = 0.20138253297645018965361149083578
y[1] (numeric) = 0.20138253297645018965361029486877
absolute error = 1.19596700360280953292691878e-24
relative error = 5.9387822068096974804949631688810e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.9913
y[1] (analytic) = 0.20139868608181955753598850016725
y[1] (numeric) = 0.20139868608181955753598728934645
absolute error = 1.21082079388080721869533886e-24
relative error = 6.0120590528028728405644795578703e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.9912
y[1] (analytic) = 0.20141484096735326461553097270413
y[1] (numeric) = 0.20141484096735326461552974700741
absolute error = 1.22569672263049012613471476e-24
relative error = 6.0854340064700578833889997127590e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.9911
y[1] (analytic) = 0.20143099763328447899774768117117
y[1] (numeric) = 0.20143099763328447899774644057637
absolute error = 1.24059480238382448004381400e-24
relative error = 6.1589071044685550714665744921069e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.991
y[1] (analytic) = 0.20144715607984640057243223871649
y[1] (numeric) = 0.20144715607984640057243098320145
absolute error = 1.25551504567861316236231810e-24
relative error = 6.2324783834673357056326983961661e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.9909
y[1] (analytic) = 0.20146331630727226101701691933857
y[1] (numeric) = 0.2014633163072722610170156488811
absolute error = 1.27045746505849812202649514e-24
relative error = 6.3061478801470427727201962909665e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.251
Order of pole = 3.568
x[1] = -1.9908
y[1] (analytic) = 0.2014794783157953237999261714718
y[1] (numeric) = 0.20147947831579532379992488604973
absolute error = 1.28542207307296278565780779e-24
relative error = 6.3799156311999937933470097001793e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.25
Order of pole = 3.568
x[1] = -1.9907
y[1] (analytic) = 0.2014956421056488841839298242745
y[1] (numeric) = 0.20149564210564888418392852386562
absolute error = 1.30040888227733446908461759e-24
relative error = 6.4537816733301836698313713042274e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.25
Order of pole = 3.568
x[1] = -1.9906
y[1] (analytic) = 0.20151180767706626922949598616288
y[1] (numeric) = 0.20151180767706626922949467074497
absolute error = 1.31541790523278678969714642e-24
relative error = 6.5277460432532875342338570344657e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.25
Order of pole = 3.568
x[1] = -1.9905
y[1] (analytic) = 0.20152797503028083779814363513441
y[1] (numeric) = 0.20152797503028083779814230468525
absolute error = 1.33044915450634207963585554e-24
relative error = 6.6018087776966635965258023254425e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.25
Order of pole = 3.568
x[1] = -1.9904
y[1] (analytic) = 0.20154414416552598055579490042365
y[1] (numeric) = 0.20154414416552598055579355492101
absolute error = 1.34550264267087379981340310e-24
relative error = 6.6759699133993559928835716241897e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.25
Order of pole = 3.568
x[1] = -1.9903
y[1] (analytic) = 0.20156031508303511997612703503331
y[1] (numeric) = 0.20156031508303511997612567445493
absolute error = 1.36057838230510895477034031e-24
relative error = 6.7502294871120976341081666872918e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.3MB, time=3.86
Complex estimate of poles used
Radius of convergence = 2.25
Order of pole = 3.568
x[1] = -1.9902
y[1] (analytic) = 0.20157648778304171034392407868317
y[1] (numeric) = 0.20157648778304171034392270300679
absolute error = 1.37567638599363050836470683e-24
relative error = 6.8245875355973130541696609887080e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.25
Order of pole = 3.568
x[1] = -1.9901
y[1] (analytic) = 0.20159266226577923775842821071911
y[1] (numeric) = 0.20159266226577923775842681992244
absolute error = 1.39079666632687980029568562e-24
relative error = 6.8990440956291212588759459295956e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.25
Order of pole = 3.568
x[1] = -1.99
y[1] (analytic) = 0.20160883853148122013669079252434
y[1] (numeric) = 0.20160883853148122013668938658511
absolute error = 1.40593923590115896346147734e-24
relative error = 6.9735992039933385746652737541340e-22 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);
Iterations = 100
Total Elapsed Time = 3 Seconds
Elapsed Time(since restart) = 3 Seconds
Expected Time Remaining = 19 Minutes 3 Seconds
Optimized Time Remaining = 18 Minutes 58 Seconds
Time to Timeout = 14 Minutes 56 Seconds
Percent Done = 0.3367 %
> quit
memory used=23.5MB, alloc=4.3MB, time=3.96