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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> INFO,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_max_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_disp_incr,
> hours_in_day,
> sec_in_minute,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_log10_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> years_in_century,
> glob_display_flag,
> glob_percent_done,
> glob_log10relerr,
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug2,
> djd_debug,
> glob_max_minutes,
> glob_look_poles,
> glob_clock_start_sec,
> days_in_year,
> glob_small_float,
> glob_relerr,
> min_in_hour,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_log10normmin,
> glob_smallish_float,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_orig_start_sec,
> glob_max_hours,
> glob_dump_analytic,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_iter,
> glob_warned,
> glob_hmin,
> glob_almost_1,
> glob_dump,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_0D0,
> array_const_5,
> array_const_1,
> #END CONST
> array_pole,
> array_y1_init,
> array_y2_init,
> array_x,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_y2_set_initial,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher_work,
> array_fact_2,
> array_y2_higher,
> array_real_pole,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_y1_higher,
> array_complex_pole,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no, good_digits;
>
>
>
>
>
> #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_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 3
> good_digits := -trunc(log10(relerr/100.0));
> else
> good_digits := -1;
> fi;# end if 3
> ;
> else
> relerr := -1.0 ;
> good_digits := -1;
> 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,"%");
> print("good digits = ",good_digits);
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_y1(ind_var);
> omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 3
> good_digits := -trunc(log10(relerr/100.0));
> else
> good_digits := -1;
> fi;# end if 3
> ;
> else
> relerr := -1.0 ;
> good_digits := -1;
> fi;# end if 2
> ;
> if (glob_iter = 1) then # if number 2
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> print("good digits = ",good_digits);
> 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, good_digits;
global DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, INFO,
glob_log10abserr, glob_warned2, glob_unchanged_h_cnt,
centuries_in_millinium, glob_max_opt_iter, glob_max_sec, glob_optimal_start,
glob_max_rel_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float,
glob_hmax, glob_h, glob_disp_incr, hours_in_day, sec_in_minute,
glob_normmax, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr,
glob_hmin_init, glob_not_yet_start_msg, years_in_century, glob_display_flag,
glob_percent_done, glob_log10relerr, glob_current_iter, glob_max_trunc_err,
glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug2, djd_debug,
glob_max_minutes, glob_look_poles, glob_clock_start_sec, days_in_year,
glob_small_float, glob_relerr, min_in_hour, glob_html_log,
glob_optimal_expect_sec, glob_log10normmin, glob_smallish_float,
glob_not_yet_finished, MAX_UNCHANGED, glob_start,
glob_optimal_clock_start_sec, glob_abserr, glob_orig_start_sec,
glob_max_hours, glob_dump_analytic, glob_optimal_done,
glob_reached_optimal_h, glob_iter, glob_warned, glob_hmin, glob_almost_1,
glob_dump, glob_subiter_method, array_const_2D0, array_const_0D0,
array_const_5, array_const_1, array_pole, array_y1_init, array_y2_init,
array_x, array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_last_rel_error, array_y2_set_initial,
array_y2_higher_work2, array_poles, array_y1_higher_work, array_fact_2,
array_y2_higher, array_real_pole, array_y2_higher_work,
array_y1_set_initial, array_y1_higher_work2, array_y1_higher,
array_complex_pole, 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_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y2[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then good_digits := -trunc(log10(relerr/100.0))
else good_digits := -1
end if
else relerr := -1.0; good_digits := -1
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, "%");
print("good digits = ", good_digits);
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_y1(ind_var);
omniout_float(ALWAYS, "y1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y1[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then good_digits := -trunc(log10(relerr/100.0))
else good_digits := -1
end if
else relerr := -1.0; good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
print("good digits = ", good_digits);
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_iolevel,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> INFO,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_max_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_disp_incr,
> hours_in_day,
> sec_in_minute,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_log10_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> years_in_century,
> glob_display_flag,
> glob_percent_done,
> glob_log10relerr,
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug2,
> djd_debug,
> glob_max_minutes,
> glob_look_poles,
> glob_clock_start_sec,
> days_in_year,
> glob_small_float,
> glob_relerr,
> min_in_hour,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_log10normmin,
> glob_smallish_float,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_orig_start_sec,
> glob_max_hours,
> glob_dump_analytic,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_iter,
> glob_warned,
> glob_hmin,
> glob_almost_1,
> glob_dump,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_0D0,
> array_const_5,
> array_const_1,
> #END CONST
> array_pole,
> array_y1_init,
> array_y2_init,
> array_x,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_y2_set_initial,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher_work,
> array_fact_2,
> array_y2_higher,
> array_real_pole,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_y1_higher,
> array_complex_pole,
> glob_last;
>
> local hnew, sz2, tmp;
>
>
>
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y1_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 (omniabs(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");
> 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
> return(hnew);
> #BOTTOM ADJUST FOR POLE
>
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, INFO,
glob_log10abserr, glob_warned2, glob_unchanged_h_cnt,
centuries_in_millinium, glob_max_opt_iter, glob_max_sec, glob_optimal_start,
glob_max_rel_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float,
glob_hmax, glob_h, glob_disp_incr, hours_in_day, sec_in_minute,
glob_normmax, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr,
glob_hmin_init, glob_not_yet_start_msg, years_in_century, glob_display_flag,
glob_percent_done, glob_log10relerr, glob_current_iter, glob_max_trunc_err,
glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug2, djd_debug,
glob_max_minutes, glob_look_poles, glob_clock_start_sec, days_in_year,
glob_small_float, glob_relerr, min_in_hour, glob_html_log,
glob_optimal_expect_sec, glob_log10normmin, glob_smallish_float,
glob_not_yet_finished, MAX_UNCHANGED, glob_start,
glob_optimal_clock_start_sec, glob_abserr, glob_orig_start_sec,
glob_max_hours, glob_dump_analytic, glob_optimal_done,
glob_reached_optimal_h, glob_iter, glob_warned, glob_hmin, glob_almost_1,
glob_dump, glob_subiter_method, array_const_2D0, array_const_0D0,
array_const_5, array_const_1, array_pole, array_y1_init, array_y2_init,
array_x, array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_last_rel_error, array_y2_set_initial,
array_y2_higher_work2, array_poles, array_y1_higher_work, array_fact_2,
array_y2_higher, array_real_pole, array_y2_higher_work,
array_y1_set_initial, array_y1_higher_work2, array_y1_higher,
array_complex_pole, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(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");
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;
return hnew
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> INFO,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_max_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_disp_incr,
> hours_in_day,
> sec_in_minute,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_log10_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> years_in_century,
> glob_display_flag,
> glob_percent_done,
> glob_log10relerr,
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug2,
> djd_debug,
> glob_max_minutes,
> glob_look_poles,
> glob_clock_start_sec,
> days_in_year,
> glob_small_float,
> glob_relerr,
> min_in_hour,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_log10normmin,
> glob_smallish_float,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_orig_start_sec,
> glob_max_hours,
> glob_dump_analytic,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_iter,
> glob_warned,
> glob_hmin,
> glob_almost_1,
> glob_dump,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_0D0,
> array_const_5,
> array_const_1,
> #END CONST
> array_pole,
> array_y1_init,
> array_y2_init,
> array_x,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_y2_set_initial,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher_work,
> array_fact_2,
> array_y2_higher,
> array_real_pole,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_y1_higher,
> array_complex_pole,
> 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_iolevel, glob_max_terms, DEBUGL, ALWAYS, INFO,
glob_log10abserr, glob_warned2, glob_unchanged_h_cnt,
centuries_in_millinium, glob_max_opt_iter, glob_max_sec, glob_optimal_start,
glob_max_rel_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float,
glob_hmax, glob_h, glob_disp_incr, hours_in_day, sec_in_minute,
glob_normmax, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr,
glob_hmin_init, glob_not_yet_start_msg, years_in_century, glob_display_flag,
glob_percent_done, glob_log10relerr, glob_current_iter, glob_max_trunc_err,
glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug2, djd_debug,
glob_max_minutes, glob_look_poles, glob_clock_start_sec, days_in_year,
glob_small_float, glob_relerr, min_in_hour, glob_html_log,
glob_optimal_expect_sec, glob_log10normmin, glob_smallish_float,
glob_not_yet_finished, MAX_UNCHANGED, glob_start,
glob_optimal_clock_start_sec, glob_abserr, glob_orig_start_sec,
glob_max_hours, glob_dump_analytic, glob_optimal_done,
glob_reached_optimal_h, glob_iter, glob_warned, glob_hmin, glob_almost_1,
glob_dump, glob_subiter_method, array_const_2D0, array_const_0D0,
array_const_5, array_const_1, array_pole, array_y1_init, array_y2_init,
array_x, array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_last_rel_error, array_y2_set_initial,
array_y2_higher_work2, array_poles, array_y1_higher_work, array_fact_2,
array_y2_higher, array_real_pole, array_y2_higher_work,
array_y1_set_initial, array_y1_higher_work2, array_y1_higher,
array_complex_pole, 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_iolevel,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> INFO,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_max_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_disp_incr,
> hours_in_day,
> sec_in_minute,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_log10_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> years_in_century,
> glob_display_flag,
> glob_percent_done,
> glob_log10relerr,
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug2,
> djd_debug,
> glob_max_minutes,
> glob_look_poles,
> glob_clock_start_sec,
> days_in_year,
> glob_small_float,
> glob_relerr,
> min_in_hour,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_log10normmin,
> glob_smallish_float,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_orig_start_sec,
> glob_max_hours,
> glob_dump_analytic,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_iter,
> glob_warned,
> glob_hmin,
> glob_almost_1,
> glob_dump,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_0D0,
> array_const_5,
> array_const_1,
> #END CONST
> array_pole,
> array_y1_init,
> array_y2_init,
> array_x,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_y2_set_initial,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher_work,
> array_fact_2,
> array_y2_higher,
> array_real_pole,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_y1_higher,
> array_complex_pole,
> 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 ((omniabs(array_y2_higher[1,m]) < glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float) or (omniabs(array_y2_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_y2_higher[1,m]/array_y2_higher[1,m-1];
> rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(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
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #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 ((omniabs(array_y1_higher[1,m]) < glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float) or (omniabs(array_y1_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_y1_higher[1,m]/array_y1_higher[1,m-1];
> rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(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[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #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 (omniabs(array_y2_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 ((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_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_y2_higher[1,m])/(array_y2_higher[1,m-1]);
> rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]);
> rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]);
> rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]);
> rm4 := (array_y2_higher[1,m-4])/(array_y2_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 ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(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 (omniabs(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 (omniabs(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
> #TOP RADII COMPLEX EQ = 2
> #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 (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif ((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]);
> rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]);
> rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]);
> rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]);
> rm4 := (array_y1_higher[1,m-4])/(array_y1_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 ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> 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 (omniabs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4
> ;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3
> ;
> #BOTTOM RADII COMPLEX EQ = 2
> 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 3
> 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 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 3
> 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 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 3
> 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 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 3
> 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 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 3
> 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 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found ) then # if number 3
> 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 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 2
> if ( not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float)))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found ) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 2
> 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 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if (array_pole[1] > array_poles[2,1]) then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 2
> #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_iolevel, glob_max_terms, DEBUGL, ALWAYS, INFO,
glob_log10abserr, glob_warned2, glob_unchanged_h_cnt,
centuries_in_millinium, glob_max_opt_iter, glob_max_sec, glob_optimal_start,
glob_max_rel_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float,
glob_hmax, glob_h, glob_disp_incr, hours_in_day, sec_in_minute,
glob_normmax, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr,
glob_hmin_init, glob_not_yet_start_msg, years_in_century, glob_display_flag,
glob_percent_done, glob_log10relerr, glob_current_iter, glob_max_trunc_err,
glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug2, djd_debug,
glob_max_minutes, glob_look_poles, glob_clock_start_sec, days_in_year,
glob_small_float, glob_relerr, min_in_hour, glob_html_log,
glob_optimal_expect_sec, glob_log10normmin, glob_smallish_float,
glob_not_yet_finished, MAX_UNCHANGED, glob_start,
glob_optimal_clock_start_sec, glob_abserr, glob_orig_start_sec,
glob_max_hours, glob_dump_analytic, glob_optimal_done,
glob_reached_optimal_h, glob_iter, glob_warned, glob_hmin, glob_almost_1,
glob_dump, glob_subiter_method, array_const_2D0, array_const_0D0,
array_const_5, array_const_1, array_pole, array_y1_init, array_y2_init,
array_x, array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_last_rel_error, array_y2_set_initial,
array_y2_higher_work2, array_poles, array_y1_higher_work, array_fact_2,
array_y2_higher, array_real_pole, array_y2_higher_work,
array_y1_set_initial, array_y1_higher_work2, array_y1_higher,
array_complex_pole, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y2_higher[1, m]) < glob_small_float
or omniabs(array_y2_higher[1, m - 1]) < glob_small_float or
omniabs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(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;
m := n - 2;
while 10 <= m and (omniabs(array_y1_higher[1, m]) < glob_small_float
or omniabs(array_y1_higher[1, m - 1]) < glob_small_float or
omniabs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y2_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 <= omniabs(array_y2_higher[1, m]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_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 omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(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 < omniabs(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 < omniabs(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;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y1_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[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= omniabs(array_y1_higher[1, m]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_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 omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < omniabs(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 < omniabs(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[2, 1] := rad_c;
array_complex_pole[2, 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;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 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[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 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[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 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[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 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[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 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;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> INFO,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_max_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_disp_incr,
> hours_in_day,
> sec_in_minute,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_log10_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> years_in_century,
> glob_display_flag,
> glob_percent_done,
> glob_log10relerr,
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug2,
> djd_debug,
> glob_max_minutes,
> glob_look_poles,
> glob_clock_start_sec,
> days_in_year,
> glob_small_float,
> glob_relerr,
> min_in_hour,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_log10normmin,
> glob_smallish_float,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_orig_start_sec,
> glob_max_hours,
> glob_dump_analytic,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_iter,
> glob_warned,
> glob_hmin,
> glob_almost_1,
> glob_dump,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_0D0,
> array_const_5,
> array_const_1,
> #END CONST
> array_pole,
> array_y1_init,
> array_y2_init,
> array_x,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_y2_set_initial,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher_work,
> array_fact_2,
> array_y2_higher,
> array_real_pole,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_y1_higher,
> array_complex_pole,
> glob_last;
>
> local iii;
>
>
>
> if ( not glob_initial_pass) then # if number 3
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2
> ;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 3
> ;
>
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, INFO,
glob_log10abserr, glob_warned2, glob_unchanged_h_cnt,
centuries_in_millinium, glob_max_opt_iter, glob_max_sec, glob_optimal_start,
glob_max_rel_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float,
glob_hmax, glob_h, glob_disp_incr, hours_in_day, sec_in_minute,
glob_normmax, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr,
glob_hmin_init, glob_not_yet_start_msg, years_in_century, glob_display_flag,
glob_percent_done, glob_log10relerr, glob_current_iter, glob_max_trunc_err,
glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug2, djd_debug,
glob_max_minutes, glob_look_poles, glob_clock_start_sec, days_in_year,
glob_small_float, glob_relerr, min_in_hour, glob_html_log,
glob_optimal_expect_sec, glob_log10normmin, glob_smallish_float,
glob_not_yet_finished, MAX_UNCHANGED, glob_start,
glob_optimal_clock_start_sec, glob_abserr, glob_orig_start_sec,
glob_max_hours, glob_dump_analytic, glob_optimal_done,
glob_reached_optimal_h, glob_iter, glob_warned, glob_hmin, glob_almost_1,
glob_dump, glob_subiter_method, array_const_2D0, array_const_0D0,
array_const_5, array_const_1, array_pole, array_y1_init, array_y2_init,
array_x, array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_last_rel_error, array_y2_set_initial,
array_y2_higher_work2, array_poles, array_y1_higher_work, array_fact_2,
array_y2_higher, array_real_pole, array_y2_higher_work,
array_y1_set_initial, array_y1_higher_work2, array_y1_higher,
array_complex_pole, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y2[iii]) then
array_norms[iii] := omniabs(array_y2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y1[iii]) then
array_norms[iii] := omniabs(array_y1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> INFO,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_max_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_disp_incr,
> hours_in_day,
> sec_in_minute,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_log10_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> years_in_century,
> glob_display_flag,
> glob_percent_done,
> glob_log10relerr,
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug2,
> djd_debug,
> glob_max_minutes,
> glob_look_poles,
> glob_clock_start_sec,
> days_in_year,
> glob_small_float,
> glob_relerr,
> min_in_hour,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_log10normmin,
> glob_smallish_float,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_orig_start_sec,
> glob_max_hours,
> glob_dump_analytic,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_iter,
> glob_warned,
> glob_hmin,
> glob_almost_1,
> glob_dump,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_0D0,
> array_const_5,
> array_const_1,
> #END CONST
> array_pole,
> array_y1_init,
> array_y2_init,
> array_x,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_y2_set_initial,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher_work,
> array_fact_2,
> array_y2_higher,
> array_real_pole,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_y1_higher,
> array_complex_pole,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
>
>
>
>
>
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D0[1] + array_y1[1];
> #emit pre sub FULL - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] - array_const_2D0[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1
> array_tmp4[1] := array_y2_higher[6,1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[2,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp1[2] := array_y1[2];
> #emit pre sub FULL CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2
> array_tmp4[2] := array_y2_higher[6,2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[2,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp1[3] := array_y1[3];
> #emit pre sub FULL CONST $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3
> array_tmp4[3] := array_y2_higher[6,3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[2,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp1[4] := array_y1[4];
> #emit pre sub FULL CONST $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4
> array_tmp4[4] := array_y2_higher[6,4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[2,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp1[5] := array_y1[5];
> #emit pre sub FULL CONST $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5
> array_tmp4[5] := array_y2_higher[6,5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[2,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_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 NOT FULL - FULL add $eq_no = 1
> array_tmp1[kkk] := array_y1[kkk];
> #emit FULL - NOT FULL sub $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y2_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y2[kkk + order_d] := temporary;
> array_y2_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_y2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> #emit diff $eq_no = 2
> array_tmp4[kkk] := array_y2_higher[6,kkk];
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2
> temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y1[kkk + order_d] := temporary;
> array_y1_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_y1_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
>
> #BOTTOM ATOMALL ???
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, INFO,
glob_log10abserr, glob_warned2, glob_unchanged_h_cnt,
centuries_in_millinium, glob_max_opt_iter, glob_max_sec, glob_optimal_start,
glob_max_rel_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float,
glob_hmax, glob_h, glob_disp_incr, hours_in_day, sec_in_minute,
glob_normmax, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr,
glob_hmin_init, glob_not_yet_start_msg, years_in_century, glob_display_flag,
glob_percent_done, glob_log10relerr, glob_current_iter, glob_max_trunc_err,
glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug2, djd_debug,
glob_max_minutes, glob_look_poles, glob_clock_start_sec, days_in_year,
glob_small_float, glob_relerr, min_in_hour, glob_html_log,
glob_optimal_expect_sec, glob_log10normmin, glob_smallish_float,
glob_not_yet_finished, MAX_UNCHANGED, glob_start,
glob_optimal_clock_start_sec, glob_abserr, glob_orig_start_sec,
glob_max_hours, glob_dump_analytic, glob_optimal_done,
glob_reached_optimal_h, glob_iter, glob_warned, glob_hmin, glob_almost_1,
glob_dump, glob_subiter_method, array_const_2D0, array_const_0D0,
array_const_5, array_const_1, array_pole, array_y1_init, array_y2_init,
array_x, array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_last_rel_error, array_y2_set_initial,
array_y2_higher_work2, array_poles, array_y1_higher_work, array_fact_2,
array_y2_higher, array_real_pole, array_y2_higher_work,
array_y1_set_initial, array_y1_higher_work2, array_y1_higher,
array_complex_pole, glob_last;
array_tmp1[1] := array_const_0D0[1] + array_y1[1];
array_tmp2[1] := array_tmp1[1] - array_const_2D0[1];
if not array_y2_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp4[1] := array_y2_higher[6, 1];
if not array_y1_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_y1[2];
array_tmp2[2] := array_tmp1[2];
if not array_y2_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp4[2] := array_y2_higher[6, 2];
if not array_y1_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_y1[3];
array_tmp2[3] := array_tmp1[3];
if not array_y2_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp4[3] := array_y2_higher[6, 3];
if not array_y1_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_y1[4];
array_tmp2[4] := array_tmp1[4];
if not array_y2_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp4[4] := array_y2_higher[6, 4];
if not array_y1_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_y1[5];
array_tmp2[5] := array_tmp1[5];
if not array_y2_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 5] := temporary
end if
end if;
kkk := 6;
array_tmp4[5] := array_y2_higher[6, 5];
if not array_y1_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_y1[kkk];
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y2[kkk + order_d] := temporary;
array_y2_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_y2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
array_tmp4[kkk] := array_y2_higher[6, kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y1_set_initial[2, kkk + order_d] then
temporary := array_tmp4[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y1[kkk + order_d] := temporary;
array_y1_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_y1_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_minute, 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_minute * 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_minute;
> 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_minute, years_in_century;
secs := secs_in;
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*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_minute;
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_minute, 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_minute * 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_minute;
> 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_minute, years_in_century;
secs := convfloat(secs_in);
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*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_minute;
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_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
>
>
>
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (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_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < 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 (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 < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 17
> factorial_2 := proc(nnn)
> local ret;
>
>
>
> ret := nnn!;
>
> # End Function number 17
> end;
factorial_2 := proc(nnn) local ret; ret := nnn! end proc
> # Begin Function number 18
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
>
>
>
> if (nnn <= glob_max_terms) then # if number 13
> if (array_fact_1[nnn] = 0) then # if number 14
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 18
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 19
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
>
>
>
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13
> if (array_fact_2[mmm,nnn] = 0) then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 19
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 20
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 21
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 21
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> return(2.0 + sin(x));
> end;
exact_soln_y1 := proc(x) return 2.0 + sin(x) end proc
> exact_soln_y2 := proc(x)
> return(2.0 - cos(x));
> end;
exact_soln_y2 := proc(x) return 2.0 - cos(x) end proc
> exact_soln_y2p := proc(x)
> return(sin(x));
> end;
exact_soln_y2p := proc(x) return sin(x) end proc
> exact_soln_y2pp := proc(x)
> return(cos(x));
> end;
exact_soln_y2pp := proc(x) return cos(x) end proc
> exact_soln_y2ppp := proc(x)
> return(-sin(x));
> end;
exact_soln_y2ppp := proc(x) return -sin(x) end proc
> exact_soln_y2pppp := proc(x)
> return(-cos(x));
> end;
exact_soln_y2pppp := proc(x) return -cos(x) end proc
>
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp,subiter;
> global
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> INFO,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_max_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_disp_incr,
> hours_in_day,
> sec_in_minute,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_log10_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> years_in_century,
> glob_display_flag,
> glob_percent_done,
> glob_log10relerr,
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug2,
> djd_debug,
> glob_max_minutes,
> glob_look_poles,
> glob_clock_start_sec,
> days_in_year,
> glob_small_float,
> glob_relerr,
> min_in_hour,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_log10normmin,
> glob_smallish_float,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_orig_start_sec,
> glob_max_hours,
> glob_dump_analytic,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_iter,
> glob_warned,
> glob_hmin,
> glob_almost_1,
> glob_dump,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_0D0,
> array_const_5,
> array_const_1,
> #END CONST
> array_pole,
> array_y1_init,
> array_y2_init,
> array_x,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_y2_set_initial,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher_work,
> array_fact_2,
> array_y2_higher,
> array_real_pole,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_y1_higher,
> array_complex_pole,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_max_terms := 30;
> DEBUGL := 3;
> ALWAYS := 1;
> INFO := 2;
> glob_log10abserr := 0.0;
> glob_warned2 := false;
> glob_unchanged_h_cnt := 0;
> centuries_in_millinium := 10;
> glob_max_opt_iter := 10;
> glob_max_sec := 10000.0;
> glob_optimal_start := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_iter := 1000;
> glob_log10_relerr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_hmax := 1.0;
> glob_h := 0.1;
> glob_disp_incr := 0.1;
> hours_in_day := 24;
> sec_in_minute := 60;
> glob_normmax := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_no_eqs := 0;
> glob_log10_abserr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_not_yet_start_msg := true;
> years_in_century := 100;
> glob_display_flag := true;
> glob_percent_done := 0.0;
> glob_log10relerr := 0.0;
> glob_current_iter := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_initial_pass := true;
> glob_clock_sec := 0.0;
> djd_debug2 := true;
> djd_debug := true;
> glob_max_minutes := 0.0;
> glob_look_poles := false;
> glob_clock_start_sec := 0.0;
> days_in_year := 365;
> glob_small_float := 0.1e-50;
> glob_relerr := 0.1e-10;
> min_in_hour := 60;
> glob_html_log := true;
> glob_optimal_expect_sec := 0.1;
> glob_log10normmin := 0.1;
> glob_smallish_float := 0.1e-100;
> glob_not_yet_finished := true;
> MAX_UNCHANGED := 10;
> glob_start := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_abserr := 0.1e-10;
> glob_orig_start_sec := 0.0;
> glob_max_hours := 0.0;
> glob_dump_analytic := false;
> glob_optimal_done := false;
> glob_reached_optimal_h := false;
> glob_iter := 0;
> glob_warned := false;
> glob_hmin := 0.00000000001;
> glob_almost_1 := 0.9990;
> glob_dump := false;
> glob_subiter_method := 3;
> #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 := 2;
> 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/mtest9_revpostode.ode#################");
> omniout_str(ALWAYS,"diff(y2,x,1) = y1 - 2.0;");
> omniout_str(ALWAYS,"diff(y1,x,1) = diff(y2,x,5);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.5;");
> omniout_str(ALWAYS,"x_end := 10.0;");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
> omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);");
> omniout_str(ALWAYS,"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);");
> omniout_str(ALWAYS,"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"glob_subiter_method := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 1;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return(2.0 + sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(2.0 - cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return(sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
> omniout_str(ALWAYS,"return(cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)");
> omniout_str(ALWAYS,"return(-sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)");
> omniout_str(ALWAYS,"return(-cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_pole:= Array(0..(max_terms + 1),[]);
> array_y1_init:= Array(0..(max_terms + 1),[]);
> array_y2_init:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y2:= Array(0..(max_terms + 1),[]);
> array_y1:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work2 := Array(0..(6+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher := Array(0..(6+ 1) ,(0..max_terms+ 1),[]);
> array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_y2_higher_work := Array(0..(6+ 1) ,(0..max_terms+ 1),[]);
> array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1[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_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=6) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_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 <= 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_y1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=6) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_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 <= 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 <=6) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_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 <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_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_y1_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 <= 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
> ;
> #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_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_y1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y2[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_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_5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_5[1] := 5;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.5;
> x_end := 10.0;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> array_y2_init[1 + 1] := exact_soln_y2p(x_start);
> array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
> array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);
> array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> glob_subiter_method := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 1;
> #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 := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y2_set_initial[1,1] := true;
> array_y2_set_initial[1,2] := true;
> array_y2_set_initial[1,3] := true;
> array_y2_set_initial[1,4] := true;
> array_y2_set_initial[1,5] := true;
> array_y2_set_initial[1,6] := false;
> array_y2_set_initial[1,7] := false;
> array_y2_set_initial[1,8] := false;
> array_y2_set_initial[1,9] := false;
> array_y2_set_initial[1,10] := false;
> array_y2_set_initial[1,11] := false;
> array_y2_set_initial[1,12] := false;
> array_y2_set_initial[1,13] := false;
> array_y2_set_initial[1,14] := false;
> array_y2_set_initial[1,15] := false;
> array_y2_set_initial[1,16] := false;
> array_y2_set_initial[1,17] := false;
> array_y2_set_initial[1,18] := false;
> array_y2_set_initial[1,19] := false;
> array_y2_set_initial[1,20] := false;
> array_y2_set_initial[1,21] := false;
> array_y2_set_initial[1,22] := false;
> array_y2_set_initial[1,23] := false;
> array_y2_set_initial[1,24] := false;
> array_y2_set_initial[1,25] := false;
> array_y2_set_initial[1,26] := false;
> array_y2_set_initial[1,27] := false;
> array_y2_set_initial[1,28] := false;
> array_y2_set_initial[1,29] := false;
> array_y2_set_initial[1,30] := false;
> array_y1_set_initial[2,1] := true;
> array_y1_set_initial[2,2] := false;
> array_y1_set_initial[2,3] := false;
> array_y1_set_initial[2,4] := false;
> array_y1_set_initial[2,5] := false;
> array_y1_set_initial[2,6] := false;
> array_y1_set_initial[2,7] := false;
> array_y1_set_initial[2,8] := false;
> array_y1_set_initial[2,9] := false;
> array_y1_set_initial[2,10] := false;
> array_y1_set_initial[2,11] := false;
> array_y1_set_initial[2,12] := false;
> array_y1_set_initial[2,13] := false;
> array_y1_set_initial[2,14] := false;
> array_y1_set_initial[2,15] := false;
> array_y1_set_initial[2,16] := false;
> array_y1_set_initial[2,17] := false;
> array_y1_set_initial[2,18] := false;
> array_y1_set_initial[2,19] := false;
> array_y1_set_initial[2,20] := false;
> array_y1_set_initial[2,21] := false;
> array_y1_set_initial[2,22] := false;
> array_y1_set_initial[2,23] := false;
> array_y1_set_initial[2,24] := false;
> array_y1_set_initial[2,25] := false;
> array_y1_set_initial[2,26] := false;
> array_y1_set_initial[2,27] := false;
> array_y1_set_initial[2,28] := false;
> array_y1_set_initial[2,29] := false;
> array_y1_set_initial[2,30] := false;
> if (glob_html_log) then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #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 := 5;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_init[term_no] * expt(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_y2_higher[r_order,term_no] := array_y2_init[it]* expt(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
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_init[term_no] * expt(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_y1_higher[r_order,term_no] := array_y1_init[it]* expt(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();
> if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> 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;
> if (glob_subiter_method = 1 ) then # if number 3
> atomall();
> elif (glob_subiter_method = 2 ) then # if number 4
> subiter := 1;
> while (subiter <= 2) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while (subiter <= 2 + glob_max_terms) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> fi;# end if 4
> ;
> if (glob_look_poles) then # if number 4
> #left paren 0004C
> check_for_pole();
> fi;# end if 4
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y2
> order_diff := 5;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 6;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[6,iii] := array_y2_higher[6,iii] / expt(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 := 6;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 5;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / expt(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 := 5;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 5;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / expt(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 := 5;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(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 := 4;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(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 := 4;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(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 := 4;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(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 := 3;
> calc_term := 4;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(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 := 3;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(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 := 3;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(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 := 3;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 5;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(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 := 5;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(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 := 4;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(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 := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(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 := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 6;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(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 := 6;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 5;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(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 := 5;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(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 := 4;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(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 := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y2_higher[ord,term_no] := array_y2_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
> #Jump Series array_y1
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #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_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y1_higher[ord,term_no] := array_y1_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 4
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 4
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 4
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff(y2,x,1) = y1 - 2.0;");
> omniout_str(INFO,"diff(y1,x,1) = diff(y2,x,5);");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 4
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-08-12T23:36:27-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest9_rev")
> ;
> logitem_str(html_log_file,"diff(y2,x,1) = y1 - 2.0;")
> ;
> 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 5
> 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 5
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 5
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 5
> ;
> log_revs(html_log_file," 119 | ")
> ;
> logitem_str(html_log_file,"mtest9_rev diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest9_rev maple results")
> ;
> logitem_str(html_log_file,"1st test with c++")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff(y1,x,1) = diff(y2,x,5);")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 5
> 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 5
> ;
> logditto(html_log_file)
> ;
> if (glob_percent_done < 100.0) then # if number 5
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 5
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 4
> ;
> if (glob_html_log) then # if number 4
> fclose(html_log_file);
> fi;# end if 4
> ;
> ;;
> #END OUTFILEMAIN
>
> # End Function number 8
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp, subiter;
global DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, INFO,
glob_log10abserr, glob_warned2, glob_unchanged_h_cnt,
centuries_in_millinium, glob_max_opt_iter, glob_max_sec, glob_optimal_start,
glob_max_rel_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float,
glob_hmax, glob_h, glob_disp_incr, hours_in_day, sec_in_minute,
glob_normmax, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr,
glob_hmin_init, glob_not_yet_start_msg, years_in_century, glob_display_flag,
glob_percent_done, glob_log10relerr, glob_current_iter, glob_max_trunc_err,
glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug2, djd_debug,
glob_max_minutes, glob_look_poles, glob_clock_start_sec, days_in_year,
glob_small_float, glob_relerr, min_in_hour, glob_html_log,
glob_optimal_expect_sec, glob_log10normmin, glob_smallish_float,
glob_not_yet_finished, MAX_UNCHANGED, glob_start,
glob_optimal_clock_start_sec, glob_abserr, glob_orig_start_sec,
glob_max_hours, glob_dump_analytic, glob_optimal_done,
glob_reached_optimal_h, glob_iter, glob_warned, glob_hmin, glob_almost_1,
glob_dump, glob_subiter_method, array_const_2D0, array_const_0D0,
array_const_5, array_const_1, array_pole, array_y1_init, array_y2_init,
array_x, array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_last_rel_error, array_y2_set_initial,
array_y2_higher_work2, array_poles, array_y1_higher_work, array_fact_2,
array_y2_higher, array_real_pole, array_y2_higher_work,
array_y1_set_initial, array_y1_higher_work2, array_y1_higher,
array_complex_pole, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_max_terms := 30;
DEBUGL := 3;
ALWAYS := 1;
INFO := 2;
glob_log10abserr := 0.;
glob_warned2 := false;
glob_unchanged_h_cnt := 0;
centuries_in_millinium := 10;
glob_max_opt_iter := 10;
glob_max_sec := 10000.0;
glob_optimal_start := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_iter := 1000;
glob_log10_relerr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_hmax := 1.0;
glob_h := 0.1;
glob_disp_incr := 0.1;
hours_in_day := 24;
sec_in_minute := 60;
glob_normmax := 0.;
glob_curr_iter_when_opt := 0;
glob_no_eqs := 0;
glob_log10_abserr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_not_yet_start_msg := true;
years_in_century := 100;
glob_display_flag := true;
glob_percent_done := 0.;
glob_log10relerr := 0.;
glob_current_iter := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_initial_pass := true;
glob_clock_sec := 0.;
djd_debug2 := true;
djd_debug := true;
glob_max_minutes := 0.;
glob_look_poles := false;
glob_clock_start_sec := 0.;
days_in_year := 365;
glob_small_float := 0.1*10^(-50);
glob_relerr := 0.1*10^(-10);
min_in_hour := 60;
glob_html_log := true;
glob_optimal_expect_sec := 0.1;
glob_log10normmin := 0.1;
glob_smallish_float := 0.1*10^(-100);
glob_not_yet_finished := true;
MAX_UNCHANGED := 10;
glob_start := 0;
glob_optimal_clock_start_sec := 0.;
glob_abserr := 0.1*10^(-10);
glob_orig_start_sec := 0.;
glob_max_hours := 0.;
glob_dump_analytic := false;
glob_optimal_done := false;
glob_reached_optimal_h := false;
glob_iter := 0;
glob_warned := false;
glob_hmin := 0.1*10^(-10);
glob_almost_1 := 0.9990;
glob_dump := false;
glob_subiter_method := 3;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 2;
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/mtest9_revpostode.ode#################");
omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;");
omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.5;");
omniout_str(ALWAYS, "x_end := 10.0;");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
;
omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);")
;
omniout_str(ALWAYS,
"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);");
omniout_str(ALWAYS,
"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "glob_subiter_method := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 1;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return(2.0 + sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(2.0 - cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return(sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
omniout_str(ALWAYS, "return(cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)");
omniout_str(ALWAYS, "return(-sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)");
omniout_str(ALWAYS, "return(-cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_pole := Array(0 .. max_terms + 1, []);
array_y1_init := Array(0 .. max_terms + 1, []);
array_y2_init := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y2 := Array(0 .. max_terms + 1, []);
array_y1 := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y2_higher_work2 := Array(0 .. 7, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_y2_higher := Array(0 .. 7, 0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 3, 0 .. 4, []);
array_y2_higher_work := Array(0 .. 7, 0 .. max_terms + 1, []);
array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 3, 0 .. 4, []);
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1[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_last_rel_error[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y2_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 6 do
term := 1;
while term <= max_terms do
array_y2_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 <= 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_y1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 6 do
term := 1;
while term <= max_terms do
array_y2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 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 <= 6 do
term := 1;
while term <= max_terms do
array_y2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_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_y1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[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_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_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[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_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_5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_5[term] := 0.; term := term + 1
end do;
array_const_5[1] := 5;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.5;
x_end := 10.0;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
array_y2_init[2] := exact_soln_y2p(x_start);
array_y2_init[3] := exact_soln_y2pp(x_start);
array_y2_init[4] := exact_soln_y2ppp(x_start);
array_y2_init[5] := exact_soln_y2pppp(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_subiter_method := 3;
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 1;
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 := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
chk_data();
array_y2_set_initial[1, 1] := true;
array_y2_set_initial[1, 2] := true;
array_y2_set_initial[1, 3] := true;
array_y2_set_initial[1, 4] := true;
array_y2_set_initial[1, 5] := true;
array_y2_set_initial[1, 6] := false;
array_y2_set_initial[1, 7] := false;
array_y2_set_initial[1, 8] := false;
array_y2_set_initial[1, 9] := false;
array_y2_set_initial[1, 10] := false;
array_y2_set_initial[1, 11] := false;
array_y2_set_initial[1, 12] := false;
array_y2_set_initial[1, 13] := false;
array_y2_set_initial[1, 14] := false;
array_y2_set_initial[1, 15] := false;
array_y2_set_initial[1, 16] := false;
array_y2_set_initial[1, 17] := false;
array_y2_set_initial[1, 18] := false;
array_y2_set_initial[1, 19] := false;
array_y2_set_initial[1, 20] := false;
array_y2_set_initial[1, 21] := false;
array_y2_set_initial[1, 22] := false;
array_y2_set_initial[1, 23] := false;
array_y2_set_initial[1, 24] := false;
array_y2_set_initial[1, 25] := false;
array_y2_set_initial[1, 26] := false;
array_y2_set_initial[1, 27] := false;
array_y2_set_initial[1, 28] := false;
array_y2_set_initial[1, 29] := false;
array_y2_set_initial[1, 30] := false;
array_y1_set_initial[2, 1] := true;
array_y1_set_initial[2, 2] := false;
array_y1_set_initial[2, 3] := false;
array_y1_set_initial[2, 4] := false;
array_y1_set_initial[2, 5] := false;
array_y1_set_initial[2, 6] := false;
array_y1_set_initial[2, 7] := false;
array_y1_set_initial[2, 8] := false;
array_y1_set_initial[2, 9] := false;
array_y1_set_initial[2, 10] := false;
array_y1_set_initial[2, 11] := false;
array_y1_set_initial[2, 12] := false;
array_y1_set_initial[2, 13] := false;
array_y1_set_initial[2, 14] := false;
array_y1_set_initial[2, 15] := false;
array_y1_set_initial[2, 16] := false;
array_y1_set_initial[2, 17] := false;
array_y1_set_initial[2, 18] := false;
array_y1_set_initial[2, 19] := false;
array_y1_set_initial[2, 20] := false;
array_y1_set_initial[2, 21] := false;
array_y1_set_initial[2, 22] := false;
array_y1_set_initial[2, 23] := false;
array_y1_set_initial[2, 24] := false;
array_y1_set_initial[2, 25] := false;
array_y1_set_initial[2, 26] := false;
array_y1_set_initial[2, 27] := false;
array_y1_set_initial[2, 28] := false;
array_y1_set_initial[2, 29] := false;
array_y1_set_initial[2, 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 := 5;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*
expt(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_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(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_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(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();
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_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;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 2 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
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 := 5;
ord := 6;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[6, iii] := array_y2_higher[6, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 6;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 5;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 5;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 5;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 5;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 4;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 4;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 4;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 3;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 3;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 3;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 5;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 5;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 6;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 6;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 5;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 5;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
term_no := glob_max_terms;
while 1 <= term_no do
array_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
expt(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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
term_no := glob_max_terms;
while 1 <= term_no do
array_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_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(y2,x,1) = y1 - 2.0;");
omniout_str(INFO, "diff(y1,x,1) = diff(y2,x,5);");
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, "2012-08-12T23:36:27-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest9_rev");
logitem_str(html_log_file, "diff(y2,x,1) = y1 - 2.0;");
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, " 119 | ");
logitem_str(html_log_file, "mtest9_rev diffeq.mxt");
logitem_str(html_log_file, "mtest9_rev maple results");
logitem_str(html_log_file, "1st test with c++");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 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;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest9_revpostode.ode#################
diff(y2,x,1) = y1 - 2.0;
diff(y1,x,1) = diff(y2,x,5);
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.5;
x_end := 10.0;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
array_y2_init[1 + 1] := exact_soln_y2p(x_start);
array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);
array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
glob_subiter_method := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 1;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(2.0 + sin(x));
end;
exact_soln_y2 := proc(x)
return(2.0 - cos(x));
end;
exact_soln_y2p := proc(x)
return(sin(x));
end;
exact_soln_y2pp := proc(x)
return(cos(x));
end;
exact_soln_y2ppp := proc(x)
return(-sin(x));
end;
exact_soln_y2pppp := proc(x)
return(-cos(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.5
y2[1] (analytic) = 1.1224174381096272838837184173962
y2[1] (numeric) = 1.1224174381096272838837184173962
absolute error = 0
relative error = 0 %
"good digits = ", -1
h = 1e-05
y1[1] (analytic) = 2.4794255386042030002732879352156
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0
relative error = 0 %
"good digits = ", -1
h = 1e-05
x[1] = 0.5
y2[1] (analytic) = 1.1224174381096272838837184173962
y2[1] (numeric) = 1.1224174381096272838837184173962
absolute error = 0
relative error = 0 %
"good digits = ", -1
h = 1e-05
y1[1] (analytic) = 2.4794255386042030002732879352156
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0
relative error = 0 %
"good digits = ", -1
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50001
y2[1] (analytic) = 1.1224222324088923741036176930462
y2[1] (numeric) = 1.1224222324088923741036176926467
absolute error = 3.995e-28
relative error = 3.5592666330442419607621867384583e-26 %
"good digits = ", 27
h = 1e-05
y1[1] (analytic) = 2.479434314405850480806678394328
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 8.7758016474805333904591124e-06
relative error = 0.00035394370387196517465434156954291 %
"good digits = ", 5
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50002
y2[1] (analytic) = 1.1224270267959152410818964164796
y2[1] (numeric) = 1.1224270267959152410818964036948
absolute error = 1.27848e-26
relative error = 1.1390317316659366367494933191236e-24 %
"good digits = ", 25
h = 1e-05
y1[1] (analytic) = 2.4794430901595545298998833339551
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 1.75515553515296265953987395e-05
relative error = 0.00070788296860647716066745198593803 %
"good digits = ", 5
h = 1e-05
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.49
NO POLE
NO POLE
x[1] = 0.50003
y2[1] (analytic) = 1.1224318212706954053798523049938
y2[1] (numeric) = 1.1224318212706954053798522079092
absolute error = 9.70846e-26
relative error = 8.6494874931549392314604213592582e-24 %
"good digits = ", 25
h = 1e-05
y1[1] (analytic) = 2.4794518658653142699775323565007
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 2.63272611112697042444212851e-05
relative error = 0.001061817794235809588896300381047 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50004
y2[1] (analytic) = 1.1224366158332323875500073461544
y2[1] (numeric) = 1.1224366158332323875500069370396
absolute error = 4.091148e-25
relative error = 3.6448810937648956007252078500415e-23 %
"good digits = ", 24
h = 1e-05
y1[1] (analytic) = 2.4794606415231288234690494952701
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 3.51029189258231957615600545e-05
relative error = 0.0014157481807922358127118646817542 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50005
y2[1] (analytic) = 1.1224414104835257081361078457399
y2[1] (numeric) = 1.1224414104835257081361065972168
absolute error = 1.2485231e-24
relative error = 1.1123280808591699917975157407833e-22 %
"good digits = ", 23
h = 1e-05
y1[1] (analytic) = 2.4794694171329973128086533022272
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 4.38785287943125353653670116e-05
relative error = 0.0017696741283080289079946886795967 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50006
y2[1] (analytic) = 1.1224462052215748876731244756871
y2[1] (numeric) = 1.1224462052215748876731213689528
absolute error = 3.1067343e-24
relative error = 2.7678246721736829776748308562343e-22 %
"good digits = ", 23
h = 1e-05
y1[1] (analytic) = 2.479478192694918860435356935751
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 5.26540907158601620690005354e-05
relative error = 0.0021235956368154616731304393721065 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.9MB, time=1.11
NO POLE
NO POLE
x[1] = 0.50007
y2[1] (analytic) = 1.1224510000473794466872523220381
y2[1] (numeric) = 1.1224510000473794466872456071405
absolute error = 6.7148976e-24
relative error = 5.9823525478765304199413033019012e-22 %
"good digits = ", 23
h = 1e-05
y1[1] (analytic) = 2.4794869682088925887929682483919
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 6.14296046895885196803131763e-05
relative error = 0.0024775127063468066290054645919845 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50008
y2[1] (analytic) = 1.122455794960938905695910932887
y2[1] (numeric) = 1.1224557949609389056958978410541
absolute error = 1.30918329e-23
relative error = 1.1663562127589702987089467615430e-21 %
"good digits = ", 22
h = 1e-05
y1[1] (analytic) = 2.479495743674917620330089874627
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 7.02050707146200568019394114e-05
relative error = 0.0028314253369343360190023508918322 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50009
y2[1] (analytic) = 1.1224605899622527852077443663289
y2[1] (numeric) = 1.1224605899622527852077207743489
absolute error = 2.35919800e-23
relative error = 2.1018092047929606539733033254184e-21 %
"good digits = ", 22
h = 1e-05
y1[1] (analytic) = 2.4795045190929930775001193186155
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 7.89804887900772268313833999e-05
relative error = 0.0031853335286103218089954817287952 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5001
y2[1] (analytic) = 1.1224653850513206057226212384082
y2[1] (numeric) = 1.1224653850513206057225812850611
absolute error = 3.99533471e-23
relative error = 3.5594279905721351037455693725130e-21 %
"good digits = ", 22
h = 1e-05
y1[1] (analytic) = 2.4795132944631180827612490419532
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 8.77558589150824879611067376e-05
relative error = 0.0035392372814070356873465959087753 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50011
y2[1] (analytic) = 1.1224701802281418877316347710696
y2[1] (numeric) = 1.1224701802281418877315704256082
absolute error = 6.43454614e-23
relative error = 5.7324873776978017431645753870461e-21 %
"good digits = ", 22
h = 1e-05
y1[1] (analytic) = 2.4795220697852917585764665514268
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 9.65311810887583031786162112e-05
relative error = 0.0038931365953567490649003463184343 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=3.9MB, time=1.72
NO POLE
NO POLE
x[1] = 0.50012
y2[1] (analytic) = 1.1224749754927161517171028401079
y2[1] (numeric) = 1.1224749754927161517170034227887
absolute error = 9.94173192e-23
relative error = 8.8569742195241597673021312393736e-21 %
"good digits = ", 22
h = 1e-05
y1[1] (analytic) = 2.4795308450595132274135544867676
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.000105306455310227140266551552
relative error = 0.0042470314704917330749798589288452 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50013
y2[1] (analytic) = 1.1224797708450429181525680231208
y2[1] (numeric) = 1.1224797708450429181524196777821
absolute error = 1.483453387e-22
relative error = 1.3215858544009245111008885871068e-20 %
"good digits = ", 21
h = 1e-05
y1[1] (analytic) = 2.4795396202857816117450907084046
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.000114081681578611471802773189
relative error = 0.004600921906844258573382292070781 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50014
y2[1] (analytic) = 1.1224845662851217075027976474608
y2[1] (numeric) = 1.1224845662851217075025827661492
absolute error = 2.148813116e-22
relative error = 1.9143364466128268561038839057737e-20 %
"good digits = ", 21
h = 1e-05
y1[1] (analytic) = 2.4795483954640960340484483852173
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0001228568598930337751604500017
relative error = 0.0049548079044465961383743959937303 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50015
y2[1] (analytic) = 1.122489361812952040223783838189
y2[1] (numeric) = 1.1224893618129520402234804378318
absolute error = 3.034003572e-22
relative error = 2.7029241213473312563366101893919e-20 %
"good digits = ", 21
h = 1e-05
y1[1] (analytic) = 2.479557170594455616805796082288
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0001316319902526165325081470724
relative error = 0.0053086894633310160706880727005611 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=3.9MB, time=2.34
NO POLE
NO POLE
x[1] = 0.50016
y2[1] (analytic) = 1.1224941574285334367627435660298
y2[1] (numeric) = 1.1224941574285334367623246171528
absolute error = 4.189488770e-22
relative error = 3.7323034086854344251475049158701e-20 %
"good digits = ", 21
h = 1e-05
y1[1] (analytic) = 2.4795659456768594825040978486537
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0001404070726564822308099134381
relative error = 0.0056625665835297883935159360618576 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50017
y2[1] (analytic) = 1.1224989531318654175581186953255
y2[1] (numeric) = 1.1224989531318654175575514028162
absolute error = 5.672925093e-22
relative error = 5.0538355311353006379301157396555e-20 %
"good digits = ", 21
h = 1e-05
y1[1] (analytic) = 2.479574720711306753635113305057
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0001491821071037533618253698414
relative error = 0.0060164392650751828525068721857212 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50018
y2[1] (analytic) = 1.1225037489229475030395760319929
y2[1] (numeric) = 1.122503748922947503038821067907
absolute error = 7.549640859e-22
relative error = 6.7257154964907232330767278629198e-20 %
"good digits = ", 21
h = 1e-05
y1[1] (analytic) = 2.4795834956977965526953977316975
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0001579570935935524221097964819
relative error = 0.0063703075079994689157616001035174 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50019
y2[1] (analytic) = 1.1225085448017792136280073714805
y2[1] (numeric) = 1.1225085448017792136270180598915
absolute error = 9.893115890e-22
relative error = 8.8133991815153611292734088557356e-20 %
"good digits = ", 21
h = 1e-05
y1[1] (analytic) = 2.4795922706363280021863021559814
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0001667320321250019130142207658
relative error = 0.0067241713123349157738282326788046 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5002
y2[1] (analytic) = 1.122513340768360069735529546726
y2[1] (numeric) = 1.1225133407683600697342510006169
absolute error = 1.2785461091e-21
relative error = 1.1390030413579187786875203485615e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.4796010455269002246139734402722
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0001755069226972243406855050566
relative error = 0.0070780306781137923396978378563839 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=3.9MB, time=2.93
NO POLE
NO POLE
x[1] = 0.50021
y2[1] (analytic) = 1.1225181368226895917654844761153
y2[1] (numeric) = 1.1225181368226895917638526863116
absolute error = 1.6317898037e-21
relative error = 1.4536868048464804456094573978165e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.4796098203695123424893543696396
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.000184281765309342216066434424
relative error = 0.0074318856053683672488000001345095 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50022
y2[1] (analytic) = 1.122522932964767300112439211442
y2[1] (numeric) = 1.1225229329647673001103800875851
absolute error = 2.0591238569e-21
relative error = 1.8343713045233881681904363510594e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.4796185951641634783281837396084
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0001930565599604780548958043928
relative error = 0.0077857360941309088589983823328401 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50023
y2[1] (analytic) = 1.1225277291945927151621859858683
y2[1] (numeric) = 1.1225277291945927151596143494279
absolute error = 2.5716364404e-21
relative error = 2.2909335542607348984429822144377e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.479627369910852754650996443907
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002018313066497543777085086914
relative error = 0.0081395821444336852505862876399874 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50024
y2[1] (analytic) = 1.122532525512165357291742261886
y2[1] (numeric) = 1.1225325255121653572885607912117
absolute error = 3.1814706743e-21
relative error = 2.8341901922605101955047085173875e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.4796361446095792939831235622154
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002106060053762937098356269998
relative error = 0.0084934237563089642262822219366202 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=3.9MB, time=3.52
NO POLE
NO POLE
x[1] = 0.50025
y2[1] (analytic) = 1.1225373219174847468693507792792
y2[1] (numeric) = 1.1225373219174847468654489066893
absolute error = 3.9018725899e-21
relative error = 3.4759401881043364404844490227396e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.4796449192603422188546924479126
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.000219380656139218581404512697
relative error = 0.0088472609297890133112254563900813 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50026
y2[1] (analytic) = 1.122542118410550404254479603087
y2[1] (numeric) = 1.1225421184105504042497323639945
absolute error = 4.7472390925e-21
relative error = 4.2290075487072096133884298968137e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.4796536938631406518006268158238
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002281552589376515273388806082
relative error = 0.0092010936649060997529715903366345 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50027
y2[1] (analytic) = 1.122546914991361849797822171568
y2[1] (numeric) = 1.1225469149913618497920890056423
absolute error = 5.7331659257e-21
relative error = 5.1072840245114543711778079340564e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.4796624684179737153606468299665
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002369298137707150873588947509
relative error = 0.0095549219616924905214881144150421 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50028
y2[1] (analytic) = 1.1225517116599186038412973441651
y2[1] (numeric) = 1.1225517116599186038344208485288
absolute error = 6.8764956363e-21
relative error = 6.1257718151190713532449932677428e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.4796712429248405320792691912968
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002457043206375318059812560812
relative error = 0.009908745820180452309149974003882 %
"good digits = ", 4
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=26.7MB, alloc=3.9MB, time=4.13
x[1] = 0.50029
y2[1] (analytic) = 1.1225565084162201867180494494711
y2[1] (numeric) = 1.122556508416220186709854083931
absolute error = 8.1953655401e-21
relative error = 7.3006262746296705526871710623495e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.4796800173837402245058072254549
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002544787795372242325192902393
relative error = 0.010262565240402251530735132922271 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5003
y2[1] (analytic) = 1.1225613052602661187524483331957
y2[1] (numeric) = 1.1225613052602661187427390775073
absolute error = 9.7092556884e-21
relative error = 8.6491986165057654875810979512255e-19 %
"good digits = ", 20
h = 1e-05
y1[1] (analytic) = 2.4796887917946719151943709705102
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002632531904689149210830352946
relative error = 0.010616380222390154323420137410111 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50031
y2[1] (analytic) = 1.1225661021920559202600894061327
y2[1] (numeric) = 1.1225661021920559202486503692969
absolute error = 1.14390368358e-20
relative error = 1.0190078618499861911384661163058e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.479697566157634726703867264706
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002720275534317264305793294904
relative error = 0.010970190766176426546775680387851 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50032
y2[1] (analytic) = 1.1225708992115891115477936921289
y2[1] (numeric) = 1.1225708992115891115343866737203
absolute error = 1.34070184086e-20
relative error = 1.1943137327019700502571650932494e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4797063404726277815979998342031
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002808018684247813247118989875
relative error = 0.011323996871793333782762165967528 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50033
y2[1] (analytic) = 1.122575696318865212913607876053
y2[1] (numeric) = 1.1225756963188652128979708795791
absolute error = 1.56369964739e-20
relative error = 1.3929569761020681114369312460497e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4797151147396502024452693808242
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002895761354472021719814456086
relative error = 0.011677798539273141335725274291684 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=3.9MB, time=4.73
NO POLE
NO POLE
x[1] = 0.50034
y2[1] (analytic) = 1.122580493513883744646804351766
y2[1] (numeric) = 1.1225804935138837446286500500558
absolute error = 1.81543017102e-20
relative error = 1.6171937616138056426769266082305e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4797238889587011118189736697964
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002983503544981115456857345808
relative error = 0.012031595768648114232391526591284 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50035
y2[1] (analytic) = 1.1225852907966442270278812700922
y2[1] (numeric) = 1.1225852907966442270068954227142
absolute error = 2.09858473780e-20
relative error = 1.8694211967722616387640576462941e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4797326631297796322972076174941
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003071245255766320239196822785
relative error = 0.012385388559950517221863850555367 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50036
y2[1] (analytic) = 1.1225900881671461803285625867913
y2[1] (numeric) = 1.1225900881671461803044024094991
absolute error = 2.41601772922e-20
relative error = 2.1521815974383260959406935851818e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4797414372528848864628633791814
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003158986486818861895754439658
relative error = 0.012739176913212614775617145976122 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50037
y2[1] (analytic) = 1.122594885625389124811798110531
y2[1] (numeric) = 1.1225948856253891247840905967365
absolute error = 2.77075137945e-20
relative error = 2.4681667580432948002410778846088e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4797502113280159969036304367535
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003246727238129966303425015379
relative error = 0.013092960828466671087493850649221 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=34.3MB, alloc=4.0MB, time=5.34
x[1] = 0.50038
y2[1] (analytic) = 1.122599683171372580731763550861
y2[1] (numeric) = 1.1225996831713725807001037451333
absolute error = 3.16598057277e-20
relative error = 2.8202222218930479063720883563726e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4797589853551720862119956864779
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003334467509690859387077512623
relative error = 0.013446740305744950073699506561664 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50039
y2[1] (analytic) = 1.122604480805096068333860566187
y2[1] (numeric) = 1.1226044808050960682978097897777
absolute error = 3.60507764093e-20
relative error = 3.2113515513001992402616865175045e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4797677593343522769852435267356
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.00034222073014927671195559152
relative error = 0.013800515345079715372798326375175 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5004
y2[1] (analytic) = 1.122609278526559107854716811747
y2[1] (numeric) = 1.1226092785265591078138008401388
absolute error = 4.09159716082e-20
relative error = 3.6447205978827115783013948433269e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.479776533265555691825455945761
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003509946613526915521680105454
relative error = 0.014154285946503230345708760152732 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50041
y2[1] (analytic) = 1.122614076335761219522185987587
y2[1] (numeric) = 1.122614076335761219475893180067
absolute error = 4.62928075200e-20
relative error = 4.1236617726281157856472170360737e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4797853071487814533395126093814
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003597685445784530662246741658
relative error = 0.014508052110047758075699062364507 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50042
y2[1] (analytic) = 1.1226188742327019235553478865384
y2[1] (numeric) = 1.1226188742327019235031272677936
absolute error = 5.22206187448e-20
relative error = 4.6516783160707357821329826116805e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4797940809840286841390909487572
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003685423798256838658030135416
relative error = 0.014861813835745561368382859217553 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.0MB, time=5.97
NO POLE
NO POLE
x[1] = 0.50043
y2[1] (analytic) = 1.1226236722173807401645084421961
y2[1] (numeric) = 1.1226236722173807401057677359312
absolute error = 5.87407062649e-20
relative error = 5.2324485683503086307085170459310e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.47980285477129650684066624812
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003773161670935065673783129044
relative error = 0.01521557112362890275171471619634 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50044
y2[1] (analytic) = 1.1226284702897971895511997768975
y2[1] (numeric) = 1.1226284702897971894853033914733
absolute error = 6.58963854242e-20
relative error = 5.8698302393123342876781301582948e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.479811628510584044065511732511
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003860899063810437922237972954
relative error = 0.015569323973730044475985705910888 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50045
y2[1] (analytic) = 1.1226332684499507919081802497024
y2[1] (numeric) = 1.1226332684499507918344472157947
absolute error = 7.37330339077e-20
relative error = 6.5678646785076247061295252655984e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4798204022018904184396986555191
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003948635976874181664107203035
relative error = 0.015923072386081248513818976228299 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50046
y2[1] (analytic) = 1.1226380666978410674194345043735
y2[1] (numeric) = 1.1226380666978410673371363646511
absolute error = 8.22981397224e-20
relative error = 7.3307811452068469773503915849845e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4798291758452147525940963870185
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004036372410117523208084518029
relative error = 0.016276816360714776560165318679622 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.0MB, time=6.58
NO POLE
NO POLE
x[1] = 0.50047
y2[1] (analytic) = 1.1226428650334675362601735173582
y2[1] (numeric) = 1.1226428650334675361685321681794
absolute error = 9.16413491788e-20
relative error = 8.1630010783587926383144042729077e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.479837949440556169164372500905
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004124108363531688910845656894
relative error = 0.016630555897662890032298737109762 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50048
y2[1] (analytic) = 1.1226476634568297185968346457712
y2[1] (numeric) = 1.1226476634568297184950201308976
absolute error = 1.018145148736e-19
relative error = 9.0691423665458129090464648149306e-18 %
"good digits = ", 19
h = 1e-05
y1[1] (analytic) = 2.4798467229879137907909928628329
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004211843837107905177049276173
relative error = 0.016984290996957850069812016647055 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50049
y2[1] (analytic) = 1.1226524619679271345870816753773
y2[1] (numeric) = 1.1226524619679271344742099317047
absolute error = 1.128717436726e-19
relative error = 1.0054023617847338178601455608806e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4798554964872867401192217179509
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004299578830837398459337827353
relative error = 0.017338021658631917534612292927974 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5005
y2[1] (analytic) = 1.1226572605667593043798048685764
y2[1] (numeric) = 1.1226572605667593042549354238809
absolute error = 1.248694446955e-19
relative error = 1.1122668429762903931962601000164e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4798642699386741397991217786374
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004387313344711395258338434218
relative error = 0.017691747882717353010916621593082 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50051
y2[1] (analytic) = 1.122662059253325748115121012388
y2[1] (numeric) = 1.1226620592533257479772546350875
absolute error = 1.378663773005e-19
relative error = 1.2280309659007618933478670552983e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4798730433420751124855543122355
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004475047378721122122663770199
relative error = 0.018045469669246416805247548066326 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.0MB, time=7.20
NO POLE
NO POLE
x[1] = 0.50052
y2[1] (analytic) = 1.1226668580276259859243734664374
y2[1] (numeric) = 1.1226668580276259857724497673668
absolute error = 1.519236990706e-19
relative error = 1.3532393691349312355277262136338e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4798818166974887808381792287879
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004562780932857805648912935723
relative error = 0.018399187018251368946428677625718 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50053
y2[1] (analytic) = 1.1226716568896595379301322109427
y2[1] (numeric) = 1.1226716568896595377630271971423
absolute error = 1.671050138004e-19
relative error = 1.4884584711380463713596548067796e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4798905900049142675214551687704
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004650514007112672481672335548
relative error = 0.018752899929764469185580245712977 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50054
y2[1] (analytic) = 1.1226764558394259242461938947025
y2[1] (numeric) = 1.1226764558394259240627174752186
absolute error = 1.834764194839e-19
relative error = 1.6342768972269446989258093188181e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4798993632643506952046395908258
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004738246601476949313516556102
relative error = 0.019106608403817976996114688554705 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50055
y2[1] (analytic) = 1.1226812548769246649775818830842
y2[1] (numeric) = 1.1226812548769246647764753267813
absolute error = 2.011065563029e-19
relative error = 1.7913059065455453556813232734104e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4799081364757971865617888594967
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004825978715941862885009242811
relative error = 0.019460312440444151573732214034598 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.0MB, time=7.83
NO POLE
NO POLE
x[1] = 0.50056
y2[1] (analytic) = 1.1226860540021552802205463060138
y2[1] (numeric) = 1.1226860540021552800004796513971
absolute error = 2.200666546167e-19
relative error = 1.9601798190349439071301761693433e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4799169096392528642717583329585
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004913710350498639984703977429
relative error = 0.019814012039675251836416372869099 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50057
y2[1] (analytic) = 1.1226908532151172900625641059664
y2[1] (numeric) = 1.1226908532151172898221335230139
absolute error = 2.404305829525e-19
relative error = 2.1415564423987644099877173726111e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4799256827547168510182024507512
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005001441505138507449145155356
relative error = 0.020167707201543536424429630030038 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50058
y2[1] (analytic) = 1.1226956525158102145823390859571
y2[1] (numeric) = 1.1226956525158102143200641899607
absolute error = 2.622748959964e-19
relative error = 2.3361174990628775780801008997780e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.479934455822188269489574821511
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005089172179852692162868862954
relative error = 0.02052139792608126370030893645457 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50059
y2[1] (analytic) = 1.1227004519042335738498019575333
y2[1] (numeric) = 1.1227004519042335735641230749474
absolute error = 2.856788825859e-19
relative error = 2.5445690531375009051046252174807e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4799432288416662423791283107017
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005176902374632421058403754861
relative error = 0.02087508421332069174886130104239 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=53.4MB, alloc=4.0MB, time=8.45
x[1] = 0.5006
y2[1] (analytic) = 1.1227052513803868879261103887678
y2[1] (numeric) = 1.1227052513803868876153857750652
absolute error = 3.107246137026e-19
relative error = 2.7676419373701007982103010934476e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4799520018131498923849151283452
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005264632089468921116271931296
relative error = 0.021228766063294078377159362912004 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50061
y2[1] (analytic) = 1.1227100509442696768636490522525
y2[1] (numeric) = 1.1227100509442696765261520617864
absolute error = 3.374969904661e-19
relative error = 3.0060921800980033165967616462193e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4799607747366383422097869167518
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005352361324353419364989815362
relative error = 0.021582443476033681114536963944263 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50062
y2[1] (analytic) = 1.1227148505958814607060296730933
y2[1] (numeric) = 1.1227148505958814603399458809642
absolute error = 3.660837921291e-19
relative error = 3.2607014322007128236114417328622e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4799695476121307145613948382496
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.000544009007927714288106903034
relative error = 0.021936116451571757212584721584918 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50063
y2[1] (analytic) = 1.1227196503352217594880910769056
y2[1] (numeric) = 1.1227196503352217590915153528331
absolute error = 3.965757240725e-19
relative error = 3.5322773940412495291852094483977e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4799783204396261321521896629142
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005527818354231318789017276986
relative error = 0.022289784989940563645145601954591 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50064
y2[1] (analytic) = 1.1227244501622900932358992378111
y2[1] (numeric) = 1.1227244501622900928068327720086
absolute error = 4.290664658025e-19
relative error = 3.8216542424143193609823053585511e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4799870932191237176994218562974
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005615546149207174261339210818
relative error = 0.022643449091172357108310493213705 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.0MB, time=9.07
NO POLE
NO POLE
x[1] = 0.50065
y2[1] (analytic) = 1.1227292500770859819667473264348
y2[1] (numeric) = 1.1227292500770859815030946074873
absolute error = 4.636527189475e-19
relative error = 4.1296930574817201524256738569570e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.479995865950622593925141667155
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005703273464195936518537319394
relative error = 0.022997108755299394020413779186427 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50066
y2[1] (analytic) = 1.1227340500796089456891557579036
y2[1] (numeric) = 1.1227340500796089451887215026469
absolute error = 5.004342552567e-19
relative error = 4.4572822497119068041638594806951e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.480004638634121883556199215175
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005791000299188832829112799594
relative error = 0.023350763982353930522028913296007 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50067
y2[1] (analytic) = 1.1227388501698585044028722398452
y2[1] (numeric) = 1.1227388501698585038633582752462
absolute error = 5.395139645990e-19
relative error = 4.8053379868112450873236754042402e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4800134112696207093242445787049
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005878726654177090509566434893
relative error = 0.023704414772368222475963992759089 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50068
y2[1] (analytic) = 1.1227436503478341780988718203883
y2[1] (numeric) = 1.1227436503478341775178739174251
absolute error = 5.809979029632e-19
relative error = 5.1748046206558603898155421564199e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4800221838571181939657278824785
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005966452529151936924399472629
relative error = 0.024058061125374525467257333055124 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=61.0MB, alloc=4.0MB, time=9.70
x[1] = 0.50069
y2[1] (analytic) = 1.1227484506135354867593569361635
y2[1] (numeric) = 1.1227484506135354861343615957046
absolute error = 6.249953404589e-19
relative error = 5.5666551142187366590230819035094e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.480030956396613460221899385342
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006054177924104599486114501264
relative error = 0.024411703041405094803173042662797 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5007
y2[1] (analytic) = 1.1227532509669619503577574603049
y2[1] (numeric) = 1.1227532509669619496861386509869
absolute error = 6.716188093180e-19
relative error = 5.9818914684911743152819590829224e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4800397288881056308388095679803
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006141902839026305655216327647
relative error = 0.024765340520492185513196598099757 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50071
y2[1] (analytic) = 1.122758051408113088858730750453
y2[1] (numeric) = 1.1227580514081130881377465985551
absolute error = 7.209841518979e-19
relative error = 6.4215451494084039071648007475089e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4800485013315938285673092206422
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006229627273908282940212854266
relative error = 0.025118973562668052349030419213205 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50072
y2[1] (analytic) = 1.1227628519369884222181616967581
y2[1] (numeric) = 1.1227628519369884214449511280734
absolute error = 7.732105686847e-19
relative error = 6.8866775147642134635569525741851e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4800572737270771761630495308651
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006317351228741758897615956495
relative error = 0.025472602167964949784589444745552 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50073
y2[1] (analytic) = 1.1227676525535874703831627698847
y2[1] (numeric) = 1.1227676525535874695547421035873
absolute error = 8.284206662974e-19
relative error = 7.3783802411234957335512311578925e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4800660460745547963864821711998
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006405074703517961131942359842
relative error = 0.025826226336415132015996708199294 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.0MB, time=10.32
NO POLE
NO POLE
x[1] = 0.50074
y2[1] (analytic) = 1.1227724532579097532920740690167
y2[1] (numeric) = 1.1227724532579097524053335635233
absolute error = 8.867405054934e-19
relative error = 7.8977757507353866336545321042499e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4800748183740258120028593869342
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006492797698228117295714517186
relative error = 0.026179846068050852961578913952735 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50075
y2[1] (analytic) = 1.1227772540499547908744633698639
y2[1] (numeric) = 1.1227772540499547899261637206889
absolute error = 9.482996491750e-19
relative error = 8.4460176384443222387808409501547e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.480083590625489345782234083817
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006580520212863455089461486014
relative error = 0.026533461362904366261862013670887 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50076
y2[1] (analytic) = 1.1227820549297221030511261726687
y2[1] (numeric) = 1.1227820549297221020378949622728
absolute error = 1.0132312103959e-18
relative error = 9.0242910985901072313302646579111e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.4800923628289445204994599157805
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006668242247415202261719805649
relative error = 0.026887072221007925279566782975256 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50077
y2[1] (analytic) = 1.1227868558972112097340857502142
y2[1] (numeric) = 1.1227868558972112086524138498448
absolute error = 1.0816719003694e-18
relative error = 9.6338133519121353341623557689430e-17 %
"good digits = ", 18
h = 1e-05
y1[1] (analytic) = 2.480101134984390458934191372663
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006755963801874586609034374474
relative error = 0.027240678642393783099604398392658 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.0MB, time=10.96
NO POLE
NO POLE
x[1] = 0.50078
y2[1] (analytic) = 1.1227916569524216308265931958329
y2[1] (numeric) = 1.1227916569524216296728311193557
absolute error = 1.1537620764772e-18
relative error = 1.0275834072447963894216575485395e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4801099070918262838708838679312
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006843684876232835975959327156
relative error = 0.027594280627094192529072014599176 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50079
y2[1] (analytic) = 1.1227964580953528862231274714163
y2[1] (numeric) = 1.1227964580953528849934816811375
absolute error = 1.2296457902788e-18
relative error = 1.0951635814426242085838399194376e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4801186791512511180987938264016
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.000693140547048117825505891186
relative error = 0.027947878175141406097248341918952 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5008
y2[1] (analytic) = 1.1228012593260044958093954554259
y2[1] (numeric) = 1.1228012593260044944999246199032
absolute error = 1.3094708355227e-18
relative error = 1.1662534439164679757720513902576e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4801274511626640844119787719614
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007019125584610841386908367458
relative error = 0.02830147128656767605558922409793 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50081
y2[1] (analytic) = 1.122806060644375979462331990904
y2[1] (numeric) = 1.122806060644375978068943194747
absolute error = 1.3933887961570e-18
relative error = 1.2409879541951681054469308470174e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4801362231260643056092974152893
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007106845218613053360094800737
relative error = 0.0286550599614052543777232163687 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50082
y2[1] (analytic) = 1.1228108620504668570500999334863
y2[1] (numeric) = 1.1228108620504668555685448391442
absolute error = 1.4815550943421e-18
relative error = 1.3195054878935689394547849394911e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4801449950414509044944097415756
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.00071945643724790422112180636
relative error = 0.029008644199686392759447163782211 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.0MB, time=11.58
NO POLE
NO POLE
x[1] = 0.50083
y2[1] (analytic) = 1.1228156635442766484320901994154
y2[1] (numeric) = 1.1228156635442766468579611609511
absolute error = 1.5741290384643e-18
relative error = 1.4019478794011555456214390852527e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4801537669088230038757770982416
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.000728228304620003602489163026
relative error = 0.02936222400144334261872177980637 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50084
y2[1] (analytic) = 1.1228204651258048734589218135542
y2[1] (numeric) = 1.1228204651258048717876479424051
absolute error = 1.6712738711491e-18
relative error = 1.4884604645693240188726415993014e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4801625387281797265666622826591
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007370001239767262933743474435
relative error = 0.029715799366708355095667225223748 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50085
y2[1] (analytic) = 1.1228252667950510519724419574014
y2[1] (numeric) = 1.1228252667950510501992851401248
absolute error = 1.7731568172766e-18
relative error = 1.5791921233994227210636125757021e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4801713104995201953851296298689
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007457718953171951118416946533
relative error = 0.030069370295513681052558687284047 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50086
y2[1] (analytic) = 1.122830068552014703805726017107
y2[1] (numeric) = 1.1228300685520147019257768851098
absolute error = 1.8799491319972e-18
relative error = 1.6742953227299612743714910706170e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.480180082222843533154045100299
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007545436186405328807571650834
relative error = 0.030422936787891571073821959139541 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.0MB, time=12.20
NO POLE
NO POLE
x[1] = 0.50087
y2[1] (analytic) = 1.1228348703966953487830776314892
y2[1] (numeric) = 1.1228348703966953467912514827409
absolute error = 1.9918261487483e-18
relative error = 1.7739261589236106852206799196067e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4801888538981488627010763674821
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007633152939458624277884322665
relative error = 0.03077649884387427546602901954734 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50088
y2[1] (analytic) = 1.1228396723290925067200287400517
y2[1] (numeric) = 1.1228396723290925046110614127799
absolute error = 2.1089673272718e-18
relative error = 1.8782444005538164151977761779855e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4801976255254353068586929057734
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007720869212323065854049705578
relative error = 0.031130056463494044257893612878792 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50089
y2[1] (analytic) = 1.1228444743492056974233396310026
y2[1] (numeric) = 1.1228444743492056951917833293697
absolute error = 2.2315563016329e-18
relative error = 1.9874135310914696382133339539698e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4802063971047019884641660780667
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007808585004989881908781428511
relative error = 0.03148360964678312720026682935539 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5009
y2[1] (analytic) = 1.122849276457034440690998989273
y2[1] (numeric) = 1.1228492764570344383312180610343
absolute error = 2.3597809282387e-18
relative error = 2.1016007915903007249743875471720e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4802151686359480303595692235113
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007896300317450300862812882957
relative error = 0.031837158393773773766132685611939 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50091
y2[1] (analytic) = 1.122854078652578256312223944538
y2[1] (numeric) = 1.1228540786525782538183906106788
memory used=80.1MB, alloc=4.0MB, time=12.82
absolute error = 2.4938333338592e-18
relative error = 2.2209772233733104509968929012797e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.480223940119172555391777745227
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007984015149695551184898100114
relative error = 0.03219070270449823315060370547815 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50092
y2[1] (analytic) = 1.1228588809358366640674601192374
y2[1] (numeric) = 1.1228588809358366614335501555895
absolute error = 2.6339099636479e-18
relative error = 2.3457177107177451923058629568554e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4802327115543746864124691980204
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0008071729501716861391812628048
relative error = 0.032544242578988754270916501107622 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50093
y2[1] (analytic) = 1.1228636833068091837283816765975
y2[1] (numeric) = 1.1228636833068091809481700474336
absolute error = 2.7802116291639e-18
relative error = 2.4760010235403081845483112855713e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4802414829415535462781233760988
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0008159443373505460048354408832
relative error = 0.032897778017277585766427354305087 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50094
y2[1] (analytic) = 1.1228684857654953350578913686542
y2[1] (numeric) = 1.1228684857654953321249478122596
absolute error = 2.9329435563946e-18
relative error = 2.6120098600818052498660718375319e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4802502542807082578500224007851
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0008247156765052575767344655695
relative error = 0.033251309019396975998607798188918 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50095
y2[1] (analytic) = 1.1228732883118946378101205842765
y2[1] (numeric) = 1.1228732883118946347178051504969
absolute error = 3.0923154337796e-18
relative error = 2.7539308895917592819579790905393e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4802590255718379439942508082317
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0008334869676349437209628730161
relative error = 0.033604835585379173051040199108315 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.0MB, time=13.45
NO POLE
NO POLE
x[1] = 0.50096
y2[1] (analytic) = 1.1228780909460066117304293971914
y2[1] (numeric) = 1.1228780909460066084718879369562
absolute error = 3.2585414602352e-18
relative error = 2.9019547950124590791288756842512e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4802677968149417275816956371335
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0008422582107387273084077019179
relative error = 0.033958357715256424729413338819153 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50097
y2[1] (analytic) = 1.1228828936678307765554066140091
y2[1] (numeric) = 1.1228828936678307731235662208291
absolute error = 3.4318403931800e-18
relative error = 3.0562763156628877547099264931206e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4802765680100187314880465164412
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0008510294058157312147585812256
relative error = 0.034311875409060978561517996966876 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50098
y2[1] (analytic) = 1.1228876964773666520128698222493
y2[1] (numeric) = 1.1228876964773666484004342256885
absolute error = 3.6124355965608e-18
relative error = 3.2170942899218182096905805510018e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4802853391570680785937957530734
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0008598005528650783205078178578
relative error = 0.034665388666825081797242533815951 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.50099
y2[1] (analytic) = 1.1228924993746137578218654383686
y2[1] (numeric) = 1.1228924993746137540213103494882
absolute error = 3.8005550888804e-18
relative error = 3.3846116979115005140643729263235e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4802941102560888917842384196288
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0008685716518858915109504844132
relative error = 0.035018897488580981408568473278276 %
"good digits = ", 3
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=87.7MB, alloc=4.0MB, time=14.10
x[1] = 0.501
y2[1] (analytic) = 1.1228973023595716136926687557886
y2[1] (numeric) = 1.1228973023595716096962371645632
absolute error = 3.9964315912254e-18
relative error = 3.5590357041802490577700971005932e-16 %
"good digits = ", 17
h = 1e-05
y1[1] (analytic) = 2.4803028813070802939494724420977
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0008773427028772936761845068821
relative error = 0.035372401874360924089566086208289 %
"good digits = ", 3
h = 1e-05
Finished!
Maximum Iterations Reached before Solution Completed!
diff(y2,x,1) = y1 - 2.0;
diff(y1,x,1) = diff(y2,x,5);
Iterations = 100
Total Elapsed Time = 14 Seconds
Elapsed Time(since restart) = 13 Seconds
Expected Time Remaining = 1 Days 12 Hours 36 Minutes 59 Seconds
Optimized Time Remaining = 1 Days 12 Hours 29 Minutes 37 Seconds
Time to Timeout = 45 Seconds
Percent Done = 0.01063 %
> quit
memory used=87.9MB, alloc=4.0MB, time=14.13