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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_warned,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_reached_optimal_h,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_warned2,
> years_in_century,
> hours_in_day,
> glob_log10normmin,
> glob_smallish_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> glob_current_iter,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug2,
> glob_log10relerr,
> glob_start,
> glob_optimal_start,
> glob_max_hours,
> glob_disp_incr,
> glob_clock_start_sec,
> days_in_year,
> min_in_hour,
> glob_max_sec,
> glob_relerr,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_iter,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_minutes,
> sec_in_min,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_5,
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_last_rel_error,
> array_y1_init,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_pole,
> array_y2_init,
> array_type_pole,
> array_x,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_real_pole,
> array_y1_set_initial,
> array_y2_higher_work,
> array_y1_higher_work,
> array_y2_higher,
> array_poles,
> array_y1_higher,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> 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 := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[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,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel,
MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium,
glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter,
glob_normmax, glob_warned2, years_in_century, hours_in_day,
glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err,
glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter,
glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2,
glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours,
glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour,
glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done,
glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr,
glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished,
glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag,
glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0,
array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1,
array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x,
array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2,
array_y2_higher_work2, array_real_pole, array_y1_set_initial,
array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles,
array_y1_higher, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y2[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
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 := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y1[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[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, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_warned,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_reached_optimal_h,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_warned2,
> years_in_century,
> hours_in_day,
> glob_log10normmin,
> glob_smallish_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> glob_current_iter,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug2,
> glob_log10relerr,
> glob_start,
> glob_optimal_start,
> glob_max_hours,
> glob_disp_incr,
> glob_clock_start_sec,
> days_in_year,
> min_in_hour,
> glob_max_sec,
> glob_relerr,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_iter,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_minutes,
> sec_in_min,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_5,
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_last_rel_error,
> array_y1_init,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_pole,
> array_y2_init,
> array_type_pole,
> array_x,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_real_pole,
> array_y1_set_initial,
> array_y2_higher_work,
> array_y1_higher_work,
> array_y2_higher,
> array_poles,
> array_y1_higher,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(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 (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(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 (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel,
MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium,
glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter,
glob_normmax, glob_warned2, years_in_century, hours_in_day,
glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err,
glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter,
glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2,
glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours,
glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour,
glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done,
glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr,
glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished,
glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag,
glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0,
array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1,
array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x,
array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2,
array_y2_higher_work2, array_real_pole, array_y1_set_initial,
array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles,
array_y1_higher, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y2_higher[1, 1]) then
tmp := abs(array_y2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < abs(array_y1_higher[1, 1]) then
tmp := abs(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 < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_warned,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_reached_optimal_h,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_warned2,
> years_in_century,
> hours_in_day,
> glob_log10normmin,
> glob_smallish_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> glob_current_iter,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug2,
> glob_log10relerr,
> glob_start,
> glob_optimal_start,
> glob_max_hours,
> glob_disp_incr,
> glob_clock_start_sec,
> days_in_year,
> min_in_hour,
> glob_max_sec,
> glob_relerr,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_iter,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_minutes,
> sec_in_min,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_5,
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_last_rel_error,
> array_y1_init,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_pole,
> array_y2_init,
> array_type_pole,
> array_x,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_real_pole,
> array_y1_set_initial,
> array_y2_higher_work,
> array_y1_higher_work,
> array_y2_higher,
> array_poles,
> array_y1_higher,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel,
MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium,
glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter,
glob_normmax, glob_warned2, years_in_century, hours_in_day,
glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err,
glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter,
glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2,
glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours,
glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour,
glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done,
glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr,
glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished,
glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag,
glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0,
array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1,
array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x,
array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2,
array_y2_higher_work2, array_real_pole, array_y1_set_initial,
array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles,
array_y1_higher, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_warned,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_reached_optimal_h,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_warned2,
> years_in_century,
> hours_in_day,
> glob_log10normmin,
> glob_smallish_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> glob_current_iter,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug2,
> glob_log10relerr,
> glob_start,
> glob_optimal_start,
> glob_max_hours,
> glob_disp_incr,
> glob_clock_start_sec,
> days_in_year,
> min_in_hour,
> glob_max_sec,
> glob_relerr,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_iter,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_minutes,
> sec_in_min,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_5,
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_last_rel_error,
> array_y1_init,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_pole,
> array_y2_init,
> array_type_pole,
> array_x,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_real_pole,
> array_y1_set_initial,
> array_y2_higher_work,
> array_y1_higher_work,
> array_y2_higher,
> array_poles,
> array_y1_higher,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y2_higher[1,m]) < glob_small_float) or (abs(array_y2_higher[1,m-1]) < glob_small_float) or (abs(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 (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #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 ((abs(array_y1_higher[1,m]) < glob_small_float) or (abs(array_y1_higher[1,m-1]) < glob_small_float) or (abs(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 (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[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 (abs(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 (abs(array_y2_higher[1,m]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (abs(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 ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #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 (abs(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 (abs(array_y1_higher[1,m]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (abs(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 ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(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 (abs(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 (abs(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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel,
MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium,
glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter,
glob_normmax, glob_warned2, years_in_century, hours_in_day,
glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err,
glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter,
glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2,
glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours,
glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour,
glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done,
glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr,
glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished,
glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag,
glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0,
array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1,
array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x,
array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2,
array_y2_higher_work2, array_real_pole, array_y1_set_initial,
array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles,
array_y1_higher, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y2_higher[1, m]) < glob_small_float or
abs(array_y2_higher[1, m - 1]) < glob_small_float or
abs(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 < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y1_higher[1, m]) < glob_small_float or
abs(array_y1_higher[1, m - 1]) < glob_small_float or
abs(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 < abs(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 < abs(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 <= abs(array_y2_higher[1, m]) or
glob_large_float <= abs(array_y2_higher[1, m - 1]) or
glob_large_float <= abs(array_y2_higher[1, m - 2]) or
glob_large_float <= abs(array_y2_higher[1, m - 3]) or
glob_large_float <= abs(array_y2_higher[1, m - 4]) or
glob_large_float <= abs(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 abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(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 <= abs(array_y1_higher[1, m]) or
glob_large_float <= abs(array_y1_higher[1, m - 1]) or
glob_large_float <= abs(array_y1_higher[1, m - 2]) or
glob_large_float <= abs(array_y1_higher[1, m - 3]) or
glob_large_float <= abs(array_y1_higher[1, m - 4]) or
glob_large_float <= abs(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 abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(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 < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[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
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_warned,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_reached_optimal_h,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_warned2,
> years_in_century,
> hours_in_day,
> glob_log10normmin,
> glob_smallish_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> glob_current_iter,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug2,
> glob_log10relerr,
> glob_start,
> glob_optimal_start,
> glob_max_hours,
> glob_disp_incr,
> glob_clock_start_sec,
> days_in_year,
> min_in_hour,
> glob_max_sec,
> glob_relerr,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_iter,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_minutes,
> sec_in_min,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_5,
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_last_rel_error,
> array_y1_init,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_pole,
> array_y2_init,
> array_type_pole,
> array_x,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_real_pole,
> array_y1_set_initial,
> array_y2_higher_work,
> array_y1_higher_work,
> array_y2_higher,
> array_poles,
> array_y1_higher,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 3
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(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 (abs(array_y1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_y1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel,
MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium,
glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter,
glob_normmax, glob_warned2, years_in_century, hours_in_day,
glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err,
glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter,
glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2,
glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours,
glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour,
glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done,
glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr,
glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished,
glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag,
glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0,
array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1,
array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x,
array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2,
array_y2_higher_work2, array_real_pole, array_y1_set_initial,
array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles,
array_y1_higher, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y2[iii]) then
array_norms[iii] := abs(array_y2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y1[iii]) then
array_norms[iii] := abs(array_y1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_warned,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_reached_optimal_h,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_warned2,
> years_in_century,
> hours_in_day,
> glob_log10normmin,
> glob_smallish_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> glob_current_iter,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug2,
> glob_log10relerr,
> glob_start,
> glob_optimal_start,
> glob_max_hours,
> glob_disp_incr,
> glob_clock_start_sec,
> days_in_year,
> min_in_hour,
> glob_max_sec,
> glob_relerr,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_iter,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_minutes,
> sec_in_min,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_5,
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_last_rel_error,
> array_y1_init,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_pole,
> array_y2_init,
> array_type_pole,
> array_x,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_real_pole,
> array_y1_set_initial,
> array_y2_higher_work,
> array_y1_higher_work,
> array_y2_higher,
> array_poles,
> array_y1_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre add $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D0[1] + array_y1[1];
> #emit pre sub $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] * (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] * (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 $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D0[2] + array_y1[2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp2[2] := (array_tmp1[2] - (array_const_2D0[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] * (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] * (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 $eq_no = 1 i = 3
> array_tmp1[3] := array_const_0D0[3] + array_y1[3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp2[3] := (array_tmp1[3] - (array_const_2D0[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] * (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] * (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 $eq_no = 1 i = 4
> array_tmp1[4] := array_const_0D0[4] + array_y1[4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp2[4] := (array_tmp1[4] - (array_const_2D0[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] * (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] * (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 $eq_no = 1 i = 5
> array_tmp1[5] := array_const_0D0[5] + array_y1[5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp2[5] := (array_tmp1[5] - (array_const_2D0[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] * (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] * (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 add $eq_no = 1
> array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk];
> #emit sub $eq_no = 1
> array_tmp2[kkk] := (array_tmp1[kkk] - (array_const_2D0[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] * (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] * (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
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel,
MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium,
glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter,
glob_normmax, glob_warned2, years_in_century, hours_in_day,
glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err,
glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter,
glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2,
glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours,
glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour,
glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done,
glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr,
glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished,
glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag,
glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0,
array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1,
array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x,
array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2,
array_y2_higher_work2, array_real_pole, array_y1_set_initial,
array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles,
array_y1_higher, 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]*glob_h*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]*glob_h*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_const_0D0[2] + array_y1[2];
array_tmp2[2] := array_tmp1[2] - array_const_2D0[2];
if not array_y2_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h*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]*glob_h*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_const_0D0[3] + array_y1[3];
array_tmp2[3] := array_tmp1[3] - array_const_2D0[3];
if not array_y2_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h*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]*glob_h*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_const_0D0[4] + array_y1[4];
array_tmp2[4] := array_tmp1[4] - array_const_2D0[4];
if not array_y2_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h*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]*glob_h*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_const_0D0[5] + array_y1[5];
array_tmp2[5] := array_tmp1[5] - array_const_2D0[5];
if not array_y2_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h*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]*glob_h*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_const_0D0[kkk] + array_y1[kkk];
array_tmp2[kkk] := array_tmp1[kkk] - array_const_2D0[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]*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]*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_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> 2.0 + sin(x);
> end;
exact_soln_y1 := proc(x) 2.0 + sin(x) end proc
> exact_soln_y2 := proc(x)
> 2.0 - cos(x);
> end;
exact_soln_y2 := proc(x) 2.0 - cos(x) end proc
> exact_soln_y2p := proc(x)
> sin(x);
> end;
exact_soln_y2p := proc(x) sin(x) end proc
> exact_soln_y2pp := proc(x)
> cos(x);
> end;
exact_soln_y2pp := proc(x) cos(x) end proc
> exact_soln_y2ppp := proc(x)
> -sin(x);
> end;
exact_soln_y2ppp := proc(x) -sin(x) end proc
> exact_soln_y2pppp := proc(x)
> -cos(x);
> end;
exact_soln_y2pppp := proc(x) -cos(x) end proc
>
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> ALWAYS,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_warned,
> glob_unchanged_h_cnt,
> centuries_in_millinium,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_reached_optimal_h,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_warned2,
> years_in_century,
> hours_in_day,
> glob_log10normmin,
> glob_smallish_float,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> glob_current_iter,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug2,
> glob_log10relerr,
> glob_start,
> glob_optimal_start,
> glob_max_hours,
> glob_disp_incr,
> glob_clock_start_sec,
> days_in_year,
> min_in_hour,
> glob_max_sec,
> glob_relerr,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_iter,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_minutes,
> sec_in_min,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_5,
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_last_rel_error,
> array_y1_init,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_pole,
> array_y2_init,
> array_type_pole,
> array_x,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_real_pole,
> array_y1_set_initial,
> array_y2_higher_work,
> array_y1_higher_work,
> array_y2_higher,
> array_poles,
> array_y1_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> glob_max_terms := 30;
> INFO := 2;
> DEBUGL := 3;
> glob_iolevel := 5;
> MAX_UNCHANGED := 10;
> glob_warned := false;
> glob_unchanged_h_cnt := 0;
> centuries_in_millinium := 10.0;
> glob_subiter_method := 3;
> glob_optimal_clock_start_sec := 0.0;
> glob_log10_relerr := 0.1e-10;
> glob_dump_analytic := false;
> glob_reached_optimal_h := false;
> djd_debug := true;
> glob_max_opt_iter := 10;
> glob_normmax := 0.0;
> glob_warned2 := false;
> years_in_century := 100.0;
> hours_in_day := 24.0;
> glob_log10normmin := 0.1;
> glob_smallish_float := 0.1e-100;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_iter := 1000;
> glob_look_poles := false;
> glob_h := 0.1;
> glob_almost_1 := 0.9990;
> glob_current_iter := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_last_good_h := 0.1;
> djd_debug2 := true;
> glob_log10relerr := 0.0;
> glob_start := 0;
> glob_optimal_start := 0.0;
> glob_max_hours := 0.0;
> glob_disp_incr := 0.1;
> glob_clock_start_sec := 0.0;
> days_in_year := 365.0;
> min_in_hour := 60.0;
> glob_max_sec := 10000.0;
> glob_relerr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_hmax := 1.0;
> glob_optimal_done := false;
> glob_no_eqs := 0;
> glob_hmin := 0.00000000001;
> glob_optimal_expect_sec := 0.1;
> glob_log10abserr := 0.0;
> glob_iter := 0;
> glob_orig_start_sec := 0.0;
> glob_small_float := 0.1e-50;
> glob_abserr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_not_yet_start_msg := true;
> glob_clock_sec := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_initial_pass := true;
> glob_not_yet_finished := true;
> glob_percent_done := 0.0;
> glob_max_minutes := 0.0;
> sec_in_min := 60.0;
> glob_display_flag := true;
> glob_dump := false;
> glob_html_log := true;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 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 := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"2.0 + sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"2.0 - cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
> omniout_str(ALWAYS,"cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)");
> omniout_str(ALWAYS,"-sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)");
> omniout_str(ALWAYS,"-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_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_y1_init:= Array(1..(max_terms + 1),[]);
> array_y2:= Array(1..(max_terms + 1),[]);
> array_y1:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_y2_init:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher_work2 := Array(1..(6+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher_work := Array(1..(6+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher := Array(1..(6+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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[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_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y2_init[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_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_m1[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 <=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
> ;
> 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 <=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_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 <=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 <=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 <=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 <=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_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[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_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_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_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_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_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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 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 := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_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] * 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]* (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] * 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]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y2();
> if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(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)
> ;
> start_array_y1();
> if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_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 * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_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 * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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,"2012-06-13T03:52:26-05:00")
> ;
> 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," 090 | ")
> ;
> logitem_str(html_log_file,"mtest9_rev diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest9_rev maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> 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;
Warning, `subiter` is implicitly declared local to procedure `mainprog`
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp,
subiter;
global ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel,
MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium,
glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter,
glob_normmax, glob_warned2, years_in_century, hours_in_day,
glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err,
glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter,
glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2,
glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours,
glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour,
glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done,
glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr,
glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished,
glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag,
glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0,
array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1,
array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x,
array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2,
array_y2_higher_work2, array_real_pole, array_y1_set_initial,
array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles,
array_y1_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
ALWAYS := 1;
DEBUGMASSIVE := 4;
glob_max_terms := 30;
INFO := 2;
DEBUGL := 3;
glob_iolevel := 5;
MAX_UNCHANGED := 10;
glob_warned := false;
glob_unchanged_h_cnt := 0;
centuries_in_millinium := 10.0;
glob_subiter_method := 3;
glob_optimal_clock_start_sec := 0.;
glob_log10_relerr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_reached_optimal_h := false;
djd_debug := true;
glob_max_opt_iter := 10;
glob_normmax := 0.;
glob_warned2 := false;
years_in_century := 100.0;
hours_in_day := 24.0;
glob_log10normmin := 0.1;
glob_smallish_float := 0.1*10^(-100);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_iter := 1000;
glob_look_poles := false;
glob_h := 0.1;
glob_almost_1 := 0.9990;
glob_current_iter := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_last_good_h := 0.1;
djd_debug2 := true;
glob_log10relerr := 0.;
glob_start := 0;
glob_optimal_start := 0.;
glob_max_hours := 0.;
glob_disp_incr := 0.1;
glob_clock_start_sec := 0.;
days_in_year := 365.0;
min_in_hour := 60.0;
glob_max_sec := 10000.0;
glob_relerr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_hmax := 1.0;
glob_optimal_done := false;
glob_no_eqs := 0;
glob_hmin := 0.1*10^(-10);
glob_optimal_expect_sec := 0.1;
glob_log10abserr := 0.;
glob_iter := 0;
glob_orig_start_sec := 0.;
glob_small_float := 0.1*10^(-50);
glob_abserr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_not_yet_start_msg := true;
glob_clock_sec := 0.;
glob_curr_iter_when_opt := 0;
glob_initial_pass := true;
glob_not_yet_finished := true;
glob_percent_done := 0.;
glob_max_minutes := 0.;
sec_in_min := 60.0;
glob_display_flag := true;
glob_dump := false;
glob_html_log := true;
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 := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "2.0 + sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "2.0 - cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
omniout_str(ALWAYS, "cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)");
omniout_str(ALWAYS, "-sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)");
omniout_str(ALWAYS, "-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_last_rel_error := Array(1 .. max_terms + 1, []);
array_y1_init := Array(1 .. max_terms + 1, []);
array_y2 := Array(1 .. max_terms + 1, []);
array_y1 := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_y2_init := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_higher_work2 := Array(1 .. 7, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_y2_higher_work := Array(1 .. 7, 1 .. max_terms + 1, []);
array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_higher := Array(1 .. 7, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1_init[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_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2_init[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_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_m1[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 <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work2[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_real_pole[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 <= 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 <= 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 <= 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_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[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_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_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_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_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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 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 := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_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]*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]*
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]*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]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y2();
if glob_small_float < abs(array_y2_higher[1, 1]) then
tmp := abs(array_y2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_y1();
if glob_small_float < abs(array_y1_higher[1, 1]) then
tmp := abs(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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]/(
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*glob_h^(calc_term - 1)/convfp(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, "2012-06-13T03:52:26-05:00");
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, " 090 | ");
logitem_str(html_log_file, "mtest9_rev diffeq.mxt");
logitem_str(html_log_file, "mtest9_rev maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
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
> mainprog();
##############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 := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
2.0 + sin(x);
end;
exact_soln_y2 := proc(x)
2.0 - cos(x);
end;
exact_soln_y2p := proc(x)
sin(x);
end;
exact_soln_y2pp := proc(x)
cos(x);
end;
exact_soln_y2ppp := proc(x)
-sin(x);
end;
exact_soln_y2pppp := proc(x)
-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 %
h = 0.0001
y1[1] (analytic) = 2.4794255386042030002732879352156
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0
relative error = 0 %
h = 0.0001
x[1] = 0.5
y2[1] (analytic) = 1.1224174381096272838837184173962
y2[1] (numeric) = 1.1224174381096272838837184173962
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 2.4794255386042030002732879352156
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5001
y2[1] (analytic) = 1.1224653850513206057226212384082
y2[1] (numeric) = 1.1224653850513206057225812850612
absolute error = 3.99533470e-23
relative error = 3.5594279816631744060018373993147e-21 %
h = 0.0001
y1[1] (analytic) = 2.4795132944631180827612490419532
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 8.77558589150824879611067376e-05
relative error = 0.0035392372814070356873465959087753 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5002
y2[1] (analytic) = 1.122513340768360069735529546726
y2[1] (numeric) = 1.122513340768360069734251000617
absolute error = 1.2785461090e-21
relative error = 1.1390030412688329777726287466527e-19 %
h = 0.0001
y1[1] (analytic) = 2.4796010455269002246139734402722
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0001755069226972243406855050566
relative error = 0.0070780306781137923396978378563839 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.9MB, time=0.19
NO POLE
NO POLE
x[1] = 0.5003
y2[1] (analytic) = 1.1225613052602661187524483331957
y2[1] (numeric) = 1.1225613052602661187427390775074
absolute error = 9.7092556883e-21
relative error = 8.6491986164166834930999012427343e-19 %
h = 0.0001
y1[1] (analytic) = 2.4796887917946719151943709705102
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0002632531904689149210830352946
relative error = 0.010616380222390154323420137410111 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5004
y2[1] (analytic) = 1.122609278526559107854716811747
y2[1] (numeric) = 1.122609278526559107813800840139
absolute error = 4.09159716080e-20
relative error = 3.6447205978648959407660893371546e-18 %
h = 0.0001
y1[1] (analytic) = 2.479776533265555691825455945761
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0003509946613526915521680105454
relative error = 0.014154285946503230345708760152732 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5005
y2[1] (analytic) = 1.1226572605667593043798048685764
y2[1] (numeric) = 1.122657260566759304254935423881
absolute error = 1.248694446954e-19
relative error = 1.1122668429753996493912495105327e-17 %
h = 0.0001
y1[1] (analytic) = 2.4798642699386741397991217786374
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0004387313344711395258338434218
relative error = 0.017691747882717353010916621593082 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5006
y2[1] (analytic) = 1.1227052513803868879261103887678
y2[1] (numeric) = 1.1227052513803868876153857750655
absolute error = 3.107246137023e-19
relative error = 2.7676419373674286810216521185989e-17 %
h = 0.0001
y1[1] (analytic) = 2.4799520018131498923849151283452
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0005264632089468921116271931296
relative error = 0.021228766063294078377159362912004 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.9MB, time=0.40
NO POLE
NO POLE
x[1] = 0.5007
y2[1] (analytic) = 1.1227532509669619503577574603049
y2[1] (numeric) = 1.1227532509669619496861386509872
absolute error = 6.716188093177e-19
relative error = 5.9818914684885023123308063921464e-17 %
h = 0.0001
y1[1] (analytic) = 2.4800397288881056308388095679803
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0006141902839026305655216327647
relative error = 0.024765340520492185513196598099757 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5008
y2[1] (analytic) = 1.1228012593260044958093954554259
y2[1] (numeric) = 1.1228012593260044944999246199035
absolute error = 1.3094708355224e-18
relative error = 1.1662534439162007869017965741049e-16 %
h = 0.0001
y1[1] (analytic) = 2.4801274511626640844119787719614
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007019125584610841386908367458
relative error = 0.02830147128656767605558922409793 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5009
y2[1] (analytic) = 1.122849276457034440690998989273
y2[1] (numeric) = 1.1228492764570344383312180610346
absolute error = 2.3597809282384e-18
relative error = 2.1016007915900335475301034839687e-16 %
h = 0.0001
y1[1] (analytic) = 2.4802151686359480303595692235113
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0007896300317450300862812882957
relative error = 0.031837158393773773766132685611939 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.501
y2[1] (analytic) = 1.1228973023595716136926687557886
y2[1] (numeric) = 1.1228973023595716096962371645635
absolute error = 3.9964315912251e-18
relative error = 3.5590357041799818917528935659069e-16 %
h = 0.0001
y1[1] (analytic) = 2.4803028813070802939494724420977
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0008773427028772936761845068821
relative error = 0.035372401874360924089566086208289 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=11.4MB, alloc=3.9MB, time=0.62
x[1] = 0.5011
y2[1] (analytic) = 1.1229453370331357557894332408103
y2[1] (numeric) = 1.1229453370331357493529439316358
absolute error = 6.4364893091745e-18
relative error = 5.7317921869464717621046234700062e-16 %
h = 0.0001
y1[1] (analytic) = 2.4803905891751837484710967307476
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.000965050570980748197808795532
relative error = 0.038907201760576793711557037472634 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5012
y2[1] (analytic) = 1.1229933804772465202460513123167
y2[1] (numeric) = 1.1229933804772465103010441743599
absolute error = 9.9450071379568e-18
relative error = 8.8558021007482691157362098073858e-16 %
h = 0.0001
y1[1] (analytic) = 2.4804782922393813152441384431453
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0010527536351783149708505079297
relative error = 0.04244155808466627011696213787216 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5013
y2[1] (analytic) = 1.1230414326914234726218156877758
y2[1] (numeric) = 1.1230414326914234577819875158068
absolute error = 1.48398281719690e-17
relative error = 1.3213963207398883990633889562694e-15 %
h = 0.0001
y1[1] (analytic) = 2.4805659904987959636273527704284
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0011404518945929633540648352128
relative error = 0.045975470878871461148362973176003 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5014
y2[1] (analytic) = 1.123089493675186090775357278548
y2[1] (numeric) = 1.1230894936751860692789673900104
absolute error = 2.14963898885376e-17
relative error = 1.9140406895084596337380334996386e-15 %
h = 0.0001
y1[1] (analytic) = 2.4806536839525507110273240475931
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0012281453483477107540361123775
relative error = 0.049508940175431694564877530195195 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5015
y2[1] (analytic) = 1.1231375634280537648694504112957
y2[1] (numeric) = 1.1231375634280537345169210419673
absolute error = 3.03525293693284e-17
relative error = 2.7024765583198954362990474455866e-15 %
h = 0.0001
y1[1] (analytic) = 2.4807413725997686229072355794206
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.001315833995565622633947644205
relative error = 0.05304196600658351760124691565663 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=3.9MB, time=0.83
NO POLE
NO POLE
x[1] = 0.5016
y2[1] (analytic) = 1.1231856419495457973758189263517
y2[1] (numeric) = 1.1231856419495457554625295276368
absolute error = 4.19132893987149e-17
relative error = 3.7316439805947654034543240004214e-15 %
h = 0.0001
y1[1] (analytic) = 2.4808290564395728127956389858385
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0014035178353698125223510506229
relative error = 0.056574548404560696527197272142876 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5017
y2[1] (analytic) = 1.123233729239181403079943152998
y2[1] (numeric) = 1.1232337292391813463242177139408
absolute error = 5.67557254390572e-17
relative error = 5.0528864974078458410914509585353e-15 %
h = 0.0001
y1[1] (analytic) = 2.4809167354710864422952230666275
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0014911968668834420219351314119
relative error = 0.060106687401594216207076782917388 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5018
y2[1] (analytic) = 1.1232818252964797090858677616068
y2[1] (numeric) = 1.1232818252964796335521542787641
absolute error = 7.55337134828427e-17
relative error = 6.7243777814090675165908313209214e-15 %
h = 0.0001
y1[1] (analytic) = 2.4810044096934327210915821853874
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0015788710892297208182942501718
relative error = 0.063638383029912279659767657636522 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5019
y2[1] (analytic) = 1.1233299301209597548210104925963
y2[1] (numeric) = 1.1233299301209596558382517109542
absolute error = 9.89827587816421e-17
relative error = 8.8115482484281063216010204630400e-15 %
h = 0.0001
y1[1] (analytic) = 2.4810920791057349069619841726739
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0016665405015319066886962374583
relative error = 0.067169635321740307618872990881736 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=3.9MB, time=1.05
NO POLE
NO POLE
x[1] = 0.502
y2[1] (analytic) = 1.1233780437121404920409717621522
y2[1] (numeric) = 1.1233780437121403641161663103213
absolute error = 1.279248054518309e-16
relative error = 1.1387511636698049527321551304247e-14 %
h = 0.0001
y1[1] (analytic) = 2.4811797437071163057841377482187
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0017542051029133055108498130031
relative error = 0.070700444309300938093178385518425 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5021
y2[1] (analytic) = 1.1234261660695407848343451446679
y2[1] (numeric) = 1.1234261660695406215612981876383
absolute error = 1.632730469570296e-16
relative error = 1.4533491553633876808755916091875e-14 %
h = 0.0001
y1[1] (analytic) = 2.4812674034967002715449594621449
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0018418648924972712716715269293
relative error = 0.074230810024814025927388232900411 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5022
y2[1] (analytic) = 1.1234742971926794096275287318546
y2[1] (numeric) = 1.1234742971926792035907912646409
absolute error = 2.060367374672137e-16
relative error = 1.8339247990101347662833473303597e-14 %
h = 0.0001
y1[1] (analytic) = 2.4813550584736102063493401550904
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0019295198694072060760522198748
relative error = 0.077760732500496642363136542000036 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5023
y2[1] (analytic) = 1.1235224370810750551895373684732
y2[1] (numeric) = 1.1235224370810747978635332740275
absolute error = 2.573260040944457e-16
relative error = 2.2903503802112024190229846458462e-14 %
h = 0.0001
y1[1] (analytic) = 2.4814427086369695604289109371521
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0020171700327665601556230019365
relative error = 0.081290211768563074600272209580537 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=3.9MB, time=1.27
NO POLE
NO POLE
x[1] = 0.5024
y2[1] (analytic) = 1.12357058573424632263681576464
y2[1] (numeric) = 1.1235705857342460042801557594592
absolute error = 3.183566600051808e-16
relative error = 2.8334371159880153120626016900052e-14 %
h = 0.0001
y1[1] (analytic) = 2.4815303539859018321508086855622
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0021048153816988318775207503466
relative error = 0.084819247861224825358418623499678 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5025
y2[1] (analytic) = 1.1236187431517117254380524846586
y2[1] (numeric) = 1.1236187431517113349830340755598
absolute error = 3.904550184090988e-16
relative error = 3.4749777964177241591693042711944e-14 %
h = 0.0001
y1[1] (analytic) = 2.4816179945195305680264410610091
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0021924559153275677531531257935
relative error = 0.088347840810690612438807491314677 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5026
y2[1] (analytic) = 1.1236669093329896894189948123286
y2[1] (numeric) = 1.1236669093329892143562873879159
absolute error = 4.750627074244127e-16
relative error = 4.2277894229920022616853460099026e-14 %
h = 0.0001
y1[1] (analytic) = 2.4817056302369793627202510425165
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0022800916327763624469631073009
relative error = 0.091875990649166368286386786435399 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5027
y2[1] (analytic) = 1.1237150842775985527672644926845
y2[1] (numeric) = 1.1237150842775979790257786730768
absolute error = 5.737414858196077e-16
relative error = 5.1057558436927830426879629990958e-14 %
h = 0.0001
y1[1] (analytic) = 2.4817932611373718590584809807915
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0023677225331688587851930455759
relative error = 0.095403697408855239552202703992763 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=3.9MB, time=1.49
NO POLE
NO POLE
x[1] = 0.5028
y2[1] (analytic) = 1.1237632679850565660371743501153
y2[1] (numeric) = 1.1237632679850558778591147185545
absolute error = 6.881780596315608e-16
relative error = 6.1238703847785133805350909704015e-14 %
h = 0.0001
y1[1] (analytic) = 2.4818808872198317480379361699548
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0024553486156287477646482347392
relative error = 0.098930961121957586656055518714595 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5029
y2[1] (analytic) = 1.123811460454881892154545782817
y2[1] (numeric) = 1.1238114604548810719656461228238
absolute error = 8.201888996599932e-16
relative error = 7.2982784792745193004855153482851e-14 %
h = 0.0001
y1[1] (analytic) = 2.4819685084834827688347479375655
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0025429698792797685614600023499
relative error = 0.10245778182067098334942923710964 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.503
y2[1] (analytic) = 1.1238596616865926064215271335312
y2[1] (numeric) = 1.1238596616865916346964672953222
absolute error = 9.717250598382090e-16
relative error = 8.6463202921610960949418515093497e-14 %
h = 0.0001
y1[1] (analytic) = 2.4820561249274487088131362528522
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0026305863232457085398483176366
relative error = 0.10598415953719021627869493626097 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5031
y2[1] (analytic) = 1.1239078716797066965214129365188
y2[1] (numeric) = 1.1239078716797055516444164564499
absolute error = 1.1448769964800689e-15
relative error = 1.0186573342252896175921696720981e-13 %
h = 0.0001
y1[1] (analytic) = 2.4821437365508534035341718530639
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0027181979466504032608839178483
relative error = 0.10951009430370728454858768163501 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=30.5MB, alloc=3.9MB, time=1.71
x[1] = 0.5032
y2[1] (analytic) = 1.1239560904337420625234640407234
y2[1] (numeric) = 1.1239560904337407206440756375698
absolute error = 1.3418793884031536e-15
relative error = 1.1938895120763245302642408999210e-13 %
h = 0.0001
y1[1] (analytic) = 2.4822313433528207367645378878518
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0028058047486177364912499526362
relative error = 0.11303558615241139928595691624867 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5033
y2[1] (analytic) = 1.1240043179482165168877286090746
y2[1] (numeric) = 1.1240043179482149517717706810076
absolute error = 1.5651159579280670e-15
relative error = 1.3924465706546980840657569167657e-13 %
h = 0.0001
y1[1] (analytic) = 2.4823189453324746404852910815948
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0028934067282716402120031463792
relative error = 0.11656063511548898320379021363783 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5034
y2[1] (analytic) = 1.1240525542226477844698639938838
y2[1] (numeric) = 1.1240525542226459673455712400517
absolute error = 1.8171242927538321e-15
relative error = 1.6165830378015434572126989312331e-13 %
h = 0.0001
y1[1] (analytic) = 2.4824065424889390949006224135825
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0029810038847360946273344783669
relative error = 0.12008524122512367016551028714358 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5035
y2[1] (analytic) = 1.1241007992565535025259594882828
y2[1] (numeric) = 1.1241007992565514019252907789532
absolute error = 2.1006006687093296e-15
relative error = 1.8686942221717160723696120595262e-13 %
h = 0.0001
y1[1] (analytic) = 2.4824941348213381284466173159652
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0030685962171351281733293807496
relative error = 0.12360940451349630474954514789207 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5036
y2[1] (analytic) = 1.1241490530494512207173599536599
y2[1] (numeric) = 1.124149053049448802312486572926
absolute error = 2.4184048733807339e-15
relative error = 2.1513204737578055642577029106497e-13 %
h = 0.0001
y1[1] (analytic) = 2.4825817223287958178000153893858
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0031561837245928175267274541702
relative error = 0.12713312501278494181417130409372 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=3.9MB, time=1.92
NO POLE
NO POLE
x[1] = 0.5037
y2[1] (analytic) = 1.1241973156008584011154903230418
y2[1] (numeric) = 1.1241973156008556275504597081467
absolute error = 2.7735650306148951e-15
relative error = 2.4671514440794465231405135742305e-13 %
h = 0.0001
y1[1] (analytic) = 2.4826693050104362878869696362058
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0032437664062332876136817009902
relative error = 0.13065640275516484606262989421157 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5038
y2[1] (analytic) = 1.1242455869102924182066809803753
y2[1] (numeric) = 1.1242455869102892489242550817546
absolute error = 3.1692824258986207e-15
relative error = 2.8190303460372925576313503835395e-13 %
h = 0.0001
y1[1] (analytic) = 2.4827568828653837118918052112356
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.00333134426118071161851727602
relative error = 0.13417923777280849160851564650062 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5039
y2[1] (analytic) = 1.1242938669772705588969940156605
y2[1] (numeric) = 1.1242938669772669499606614018517
absolute error = 3.6089363326138088e-15
relative error = 3.2099582134310169248261945844324e-13 %
h = 0.0001
y1[1] (analytic) = 2.4828444558927623112657776898846
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.003418917288559310992489754669
relative error = 0.1377016300978855615414385576659 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.504
y2[1] (analytic) = 1.1243421558013100225170503558855
y2[1] (numeric) = 1.1243421558013059264282111875028
absolute error = 4.0960888391683827e-15
relative error = 3.6430981601407016810339461234989e-13 %
h = 0.0001
y1[1] (analytic) = 2.4829320240916963557358308536409
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0035064854874933554625429184253
relative error = 0.14122357976256294749295818319025 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.0MB, time=2.14
NO POLE
NO POLE
x[1] = 0.5041
y2[1] (analytic) = 1.1243904533819279208268577717167
y2[1] (numeric) = 1.1243904533819232863371807687354
absolute error = 4.6344896770029813e-15
relative error = 4.1217796389709817043255671342151e-13 %
h = 0.0001
y1[1] (analytic) = 2.4830195874613101633133539927949
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0035940488571071630400660575793
relative error = 0.14474508679900474920279043209641 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5042
y2[1] (analytic) = 1.1244387597186412780206397598942
y2[1] (numeric) = 1.1244387597186360499395902865397
absolute error = 5.2280810494733545e-15
relative error = 4.6495027001573057100556050862084e-13 %
h = 0.0001
y1[1] (analytic) = 2.4831071460007281003029387263179
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0036816073965251000296507911023
relative error = 0.14826615123937227408528675881179 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5043
y2[1] (analytic) = 1.1244870748109670307316653012861
y2[1] (numeric) = 1.1244870748109611497292036928686
absolute error = 5.8810024616084175e-15
relative error = 5.2299422495336809562984666182024e-13 %
h = 0.0001
y1[1] (analytic) = 2.483194699709074581311135338809
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0037691611048715810378474035934
relative error = 0.1517867731158240367961856449255 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5044
y2[1] (analytic) = 1.1245353986584220280370794945515
y2[1] (numeric) = 1.1245353986584154304415287506379
absolute error = 6.5975955507439136e-15
relative error = 5.8669523063612649070641305265234e-13 %
h = 0.0001
y1[1] (analytic) = 2.4832822485854740692552086344221
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0038567099812710689819206992065
relative error = 0.15530695246051575879963626359932 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.0MB, time=2.36
NO POLE
NO POLE
x[1] = 0.5045
y2[1] (analytic) = 1.1245837312605230314627350653647
y2[1] (numeric) = 1.124583731260515649053817033726
absolute error = 7.3824089180316387e-15
relative error = 6.5645702608171707184351871962644e-13 %
h = 0.0001
y1[1] (analytic) = 2.4833697926290510753718933076862
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0039442540248480750986053724706
relative error = 0.15882668930560036793549421948315 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5046
y2[1] (analytic) = 1.1246320726167867149880247511533
y2[1] (numeric) = 1.124632072616778474785063926974
absolute error = 8.2402029608241793e-15
relative error = 7.3270211311428525629620837216456e-13 %
h = 0.0001
y1[1] (analytic) = 2.4834573318389301592261488311309
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0040317932347271589528608959153
relative error = 0.1623459836832279979868892569658 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5047
y2[1] (analytic) = 1.1246804227267296650507145612998
y2[1] (numeric) = 1.1246804227267204890960086261857
absolute error = 9.1759547059351141e-15
relative error = 8.1587218204514356916416315044141e-13 %
h = 0.0001
y1[1] (analytic) = 2.4835448662142359287199138596289
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0041193276100329284466259244133
relative error = 0.16586483562554598824806482962048 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5048
y2[1] (analytic) = 1.12472878158986838055177791276
y2[1] (numeric) = 1.1247287815898581856891341381278
absolute error = 1.01948626437746322e-14
relative error = 9.0642853731933591073057686542243e-13 %
h = 0.0001
y1[1] (analytic) = 2.4836323957540930401008601513698
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0042068571498900398275722161542
relative error = 0.16938324516469888309248942383736 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.0MB, time=2.58
NO POLE
NO POLE
x[1] = 0.5049
y2[1] (analytic) = 1.1247771492057192728602306410493
y2[1] (numeric) = 1.1247771492057079705086672805296
absolute error = 1.13023515633605197e-14
relative error = 1.0048525231279698051639080362516e-12 %
h = 0.0001
y1[1] (analytic) = 2.4837199204576261979711460053762
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0042943818534231976978580701606
relative error = 0.17290121233282843154123952953543 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.505
y2[1] (analytic) = 1.1248255255737986658179668865485
y2[1] (numeric) = 1.1248255255737861617405786820832
absolute error = 1.25040773882044653e-14
relative error = 1.1116459489862532836901440217852e-12 %
h = 0.0001
y1[1] (analytic) = 2.4838074403239601552961692154743
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0043819017197571550228812802587
relative error = 0.17641873716207358683165415092659 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5051
y2[1] (analytic) = 1.1248739106936227957445958560807
y2[1] (numeric) = 1.1248739106936089898125827824433
absolute error = 1.38059320130736374e-14
relative error = 1.2273315152771732638620767021862e-12 %
h = 0.0001
y1[1] (analytic) = 2.4838949553522197134133195406332
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0044694167480167131400316054176
relative error = 0.17993581968457050598626075041799 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5052
y2[1] (analytic) = 1.1249223045647078114422794597113
y2[1] (numeric) = 1.1249223045646925973941378322274
absolute error = 1.52140481416274839e-14
relative error = 1.3524532387607522105467943310908e-12 %
h = 0.0001
y1[1] (analytic) = 2.4839824655415297220407306915832
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0045569269373267217674427563676
relative error = 0.1834524599324525493819725186141 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=49.5MB, alloc=4.0MB, time=2.80
x[1] = 0.5053
y2[1] (analytic) = 1.1249707071865697742005708227225
y2[1] (numeric) = 1.1249707071865530393964458930158
absolute error = 1.67348041249297067e-14
relative error = 1.4875768780488199749688607474205e-12 %
h = 0.0001
y1[1] (analytic) = 2.4840699708910150792860318336276
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.004644432286812079012743898412
relative error = 0.18696865793785028031955686358144 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5054
y2[1] (analytic) = 1.1250191185587246578012536727134
y2[1] (numeric) = 1.1250191185587062829724528373515
absolute error = 1.83748288008353619e-14
relative error = 1.6332903590452376588433787333975e-12 %
h = 0.0001
y1[1] (analytic) = 2.4841574713998007316550986055588
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0047319327955977313818106703432
relative error = 0.1904844137328914645933750124228 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5055
y2[1] (analytic) = 1.1250675386806883485231826017783
y2[1] (numeric) = 1.1250675386806682075168483487401
absolute error = 2.01410063342530382e-14
relative error = 1.7902042003515105235784214681932e-12 %
h = 0.0001
y1[1] (analytic) = 2.4842449670670116740608036545925
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0048194284628086737875157193769
relative error = 0.1939997273497010700613926183604 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5056
y2[1] (analytic) = 1.1251159675519766451471242037142
y2[1] (numeric) = 1.1251159675519546046660659216501
absolute error = 2.20404810582820641e-14
relative error = 1.9589519386377268352341251832706e-12 %
h = 0.0001
y1[1] (analytic) = 2.4843324578917729498317666872315
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0049069192875699495584787520159
relative error = 0.19751459882040126621546126646809 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5057
y2[1] (analytic) = 1.1251644051721052589605990862088
y2[1] (numeric) = 1.1251644051720811782982828615126
absolute error = 2.40806623162246962e-14
relative error = 2.1401905539787597266574190464716e-12 %
h = 0.0001
y1[1] (analytic) = 2.4844199438732096507211040359722
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0049944052690066504478161007566
relative error = 0.20102902817711142375187077128874 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.0MB, time=3.01
NO POLE
NO POLE
x[1] = 0.5058
y2[1] (analytic) = 1.1252128515405898137627247579617
y2[1] (numeric) = 1.1252128515405635445334202847215
absolute error = 2.62692293044732402e-14
relative error = 2.3346008951556691355967337004784e-12 %
h = 0.0001
y1[1] (analytic) = 2.4845074250104469169151777417664
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0050818864062439166418898065508
relative error = 0.20454301545194811414217215958604 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5059
y2[1] (analytic) = 1.125261306656945845869059390689
y2[1] (numeric) = 1.1252613066569172317331431186334
absolute error = 2.86141359162720556e-14
relative error = 2.5428881049222408639024943325617e-12 %
h = 0.0001
y1[1] (analytic) = 2.4845949013026099370423441521499
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0051693626984069367690562169343
relative error = 0.20805656067702510920427123146752 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.506
y2[1] (analytic) = 1.1253097705206888041164464559634
y2[1] (numeric) = 1.1253097705206576805008601015676
absolute error = 3.11236155863543958e-14
relative error = 2.7657820452365999047702352938993e-12 %
h = 0.0001
y1[1] (analytic) = 2.4846823727488239481817020349524
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0052568341446209479084140997368
relative error = 0.2115696638844533806737925932691 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5061
y2[1] (analytic) = 1.125358243131334049867860236842
y2[1] (numeric) = 1.1253582431313002436817237828062
absolute error = 3.38061861364540358e-14
relative error = 3.0040377224578352690431124989298e-12 %
h = 0.0001
y1[1] (analytic) = 2.4847698393482142358718402074983
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0053443007440112355985522722827
relative error = 0.21508232510634109977571405542669 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.0MB, time=3.23
NO POLE
NO POLE
x[1] = 0.5062
y2[1] (analytic) = 1.1254067244883968570172522142328
y2[1] (numeric) = 1.1254067244883601863626305225941
absolute error = 3.66706546216916387e-14
relative error = 3.2584357125075734923532679076673e-12 %
h = 0.0001
y1[1] (analytic) = 2.4848573010999061341195846812144
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0054317624957031338462967459988
relative error = 0.21859454437479363679627128885001 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5063
y2[1] (analytic) = 1.1254552145913924119943983279504
y2[1] (numeric) = 1.1254552145913526858722204921387
absolute error = 3.97261221778358117e-14
relative error = 3.5297825859964380001101863411506e-12 %
h = 0.0001
y1[1] (analytic) = 2.4849447580030250254087453215537
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0055192193988220251354573863381
relative error = 0.22210632172191356065513263307314 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5064
y2[1] (analytic) = 1.1255037134398358137697471124149
y2[1] (numeric) = 1.1255037134397928317808776736103
absolute error = 4.29819888694388046e-14
relative error = 3.8189113333153317513726772595572e-12 %
h = 0.0001
y1[1] (analytic) = 2.4850322100566963407088620231503
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0056066714524933404355740879347
relative error = 0.22561765717980063847784394972158 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5065
y2[1] (analytic) = 1.1255522210332420738592687069431
y2[1] (numeric) = 1.1255522210331956259007298601418
absolute error = 4.64479585388468013e-14
relative error = 4.1266817896914804001380728790430e-12 %
h = 0.0001
y1[1] (analytic) = 2.4851196572600455594839504001169
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0056941186558425592106624649013
relative error = 0.22912855078055183516854341472728 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.0MB, time=3.45
NO POLE
NO POLE
x[1] = 0.5066
y2[1] (analytic) = 1.1256007373711261163293047405846
y2[1] (numeric) = 1.125600737371075982285648655829
absolute error = 5.01340436560847556e-14
relative error = 4.4539810602091733233471490516041e-12 %
h = 0.0001
y1[1] (analytic) = 2.4852070996121982097012469913967
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0057815610079952094279590561811
relative error = 0.23263900255626131298294614276802 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5067
y2[1] (analytic) = 1.1256492624530027778014190914547
y2[1] (numeric) = 1.1256492624529487272312494757303
absolute error = 5.40505701696157244e-14
relative error = 4.8017239447951400644832596296155e-12 %
h = 0.0001
y1[1] (analytic) = 2.4852945371122798678399539810846
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.005868998508076867566666045869
relative error = 0.23614901253902043110159853756371 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5068
y2[1] (analytic) = 1.1256977962783868074572495205144
y2[1] (numeric) = 1.1256977962783285992748915458669
absolute error = 5.82081823579746475e-14
relative error = 5.1708533631684994348145102154945e-12 %
h = 0.0001
y1[1] (analytic) = 2.4853819697594161588999834336272
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0059564311552131586266954984116
relative error = 0.23965858076091774520340226147838 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5069
y2[1] (analytic) = 1.1257463388467928670433601797501
y2[1] (numeric) = 1.1257463388467302491956779032226
absolute error = 6.26178476822765275e-14
relative error = 5.5623407797552189360431910220380e-12 %
h = 0.0001
y1[1] (analytic) = 2.4854693975527327564107010438169
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0060438589485297561374131086013
relative error = 0.2431677072540390070394077181413 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.0MB, time=3.66
NO POLE
NO POLE
x[1] = 0.507
y2[1] (analytic) = 1.1257948901577355308760949947039
y2[1] (numeric) = 1.1257948901576682400144553957441
absolute error = 6.72908616395989598e-14
relative error = 5.9771866285670218968550162568950e-12 %
h = 0.0001
y1[1] (analytic) = 2.4855568204913553824396694014904
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0061312818871523821663814662748
relative error = 0.24667639205046716400687694163286 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5071
y2[1] (analytic) = 1.1258434502107292858464319213063
y2[1] (numeric) = 1.1258434502106570469938146823407
absolute error = 7.22388526172389656e-14
relative error = 6.4164207380446800131773284727611e-12 %
h = 0.0001
y1[1] (analytic) = 2.4856442385744098076013907708465
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0062186999702068073281028356309
relative error = 0.25018463518228235872361578599722 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5072
y2[1] (analytic) = 1.125892019005288531424838076962
y2[1] (numeric) = 1.1258920190052110576380902328845
absolute error = 7.74737867478440775e-14
relative error = 6.8811027558656287285024841520392e-12 %
h = 0.0001
y1[1] (analytic) = 2.4857316518010218510660493842931
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0063061131968188507927614490775
relative error = 0.25369243668156192860257530867599 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5073
y2[1] (analytic) = 1.1259405965409275796661257458414
y2[1] (numeric) = 1.1259405965408445716933603282104
absolute error = 8.30079727654176310e-14
relative error = 7.3723225737158432590008025600716e-12 %
h = 0.0001
y1[1] (analytic) = 2.4858190601703173805682532507384
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0063935215661143802949653155228
relative error = 0.25719979658038040542672224169378 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=68.6MB, alloc=4.0MB, time=3.89
x[1] = 0.5074
y2[1] (analytic) = 1.1259891828171606552143092583286
y2[1] (numeric) = 1.1259891828170718011474470601158
absolute error = 8.88540668621982128e-14
relative error = 7.8912007520259128946470242922356e-12 %
h = 0.0001
y1[1] (analytic) = 2.4859064636814223124157754782377
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0064809250772193121424875430221
relative error = 0.2607067149108095149241784443146 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5075
y2[1] (analytic) = 1.1260377778335018953074627445769
y2[1] (numeric) = 1.126037777833406870229916331361
absolute error = 9.50250775464132159e-14
relative error = 8.4388889446712511673818542269546e-12 %
h = 0.0001
y1[1] (analytic) = 2.485993862333462611498295110908
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0065683237292596112250071756924
relative error = 0.26421319170491817634362923095228 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5076
y2[1] (analytic) = 1.126086381589465349782578762124
y2[1] (numeric) = 1.126086381589363815412077855669
absolute error = 1.015343705009064550e-13
relative error = 9.0165703236363798278974674618470e-12 %
h = 0.0001
y1[1] (analytic) = 2.4860812561255642912961374800242
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0066557175213612910228495448086
relative error = 0.2677192269947725020300004682148 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5077
y2[1] (analytic) = 1.1261349940845649810804277975184
y2[1] (numeric) = 1.1261349940844565854069851577255
absolute error = 1.083956734426397929e-13
relative error = 9.6254600036432243636516425070035e-12 %
h = 0.0001
y1[1] (analytic) = 2.4861686450568534138890140692085
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0067431064526504136157261339929
relative error = 0.27122482081243579700040433490639 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5078
y2[1] (analytic) = 1.1261836153183146642504186419074
y2[1] (numeric) = 1.126183615318199041169435573179
absolute error = 1.156230809830687284e-13
relative error = 1.0266805466743358812700560453097e-11 %
h = 0.0001
y1[1] (analytic) = 2.486256029126456089964761893626
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0068304905222530896914739584104
relative error = 0.2747299731899685585203536388995 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.0MB, time=4.11
NO POLE
NO POLE
x[1] = 0.5079
y2[1] (analytic) = 1.1262322452902281869554596405387
y2[1] (numeric) = 1.1262322452901049558959702486407
absolute error = 1.232310594893918980e-13
relative error = 1.0941886986874137827520629868585e-11 %
h = 0.0001
y1[1] (analytic) = 2.486343408333498478828082393099
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0069178697292954785547944578834
relative error = 0.2782346841594284756802445848015 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.508
y2[1] (analytic) = 1.1262808839998192494768208161278
y2[1] (numeric) = 1.1262808839996880150248741416844
absolute error = 1.312344519466744434e-13
relative error = 1.1652018054378653956058284869067e-11 %
h = 0.0001
y1[1] (analytic) = 2.4864307826771067884092798390526
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.007005244072903788135991903837
relative error = 0.28173895375287042897210788637658 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5081
y2[1] (analytic) = 1.1263295314466014647189968660408
y2[1] (numeric) = 1.1263295314464618162361760208468
absolute error = 1.396484828208451940e-13
relative error = 1.2398545800489457898370455326369e-11 %
h = 0.0001
y1[1] (analytic) = 2.4865181521564072752729992552048
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0070926135522042749997113199892
relative error = 0.28524278200234648986662811774034 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5082
y2[1] (analytic) = 1.1263781876300883582145710332457
y2[1] (numeric) = 1.1263781876299398694516484656273
absolute error = 1.484887629225676184e-13
relative error = 1.3182851421775979963172483994906e-11 %
h = 0.0001
y1[1] (analytic) = 2.4866055167705262446269638519124
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0071799781663232443536759166968
relative error = 0.28874616893990592039043119730001 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.0MB, time=4.33
NO POLE
NO POLE
x[1] = 0.5083
y2[1] (analytic) = 1.1264268525497933681290798509824
y2[1] (numeric) = 1.1264268525496355968348078664879
absolute error = 1.577712942719844945e-13
relative error = 1.4006350604555590597661469857467e-11 %
h = 0.0001
y1[1] (analytic) = 2.4866928765185900503307119740863
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0072673379143870500574240388707
relative error = 0.2922491145975951727036398985382 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5084
y2[1] (analytic) = 1.1264755262052298452658787611032
y2[1] (numeric) = 1.1264755262050623327909144248535
absolute error = 1.675124749643362497e-13
relative error = 1.4870493949268238072457237858129e-11 %
h = 0.0001
y1[1] (analytic) = 2.4867802313997250949043335625894
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0073546927955220946310456273738
relative error = 0.29575161900745788867769728175415 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5085
y2[1] (analytic) = 1.1265242085959110530710086060352
y2[1] (numeric) = 1.1265242085957333239669721531116
absolute error = 1.777291040364529236e-13
relative error = 1.5776767394814601523147807762084e-11 %
h = 0.0001
y1[1] (analytic) = 2.4868675814130578295372061290281
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0074420428088548292639181938125
relative error = 0.29925368220153489947345794082024 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5086
y2[1] (analytic) = 1.126572899721350167638062994316
y2[1] (numeric) = 1.1265728997211617292517288746125
absolute error = 1.884383863341197035e-13
relative error = 1.6726692642857697403250106967312e-11 %
h = 0.0001
y1[1] (analytic) = 2.4869549265577147540967302438511
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0075293879535117538234423086355
relative error = 0.30275530421186422511954695915242 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.0MB, time=4.55
NO POLE
NO POLE
x[1] = 0.5087
y2[1] (analytic) = 1.1266215995810602777130565396536
y2[1] (numeric) = 1.1266215995808606197756762236692
absolute error = 1.996579373803159844e-13
relative error = 1.7721827582087877567460973709140e-11 %
h = 0.0001
y1[1] (analytic) = 2.4870422668328224171370645376684
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0076167282286194168637766024528
relative error = 0.3062564850704810740909864690931 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5088
y2[1] (analytic) = 1.1266703081745543846992939734623
y2[1] (numeric) = 1.1266703081743429789110496455574
absolute error = 2.114057882443279049e-13
relative error = 1.8763766712451157217206964985886e-11 %
h = 0.0001
y1[1] (analytic) = 2.4871296022375074159078602157024
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0077040636333044156345722804868
relative error = 0.30975722480941784288808970889725 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5089
y2[1] (analytic) = 1.1267190255013454026622401308252
y2[1] (numeric) = 1.1267190255011217022718283965156
absolute error = 2.237003904117343096e-13
relative error = 1.9854141569340810909273242252550e-11 %
h = 0.0001
y1[1] (analytic) = 2.4872169327708963963629950852839
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0077913941666933960897071500683
relative error = 0.31325752346070411561562247158066 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.509
y2[1] (analytic) = 1.126767751560946158334390809836
y2[1] (numeric) = 1.1267677515607095977137355437449
absolute error = 2.365606206552660911e-13
relative error = 2.0994621147752175089968880977799e-11 %
h = 0.0001
y1[1] (analytic) = 2.4873042584321160531693070963062
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0078787198279130528960191610906
relative error = 0.31675738105636666356223183993781 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.0MB, time=4.79
NO POLE
NO POLE
x[1] = 0.5091
y2[1] (analytic) = 1.1268164863528693911201445042698
y2[1] (numeric) = 1.1268164863526193853342379654093
absolute error = 2.500057859065388605e-13
relative error = 2.2186912326400595284285708557927e-11 %
h = 0.0001
y1[1] (analytic) = 2.4873915792202931297153273945494
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0079660406160901294420394593338
relative error = 0.32025679762842944478014210202461 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5092
y2[1] (analytic) = 1.1268652298766277531006750095348
y2[1] (numeric) = 1.1268652298763636974725463506354
absolute error = 2.640556281286588994e-13
relative error = 2.3432760291802456473213705750257e-11 %
h = 0.0001
y1[1] (analytic) = 2.487478895134554418120012887788
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0080533565303514178467249525724
relative error = 0.32375577320891360366511774147363 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5093
y2[1] (analytic) = 1.1269139821317338090388049018571
y2[1] (numeric) = 1.1269139821314550787096151995126
absolute error = 2.787303291897023445e-13
relative error = 2.4733948962319235063517289138662e-11 %
h = 0.0001
y1[1] (analytic) = 2.4875662061740267592414783245936
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.008140667569823758968190389378
relative error = 0.32725430782983747053669339698971 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5094
y2[1] (analytic) = 1.1269627431177000363838798906477
y2[1] (numeric) = 1.1269627431174059858681428230931
absolute error = 2.940505157370675546e-13
relative error = 2.6092301412164510778728624243945e-11 %
h = 0.0001
y1[1] (analytic) = 2.4876535123378370426857278857469
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0082279737336340424124399505313
relative error = 0.3307524015232165612186706855019 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=87.7MB, alloc=4.0MB, time=5.01
x[1] = 0.5095
y2[1] (analytic) = 1.1270115128340388252766440440054
y2[1] (numeric) = 1.1270115128337287880125713433916
absolute error = 3.100372640727006138e-13
relative error = 2.7509680295373877194885591658868e-11 %
h = 0.0001
y1[1] (analytic) = 2.4877408136251122068153862881703
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0083152750209092065420983529547
relative error = 0.33425005432106357661988178336379 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5096
y2[1] (analytic) = 1.1270602912802624785541158873053
y2[1] (numeric) = 1.1270602912799357664490866933857
absolute error = 3.267121050291939196e-13
relative error = 2.8987988269737689231769481234105e-11 %
h = 0.0001
y1[1] (analytic) = 2.4878281100349792387584294012944
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0084025714307762384851414660788
relative error = 0.3377472662553884023152196601067 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5097
y2[1] (analytic) = 1.1271090784558832117544653748244
y2[1] (numeric) = 1.1271090784555391147256186170157
absolute error = 3.440970288467578087e-13
relative error = 3.0529168420696586314053129185082e-11 %
h = 0.0001
y1[1] (analytic) = 2.4879154015665651744169143757705
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0084898629623621741436264405549
relative error = 0.34124403735819810812693485923398 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5098
y2[1] (analytic) = 1.1271578743604131531218917343559
y2[1] (numeric) = 1.1271578743600509386318406691846
absolute error = 3.622144900510651713e-13
relative error = 3.2135204685199729779104375153932e-11 %
h = 0.0001
y1[1] (analytic) = 2.4880026882189970984757092844435
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.0085771496147940982024213492279
relative error = 0.34474036766149694770619872066933 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5099
y2[1] (analytic) = 1.1272066789933643436115021847631
y2[1] (numeric) = 1.1272066789929832561991702157581
absolute error = 3.810874123319690050e-13
relative error = 3.3808122275525693174641584394278e-11 %
h = 0.0001
y1[1] (analytic) = 2.4880899699914021444112222754956
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.00866443138719914413793434028
relative error = 0.34823625719728635811493293934347 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.0MB, time=5.23
NO POLE
NO POLE
x[1] = 0.51
y2[1] (analytic) = 1.1272554923542487368941915264245
y2[1] (numeric) = 1.1272554923538479977007684335648
absolute error = 4.007391934230928597e-13
relative error = 3.5549988103065944155883831730206e-11 %
h = 0.0001
y1[1] (analytic) = 2.4881772468829074945001302376746
y1[1] (numeric) = 2.4794255386042030002732879352156
absolute error = 0.008751708278704494226842302459
relative error = 0.35173170599756495940790535457244 %
h = 0.0001
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 = 5 Seconds
Elapsed Time(since restart) = 5 Seconds
Expected Time Remaining = 1 Hours 22 Minutes 4 Seconds
Optimized Time Remaining = 1 Hours 21 Minutes 50 Seconds
Time to Timeout = 14 Minutes 54 Seconds
Percent Done = 0.1063 %
> quit
memory used=92.4MB, alloc=4.0MB, time=5.28