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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> INFO,
> glob_iolevel,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> #Top Generate Globals Decl
> glob_h,
> glob_subiter_method,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_warned,
> glob_relerr,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_dump_analytic,
> glob_max_sec,
> glob_abserr,
> glob_not_yet_finished,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_hmin,
> glob_initial_pass,
> hours_in_day,
> glob_display_flag,
> glob_html_log,
> glob_log10normmin,
> glob_log10abserr,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_large_float,
> glob_hmin_init,
> djd_debug,
> glob_log10relerr,
> glob_log10_abserr,
> glob_look_poles,
> glob_disp_incr,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_almost_1,
> years_in_century,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmax,
> min_in_hour,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_log10_relerr,
> glob_max_opt_iter,
> glob_percent_done,
> glob_optimal_start,
> glob_no_eqs,
> centuries_in_millinium,
> days_in_year,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_y2_init,
> array_x,
> array_last_rel_error,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_complex_pole,
> array_real_pole,
> array_y2_higher,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher,
> array_y2_set_initial,
> array_y1_higher_work,
> 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 INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL,
glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec,
glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec,
djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED,
glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr,
glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h,
glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag,
glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter,
glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours,
glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr,
glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done,
glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century,
glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax,
min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter,
glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start,
glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump,
array_const_0D0, array_const_1D0, array_const_1, array_const_5,
array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error,
array_y1_init, array_y2_init, array_x, array_last_rel_error,
array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2,
array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2,
array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work,
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
> INFO,
> glob_iolevel,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> #Top Generate Globals Decl
> glob_h,
> glob_subiter_method,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_warned,
> glob_relerr,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_dump_analytic,
> glob_max_sec,
> glob_abserr,
> glob_not_yet_finished,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_hmin,
> glob_initial_pass,
> hours_in_day,
> glob_display_flag,
> glob_html_log,
> glob_log10normmin,
> glob_log10abserr,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_large_float,
> glob_hmin_init,
> djd_debug,
> glob_log10relerr,
> glob_log10_abserr,
> glob_look_poles,
> glob_disp_incr,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_almost_1,
> years_in_century,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmax,
> min_in_hour,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_log10_relerr,
> glob_max_opt_iter,
> glob_percent_done,
> glob_optimal_start,
> glob_no_eqs,
> centuries_in_millinium,
> days_in_year,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_y2_init,
> array_x,
> array_last_rel_error,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_complex_pole,
> array_real_pole,
> array_y2_higher,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher,
> array_y2_set_initial,
> array_y1_higher_work,
> 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 INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL,
glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec,
glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec,
djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED,
glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr,
glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h,
glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag,
glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter,
glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours,
glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr,
glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done,
glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century,
glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax,
min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter,
glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start,
glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump,
array_const_0D0, array_const_1D0, array_const_1, array_const_5,
array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error,
array_y1_init, array_y2_init, array_x, array_last_rel_error,
array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2,
array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2,
array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work,
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
> INFO,
> glob_iolevel,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> #Top Generate Globals Decl
> glob_h,
> glob_subiter_method,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_warned,
> glob_relerr,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_dump_analytic,
> glob_max_sec,
> glob_abserr,
> glob_not_yet_finished,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_hmin,
> glob_initial_pass,
> hours_in_day,
> glob_display_flag,
> glob_html_log,
> glob_log10normmin,
> glob_log10abserr,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_large_float,
> glob_hmin_init,
> djd_debug,
> glob_log10relerr,
> glob_log10_abserr,
> glob_look_poles,
> glob_disp_incr,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_almost_1,
> years_in_century,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmax,
> min_in_hour,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_log10_relerr,
> glob_max_opt_iter,
> glob_percent_done,
> glob_optimal_start,
> glob_no_eqs,
> centuries_in_millinium,
> days_in_year,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_y2_init,
> array_x,
> array_last_rel_error,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_complex_pole,
> array_real_pole,
> array_y2_higher,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher,
> array_y2_set_initial,
> array_y1_higher_work,
> 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 INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL,
glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec,
glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec,
djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED,
glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr,
glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h,
glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag,
glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter,
glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours,
glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr,
glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done,
glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century,
glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax,
min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter,
glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start,
glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump,
array_const_0D0, array_const_1D0, array_const_1, array_const_5,
array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error,
array_y1_init, array_y2_init, array_x, array_last_rel_error,
array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2,
array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2,
array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work,
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
> INFO,
> glob_iolevel,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> #Top Generate Globals Decl
> glob_h,
> glob_subiter_method,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_warned,
> glob_relerr,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_dump_analytic,
> glob_max_sec,
> glob_abserr,
> glob_not_yet_finished,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_hmin,
> glob_initial_pass,
> hours_in_day,
> glob_display_flag,
> glob_html_log,
> glob_log10normmin,
> glob_log10abserr,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_large_float,
> glob_hmin_init,
> djd_debug,
> glob_log10relerr,
> glob_log10_abserr,
> glob_look_poles,
> glob_disp_incr,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_almost_1,
> years_in_century,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmax,
> min_in_hour,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_log10_relerr,
> glob_max_opt_iter,
> glob_percent_done,
> glob_optimal_start,
> glob_no_eqs,
> centuries_in_millinium,
> days_in_year,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_y2_init,
> array_x,
> array_last_rel_error,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_complex_pole,
> array_real_pole,
> array_y2_higher,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher,
> array_y2_set_initial,
> array_y1_higher_work,
> 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 - 5 - 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 - 5 - 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 INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL,
glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec,
glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec,
djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED,
glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr,
glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h,
glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag,
glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter,
glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours,
glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr,
glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done,
glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century,
glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax,
min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter,
glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start,
glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump,
array_const_0D0, array_const_1D0, array_const_1, array_const_5,
array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error,
array_y1_init, array_y2_init, array_x, array_last_rel_error,
array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2,
array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2,
array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work,
glob_last;
n := glob_max_terms;
m := n - 6;
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 - 6;
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
> INFO,
> glob_iolevel,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> #Top Generate Globals Decl
> glob_h,
> glob_subiter_method,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_warned,
> glob_relerr,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_dump_analytic,
> glob_max_sec,
> glob_abserr,
> glob_not_yet_finished,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_hmin,
> glob_initial_pass,
> hours_in_day,
> glob_display_flag,
> glob_html_log,
> glob_log10normmin,
> glob_log10abserr,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_large_float,
> glob_hmin_init,
> djd_debug,
> glob_log10relerr,
> glob_log10_abserr,
> glob_look_poles,
> glob_disp_incr,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_almost_1,
> years_in_century,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmax,
> min_in_hour,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_log10_relerr,
> glob_max_opt_iter,
> glob_percent_done,
> glob_optimal_start,
> glob_no_eqs,
> centuries_in_millinium,
> days_in_year,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_y2_init,
> array_x,
> array_last_rel_error,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_complex_pole,
> array_real_pole,
> array_y2_higher,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher,
> array_y2_set_initial,
> array_y1_higher_work,
> 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 INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL,
glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec,
glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec,
djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED,
glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr,
glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h,
glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag,
glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter,
glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours,
glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr,
glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done,
glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century,
glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax,
min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter,
glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start,
glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump,
array_const_0D0, array_const_1D0, array_const_1, array_const_5,
array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error,
array_y1_init, array_y2_init, array_x, array_last_rel_error,
array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2,
array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2,
array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work,
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
> INFO,
> glob_iolevel,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> #Top Generate Globals Decl
> glob_h,
> glob_subiter_method,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_warned,
> glob_relerr,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_dump_analytic,
> glob_max_sec,
> glob_abserr,
> glob_not_yet_finished,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_hmin,
> glob_initial_pass,
> hours_in_day,
> glob_display_flag,
> glob_html_log,
> glob_log10normmin,
> glob_log10abserr,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_large_float,
> glob_hmin_init,
> djd_debug,
> glob_log10relerr,
> glob_log10_abserr,
> glob_look_poles,
> glob_disp_incr,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_almost_1,
> years_in_century,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmax,
> min_in_hour,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_log10_relerr,
> glob_max_opt_iter,
> glob_percent_done,
> glob_optimal_start,
> glob_no_eqs,
> centuries_in_millinium,
> days_in_year,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_y2_init,
> array_x,
> array_last_rel_error,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_complex_pole,
> array_real_pole,
> array_y2_higher,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher,
> array_y2_set_initial,
> array_y1_higher_work,
> 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 assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y2_set_initial[1,6] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[1] * (glob_h ^ (5)) * factorial_3(0,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,4] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,3] := temporary
> ;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[5,2] := temporary
> ;
> temporary := temporary / glob_h * (6.0);
> array_y2_higher[6,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> # emit pre mult $eq_no = 2 i = 1
> array_tmp3[1] := (array_m1[1] * (array_y2[1]));
> #emit pre add $eq_no = 2 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_1D0[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 assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y2_set_initial[1,7] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[2] * (glob_h ^ (5)) * factorial_3(1,6);
> array_y2[7] := temporary;
> array_y2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,5] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,4] := temporary
> ;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[5,3] := temporary
> ;
> temporary := temporary / glob_h * (6.0);
> array_y2_higher[6,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> # emit pre mult $eq_no = 2 i = 2
> array_tmp3[2] := ats(2,array_m1,array_y2,1);
> #emit pre add $eq_no = 2 i = 2
> array_tmp4[2] := array_tmp3[2] + array_const_1D0[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 assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y2_set_initial[1,8] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[3] * (glob_h ^ (5)) * factorial_3(2,7);
> array_y2[8] := temporary;
> array_y2_higher[1,8] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,7] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,6] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,5] := temporary
> ;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[5,4] := temporary
> ;
> temporary := temporary / glob_h * (6.0);
> array_y2_higher[6,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> # emit pre mult $eq_no = 2 i = 3
> array_tmp3[3] := ats(3,array_m1,array_y2,1);
> #emit pre add $eq_no = 2 i = 3
> array_tmp4[3] := array_tmp3[3] + array_const_1D0[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 assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y2_set_initial[1,9] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[4] * (glob_h ^ (5)) * factorial_3(3,8);
> array_y2[9] := temporary;
> array_y2_higher[1,9] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,8] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,7] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,6] := temporary
> ;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[5,5] := temporary
> ;
> temporary := temporary / glob_h * (6.0);
> array_y2_higher[6,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> # emit pre mult $eq_no = 2 i = 4
> array_tmp3[4] := ats(4,array_m1,array_y2,1);
> #emit pre add $eq_no = 2 i = 4
> array_tmp4[4] := array_tmp3[4] + array_const_1D0[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 assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y2_set_initial[1,10] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[5] * (glob_h ^ (5)) * factorial_3(4,9);
> array_y2[10] := temporary;
> array_y2_higher[1,10] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,9] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,8] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,7] := temporary
> ;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[5,6] := temporary
> ;
> temporary := temporary / glob_h * (6.0);
> array_y2_higher[6,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> # emit pre mult $eq_no = 2 i = 5
> array_tmp3[5] := ats(5,array_m1,array_y2,1);
> #emit pre add $eq_no = 2 i = 5
> array_tmp4[5] := array_tmp3[5] + array_const_1D0[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 assign $eq_no = 1
> order_d := 5;
> 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_tmp1[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 mult $eq_no = 2
> array_tmp3[kkk] := ats(kkk,array_m1,array_y2,1);
> #emit add $eq_no = 2
> array_tmp4[kkk] := array_tmp3[kkk] + array_const_1D0[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 INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL,
glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec,
glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec,
djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED,
glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr,
glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h,
glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag,
glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter,
glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours,
glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr,
glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done,
glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century,
glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax,
min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter,
glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start,
glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump,
array_const_0D0, array_const_1D0, array_const_1, array_const_5,
array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error,
array_y1_init, array_y2_init, array_x, array_last_rel_error,
array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2,
array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2,
array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work,
glob_last;
array_tmp1[1] := array_const_0D0[1] + array_y1[1];
if not array_y2_set_initial[1, 6] then
if 1 <= glob_max_terms then
temporary := array_tmp1[1]*glob_h^5*factorial_3(0, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 4] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 3] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[5, 2] := temporary;
temporary := temporary*6.0/glob_h;
array_y2_higher[6, 1] := temporary
end if
end if;
kkk := 2;
array_tmp3[1] := array_m1[1]*array_y2[1];
array_tmp4[1] := array_tmp3[1] + array_const_1D0[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];
if not array_y2_set_initial[1, 7] then
if 2 <= glob_max_terms then
temporary := array_tmp1[2]*glob_h^5*factorial_3(1, 6);
array_y2[7] := temporary;
array_y2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 4] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[5, 3] := temporary;
temporary := temporary*6.0/glob_h;
array_y2_higher[6, 2] := temporary
end if
end if;
kkk := 3;
array_tmp3[2] := ats(2, array_m1, array_y2, 1);
array_tmp4[2] := array_tmp3[2] + array_const_1D0[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];
if not array_y2_set_initial[1, 8] then
if 3 <= glob_max_terms then
temporary := array_tmp1[3]*glob_h^5*factorial_3(2, 7);
array_y2[8] := temporary;
array_y2_higher[1, 8] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 7] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 6] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 5] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[5, 4] := temporary;
temporary := temporary*6.0/glob_h;
array_y2_higher[6, 3] := temporary
end if
end if;
kkk := 4;
array_tmp3[3] := ats(3, array_m1, array_y2, 1);
array_tmp4[3] := array_tmp3[3] + array_const_1D0[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];
if not array_y2_set_initial[1, 9] then
if 4 <= glob_max_terms then
temporary := array_tmp1[4]*glob_h^5*factorial_3(3, 8);
array_y2[9] := temporary;
array_y2_higher[1, 9] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 8] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 7] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[5, 5] := temporary;
temporary := temporary*6.0/glob_h;
array_y2_higher[6, 4] := temporary
end if
end if;
kkk := 5;
array_tmp3[4] := ats(4, array_m1, array_y2, 1);
array_tmp4[4] := array_tmp3[4] + array_const_1D0[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];
if not array_y2_set_initial[1, 10] then
if 5 <= glob_max_terms then
temporary := array_tmp1[5]*glob_h^5*factorial_3(4, 9);
array_y2[10] := temporary;
array_y2_higher[1, 10] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 9] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 8] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 7] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[5, 6] := temporary;
temporary := temporary*6.0/glob_h;
array_y2_higher[6, 5] := temporary
end if
end if;
kkk := 6;
array_tmp3[5] := ats(5, array_m1, array_y2, 1);
array_tmp4[5] := array_tmp3[5] + array_const_1D0[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];
order_d := 5;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := array_tmp1[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_tmp3[kkk] := ats(kkk, array_m1, array_y2, 1);
array_tmp4[kkk] := array_tmp3[kkk] + array_const_1D0[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)
> 1.0 + cos(x);
> end;
exact_soln_y1 := proc(x) 1.0 + cos(x) end proc
> exact_soln_y2 := proc(x)
> 1.0 + sin(x);
> end;
exact_soln_y2 := proc(x) 1.0 + sin(x) end proc
> exact_soln_y2p := proc(x)
> cos(x);
> end;
exact_soln_y2p := proc(x) cos(x) end proc
> exact_soln_y2pp := proc(x)
> -sin(x);
> end;
exact_soln_y2pp := proc(x) -sin(x) end proc
> exact_soln_y2ppp := proc(x)
> -cos(x);
> end;
exact_soln_y2ppp := proc(x) -cos(x) end proc
> exact_soln_y2pppp := proc(x)
> sin(x);
> end;
exact_soln_y2pppp := proc(x) sin(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
> INFO,
> glob_iolevel,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> #Top Generate Globals Decl
> glob_h,
> glob_subiter_method,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_warned,
> glob_relerr,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_dump_analytic,
> glob_max_sec,
> glob_abserr,
> glob_not_yet_finished,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_hmin,
> glob_initial_pass,
> hours_in_day,
> glob_display_flag,
> glob_html_log,
> glob_log10normmin,
> glob_log10abserr,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_large_float,
> glob_hmin_init,
> djd_debug,
> glob_log10relerr,
> glob_log10_abserr,
> glob_look_poles,
> glob_disp_incr,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_almost_1,
> years_in_century,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_hmax,
> min_in_hour,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_log10_relerr,
> glob_max_opt_iter,
> glob_percent_done,
> glob_optimal_start,
> glob_no_eqs,
> centuries_in_millinium,
> days_in_year,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_m1,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_y2_init,
> array_x,
> array_last_rel_error,
> array_y2_higher_work,
> array_y1_set_initial,
> array_y1_higher_work2,
> array_complex_pole,
> array_real_pole,
> array_y2_higher,
> array_y2_higher_work2,
> array_poles,
> array_y1_higher,
> array_y2_set_initial,
> array_y1_higher_work,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> glob_iolevel := 5;
> ALWAYS := 1;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> DEBUGL := 3;
> glob_h := 0.1;
> glob_subiter_method := 3;
> glob_max_minutes := 0.0;
> glob_orig_start_sec := 0.0;
> glob_warned := false;
> glob_relerr := 0.1e-10;
> glob_not_yet_start_msg := true;
> glob_clock_start_sec := 0.0;
> djd_debug2 := true;
> glob_warned2 := false;
> glob_optimal_expect_sec := 0.1;
> MAX_UNCHANGED := 10;
> glob_smallish_float := 0.1e-100;
> glob_dump_analytic := false;
> glob_max_sec := 10000.0;
> glob_abserr := 0.1e-10;
> glob_not_yet_finished := true;
> glob_normmax := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_last_good_h := 0.1;
> glob_hmin := 0.00000000001;
> glob_initial_pass := true;
> hours_in_day := 24.0;
> glob_display_flag := true;
> glob_html_log := true;
> glob_log10normmin := 0.1;
> glob_log10abserr := 0.0;
> glob_current_iter := 0;
> glob_start := 0;
> glob_small_float := 0.1e-50;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_hours := 0.0;
> glob_large_float := 9.0e100;
> glob_hmin_init := 0.001;
> djd_debug := true;
> glob_log10relerr := 0.0;
> glob_log10_abserr := 0.1e-10;
> glob_look_poles := false;
> glob_disp_incr := 0.1;
> glob_optimal_done := false;
> glob_reached_optimal_h := false;
> glob_clock_sec := 0.0;
> glob_almost_1 := 0.9990;
> years_in_century := 100.0;
> glob_iter := 0;
> glob_curr_iter_when_opt := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_hmax := 1.0;
> min_in_hour := 60.0;
> sec_in_min := 60.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_iter := 1000;
> glob_log10_relerr := 0.1e-10;
> glob_max_opt_iter := 10;
> glob_percent_done := 0.0;
> glob_optimal_start := 0.0;
> glob_no_eqs := 0;
> centuries_in_millinium := 10.0;
> days_in_year := 365.0;
> glob_dump := false;
> #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/mtest7postode.ode#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 5 ) = y1 ;");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.0;");
> omniout_str(ALWAYS,"x_end := 5.0;");
> 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 := 20;");
> 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,"1.0 + cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"1.0 + sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
> omniout_str(ALWAYS,"-sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)");
> omniout_str(ALWAYS,"-cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)");
> omniout_str(ALWAYS,"sin(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_type_pole:= 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_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_m1:= 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_y1_init:= Array(1..(max_terms + 1),[]);
> array_y2_init:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_y2_higher_work := Array(1..(6+ 1) ,(1..max_terms+ 1),[]);
> array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y2_higher := Array(1..(6+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher_work2 := 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),[]);
> array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> 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_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_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_y1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=6 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 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 <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=6 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=6 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y1_higher[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_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 <= 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
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_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_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1D0[1] := 1.0;
> array_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_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_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 := 0.0;
> x_end := 5.0;
> 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 := 20;
> #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 <= 6 do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while subiter <= 6 + 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 , 5 ) = y1 ;");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
> 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,"2012-06-13T03:17:17-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest7")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 5 ) = y1 ;")
> ;
> 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,"mtest7 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest7 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 ) = m1 * y2 + 1.0;")
> ;
> 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 INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL,
glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec,
glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec,
djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED,
glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr,
glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h,
glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag,
glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter,
glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours,
glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr,
glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done,
glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century,
glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax,
min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter,
glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start,
glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump,
array_const_0D0, array_const_1D0, array_const_1, array_const_5,
array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error,
array_y1_init, array_y2_init, array_x, array_last_rel_error,
array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2,
array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2,
array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
glob_iolevel := 5;
ALWAYS := 1;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
DEBUGL := 3;
glob_h := 0.1;
glob_subiter_method := 3;
glob_max_minutes := 0.;
glob_orig_start_sec := 0.;
glob_warned := false;
glob_relerr := 0.1*10^(-10);
glob_not_yet_start_msg := true;
glob_clock_start_sec := 0.;
djd_debug2 := true;
glob_warned2 := false;
glob_optimal_expect_sec := 0.1;
MAX_UNCHANGED := 10;
glob_smallish_float := 0.1*10^(-100);
glob_dump_analytic := false;
glob_max_sec := 10000.0;
glob_abserr := 0.1*10^(-10);
glob_not_yet_finished := true;
glob_normmax := 0.;
glob_unchanged_h_cnt := 0;
glob_last_good_h := 0.1;
glob_hmin := 0.1*10^(-10);
glob_initial_pass := true;
hours_in_day := 24.0;
glob_display_flag := true;
glob_html_log := true;
glob_log10normmin := 0.1;
glob_log10abserr := 0.;
glob_current_iter := 0;
glob_start := 0;
glob_small_float := 0.1*10^(-50);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_hours := 0.;
glob_large_float := 0.90*10^101;
glob_hmin_init := 0.001;
djd_debug := true;
glob_log10relerr := 0.;
glob_log10_abserr := 0.1*10^(-10);
glob_look_poles := false;
glob_disp_incr := 0.1;
glob_optimal_done := false;
glob_reached_optimal_h := false;
glob_clock_sec := 0.;
glob_almost_1 := 0.9990;
years_in_century := 100.0;
glob_iter := 0;
glob_curr_iter_when_opt := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_hmax := 1.0;
min_in_hour := 60.0;
sec_in_min := 60.0;
glob_optimal_clock_start_sec := 0.;
glob_max_iter := 1000;
glob_log10_relerr := 0.1*10^(-10);
glob_max_opt_iter := 10;
glob_percent_done := 0.;
glob_optimal_start := 0.;
glob_no_eqs := 0;
centuries_in_millinium := 10.0;
days_in_year := 365.0;
glob_dump := false;
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/mtest7postode.ode#################");
omniout_str(ALWAYS, "diff ( y2 , x , 5 ) = y1 ;");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.0;");
omniout_str(ALWAYS, "x_end := 5.0;");
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 := 20;");
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, "1.0 +\tcos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "1.0 +\tsin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
omniout_str(ALWAYS, "-sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)");
omniout_str(ALWAYS, "-cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)");
omniout_str(ALWAYS, "sin(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_type_pole := 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_pole := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_m1 := 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_y1_init := Array(1 .. max_terms + 1, []);
array_y2_init := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_y2_higher_work := Array(1 .. 7, 1 .. max_terms + 1, []);
array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_y2_higher := Array(1 .. 7, 1 .. max_terms + 1, []);
array_y2_higher_work2 := Array(1 .. 7, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
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_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_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_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_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 6 do
term := 1;
while term <= max_terms do
array_y2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 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 <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 6 do
term := 1;
while term <= max_terms do
array_y2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 6 do
term := 1;
while term <= max_terms do
array_y2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher[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_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 <= max_terms do
array_y1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_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_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 1.0;
array_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_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_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.;
x_end := 5.0;
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 := 20;
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 <= 6 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 6 + 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 , 5 ) = y1 ;");
omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-13T03:17:17-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest7")
;
logitem_str(html_log_file, "diff ( y2 , x , 5 ) = y1 ;");
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,
"mtest7 diffeq.mxt");
logitem_str(html_log_file,
"mtest7 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 ) = m1 * y2 + 1.0;")
;
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/mtest7postode.ode#################
diff ( y2 , x , 5 ) = y1 ;
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 5.0;
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 := 20;
#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)
1.0 + cos(x);
end;
exact_soln_y2 := proc(x)
1.0 + sin(x);
end;
exact_soln_y2p := proc(x)
cos(x);
end;
exact_soln_y2pp := proc(x)
-sin(x);
end;
exact_soln_y2ppp := proc(x)
-cos(x);
end;
exact_soln_y2pppp := proc(x)
sin(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0
y2[1] (analytic) = 1
y2[1] (numeric) = 1
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 2
y1[1] (numeric) = 2
absolute error = 0
relative error = 0 %
h = 0.0001
x[1] = 0
y2[1] (analytic) = 1
y2[1] (numeric) = 1
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 2
y1[1] (numeric) = 2
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3.8MB, alloc=3.1MB, time=0.19
x[1] = 0.0001
y2[1] (analytic) = 1.0000999999998333333334166666666
y2[1] (numeric) = 1.0000999999998333333335
absolute error = 8.33333334e-23
relative error = 8.3325000899923895110631980367746e-21 %
h = 0.0001
y1[1] (analytic) = 1.9999999950000000041666666652778
y1[1] (numeric) = 1.9999999950000000041666665666667
absolute error = 9.86111e-26
relative error = 4.9305550123263875205439791957706e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0002
y2[1] (analytic) = 1.0001999999986666666693333333308
y2[1] (numeric) = 1.0001999999986666666719999999975
absolute error = 2.6666666667e-21
relative error = 2.6661334400155517342327311669123e-19 %
h = 0.0001
y1[1] (analytic) = 1.9999999800000000666666665777778
y1[1] (numeric) = 1.9999999800000000666666662944445
absolute error = 2.833333e-25
relative error = 1.4166665141666650944444338685184e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=0.38
NO POLE
NO POLE
x[1] = 0.0003
y2[1] (analytic) = 1.0002999999955000000202499999566
y2[1] (numeric) = 1.0002999999955000000404999999566
absolute error = 2.02500000000e-20
relative error = 2.0243926822044484324991763133255e-18 %
h = 0.0001
y1[1] (analytic) = 1.9999999550000003374999989875
y1[1] (numeric) = 1.9999999550000003374999976833334
absolute error = 1.3041666e-24
relative error = 6.5208331467187447007811655599598e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.4MB, time=0.58
NO POLE
NO POLE
x[1] = 0.0004
y2[1] (analytic) = 1.0003999999893333334186666663416
y2[1] (numeric) = 1.0003999999893333335039999996749
absolute error = 8.53333333333e-20
relative error = 8.5299213648750358128389781703723e-18 %
h = 0.0001
y1[1] (analytic) = 1.9999999200000010666666609777778
y1[1] (numeric) = 1.9999999200000010666666549000001
absolute error = 6.0777777e-24
relative error = 3.0388889715555572414815134735808e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.4MB, time=0.78
NO POLE
NO POLE
x[1] = 0.0005
y2[1] (analytic) = 1.0004999999791666669270833317832
y2[1] (numeric) = 1.0004999999791666671874999984499
absolute error = 2.604166666667e-19
relative error = 2.6028652341041742712303922838289e-17 %
h = 0.0001
y1[1] (analytic) = 1.9999998750000026041666449652779
y1[1] (numeric) = 1.999999875000002604166622777778
absolute error = 2.21874999e-23
relative error = 1.1093750643359400764974851311606e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.4MB, time=0.99
NO POLE
NO POLE
x[1] = 0.0006
y2[1] (analytic) = 1.0005999999640000006479999944457
y2[1] (numeric) = 1.0005999999640000012959999944457
absolute error = 6.480000000000e-19
relative error = 6.4761143316341596159727240608099e-17 %
h = 0.0001
y1[1] (analytic) = 1.9999998200000053999999352000004
y1[1] (numeric) = 1.9999998200000053999998698166672
absolute error = 6.53833332e-23
relative error = 3.2691669542250170535008643285404e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=1.18
NO POLE
NO POLE
x[1] = 0.0007
y2[1] (analytic) = 1.0006999999428333347339166503265
y2[1] (numeric) = 1.0006999999428333361344999836598
absolute error = 1.4005833333333e-18
relative error = 1.3996036108856906876473507043409e-16 %
h = 0.0001
y1[1] (analytic) = 1.9999997550000100041665032652792
y1[1] (numeric) = 1.9999997550000100041663391833349
absolute error = 1.640819443e-22
relative error = 8.2040982200019909126615857799349e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.4MB, time=1.38
NO POLE
NO POLE
x[1] = 0.0008
y2[1] (analytic) = 1.0007999999146666693973332917232
y2[1] (numeric) = 1.0007999999146666721279999583898
absolute error = 2.7306666666666e-18
relative error = 2.7284838797955941416453279035350e-16 %
h = 0.0001
y1[1] (analytic) = 1.9999996800000170666663025777819
y1[1] (numeric) = 1.9999996800000170666659377111154
absolute error = 3.648666665e-22
relative error = 1.8243336243933643352916975997600e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.4MB, time=1.58
NO POLE
NO POLE
x[1] = 0.0009
y2[1] (analytic) = 1.0008999998785000049207499050998
y2[1] (numeric) = 1.0008999998785000098414999050998
absolute error = 4.9207500000000e-18
relative error = 4.9163253078202952349966615837303e-16 %
h = 0.0001
y1[1] (analytic) = 1.9999995950000273374992618875107
y1[1] (numeric) = 1.9999995950000273374985229000108
absolute error = 7.389874999e-22
relative error = 3.6949382477249446591154835205820e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=34.3MB, alloc=4.4MB, time=1.78
x[1] = 0.001
y2[1] (analytic) = 1.000999999833333341666666468254
y2[1] (numeric) = 1.0009999998333333499999998015873
absolute error = 8.3333333333333e-18
relative error = 8.3250083263944069114458875295451e-16 %
h = 0.0001
y1[1] (analytic) = 1.9999995000000416666652777778026
y1[1] (numeric) = 1.9999995000000416666638879166916
absolute error = 1.3898611110e-21
relative error = 6.9493072923266783044391452117439e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0011
y2[1] (analytic) = 1.0010999997781666800875829466831
y2[1] (numeric) = 1.0010999997781666935084996133498
absolute error = 1.34209166666667e-17
relative error = 1.3406169882769588624917227827023e-15 %
h = 0.0001
y1[1] (analytic) = 1.9999993950000610041642061653309
y1[1] (numeric) = 1.9999993950000610041617445944978
absolute error = 2.4615708331e-21
relative error = 1.2307857888626635894265526052009e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.4MB, time=1.99
NO POLE
NO POLE
x[1] = 0.0012
y2[1] (analytic) = 1.0011999997120000207359992890514
y2[1] (numeric) = 1.0011999997120000414719992890515
absolute error = 2.07360000000001e-17
relative error = 2.0711146630008899121031003946817e-15 %
h = 0.0001
y1[1] (analytic) = 1.9999992800000863999958528001066
y1[1] (numeric) = 1.9999992800000863999917044334402
absolute error = 4.1483666664e-21
relative error = 2.0741840799061791614765472126148e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.5MB, time=2.19
NO POLE
NO POLE
x[1] = 0.0013
y2[1] (analytic) = 1.0012999996338333642744154216564
y2[1] (numeric) = 1.0012999996338333952154987549898
absolute error = 3.09410833333334e-17
relative error = 3.0900912158841788720717975224660e-15 %
h = 0.0001
y1[1] (analytic) = 1.9999991550001190041599627654801
y1[1] (numeric) = 1.9999991550001190041532576002026
absolute error = 6.7051652775e-21
relative error = 3.3525840552165638432736259786367e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.5MB, time=2.39
NO POLE
NO POLE
x[1] = 0.0014
y2[1] (analytic) = 1.0013999995426667114853312417956
y2[1] (numeric) = 1.0013999995426667563039979084623
absolute error = 4.48186666666667e-17
relative error = 4.4756008275549343364736079896743e-15 %
h = 0.0001
y1[1] (analytic) = 1.9999990200001600666562089781438
y1[1] (numeric) = 1.9999990200001600666457499281441
absolute error = 1.04590499997e-20
relative error = 5.2295275623180869993674032176490e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.5MB, time=2.59
NO POLE
NO POLE
x[1] = 0.0015
y2[1] (analytic) = 1.0014999994375000632812466099331
y2[1] (numeric) = 1.0014999994375001265624966099332
absolute error = 6.32812500000001e-17
relative error = 6.3186470330047414440472350729720e-15 %
h = 0.0001
y1[1] (analytic) = 1.9999988750002109374841796881356
y1[1] (numeric) = 1.9999988750002109374683579173027
absolute error = 1.58217708329e-20
relative error = 7.9108898663247154560494314653770e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.5MB, time=2.79
NO POLE
NO POLE
x[1] = 0.0016
y2[1] (analytic) = 1.0015999993173334207146613405665
y2[1] (numeric) = 1.0015999993173335080959946738999
absolute error = 8.73813333333334e-17
relative error = 8.7241746598333091774323464342129e-15 %
h = 0.0001
y1[1] (analytic) = 1.999998720000273066643364978843
y1[1] (numeric) = 1.999998720000273066620061734399
absolute error = 2.33032444440e-20
relative error = 1.1651629679041403750795306708047e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.5MB, time=2.99
NO POLE
NO POLE
x[1] = 0.0017
y2[1] (analytic) = 1.0016999991811667849880751916933
y2[1] (numeric) = 1.00169999918116690330949185836
absolute error = 1.183214166666667e-16
relative error = 1.1812061172345790182359418021288e-14 %
h = 0.0001
y1[1] (analytic) = 1.9999985550003480041331422670079
y1[1] (numeric) = 1.9999985550003480040996162128417
absolute error = 3.35260541662e-20
relative error = 1.6763039194392901145409240284449e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.5MB, time=3.20
NO POLE
NO POLE
x[1] = 0.0018
y2[1] (analytic) = 1.0017999990280001574639878527777
y2[1] (numeric) = 1.0017999990280003149279878527777
absolute error = 1.574640000000000e-16
relative error = 1.5718107421918544558862995765201e-14 %
h = 0.0001
y1[1] (analytic) = 1.9999983800004373999527608027331
y1[1] (numeric) = 1.9999983800004373999055198527337
absolute error = 4.72409499994e-20
relative error = 2.3620494132295081357507073237365e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=64.8MB, alloc=4.5MB, time=3.40
x[1] = 0.0019
y2[1] (analytic) = 1.0018999988568335396748989311172
y2[1] (numeric) = 1.0018999988568337460164822644505
absolute error = 2.063415833333333e-16
relative error = 2.0595027804049181590030883458369e-14 %
h = 0.0001
y1[1] (analytic) = 1.99999819500054300410132516949
y1[1] (numeric) = 1.9999981950005430040359818208795
absolute error = 6.53433486105e-20
relative error = 3.2671703791453801352477700359052e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.002
y2[1] (analytic) = 1.0019999986666669333333079365093
y2[1] (numeric) = 1.001999998666667199999974603176
absolute error = 2.666666666666667e-16
relative error = 2.6613439822506236859372959788106e-14 %
h = 0.0001
y1[1] (analytic) = 1.999998000000666666577777784127
y1[1] (numeric) = 1.9999980000006666664888869507944
absolute error = 8.88908333326e-20
relative error = 4.4445461111746296594568032821926e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.5MB, time=3.60
NO POLE
NO POLE
x[1] = 0.0021
y2[1] (analytic) = 1.0020999984565003403417142641184
y2[1] (numeric) = 1.0020999984565006806834642641184
absolute error = 3.403417500000000e-16
relative error = 3.3962853060993565652797062674565e-14 %
h = 0.0001
y1[1] (analytic) = 1.9999977950008103373808803968807
y1[1] (numeric) = 1.9999977950008103372617587427149
absolute error = 1.191216541658e-19
relative error = 5.9560892748760123299119473028844e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.5MB, time=3.80
NO POLE
NO POLE
x[1] = 0.0022
y2[1] (analytic) = 1.0021999982253337628026171754421
y2[1] (numeric) = 1.0021999982253341922719505087753
absolute error = 4.294693333333332e-16
relative error = 4.2852657562744446767894289890015e-14 %
h = 0.0001
y1[1] (analytic) = 1.9999975800009760665091945913879
y1[1] (numeric) = 1.9999975800009760663517203636111
absolute error = 1.574742277768e-19
relative error = 7.8737209160384657688991353151169e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.5MB, time=4.00
NO POLE
NO POLE
x[1] = 0.0023
y2[1] (analytic) = 1.0022999979721672030285157772778
y2[1] (numeric) = 1.0022999979721677393904324439444
absolute error = 5.363619166666666e-16
relative error = 5.3513111618459845164031384494473e-14 %
h = 0.0001
y1[1] (analytic) = 1.9999973550011660039610612847001
y1[1] (numeric) = 1.9999973550011660037554536472013
absolute error = 2.056076374988e-19
relative error = 1.0280395470757016585234344386440e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.5MB, time=4.20
NO POLE
NO POLE
x[1] = 0.0024
y2[1] (analytic) = 1.0023999976960006635519089985901
y2[1] (numeric) = 1.00239999769600132710390899859
absolute error = 6.635519999999999e-16
relative error = 6.6196328963005075824085437547900e-14 %
h = 0.0001
y1[1] (analytic) = 1.9999971200013823997345792273004
y1[1] (numeric) = 1.9999971200013823994691560939684
absolute error = 2.654231333320e-19
relative error = 1.3271175777083945965946293403904e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.5MB, time=4.41
NO POLE
NO POLE
x[1] = 0.0025
y2[1] (analytic) = 1.0024999973958341471352955651767
y2[1] (numeric) = 1.0024999973958349609373788985099
absolute error = 8.138020833333332e-16
relative error = 8.1177265381279184573429779477856e-14 %
h = 0.0001
y1[1] (analytic) = 1.999996875001627603827582503122
y1[1] (numeric) = 1.999996875001627603488495871179
absolute error = 3.390866319430e-19
relative error = 1.6954358088320715512058610008034e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.5MB, time=4.61
NO POLE
NO POLE
x[1] = 0.0026
y2[1] (analytic) = 1.0025999970706676567811739720353
y2[1] (numeric) = 1.0025999970706686468958406387018
absolute error = 9.901146666666665e-16
relative error = 9.8754704723670457402825502015967e-14 %
h = 0.0001
y1[1] (analytic) = 1.9999966200019040662376170295702
y1[1] (numeric) = 1.9999966200019040658085648129051
absolute error = 4.290522166651e-19
relative error = 2.1452647088208155441268610530344e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=91.5MB, alloc=4.5MB, time=4.82
x[1] = 0.0027
y2[1] (analytic) = 1.0026999967195011957420424533305
y2[1] (numeric) = 1.0026999967195023914842924533303
absolute error = 1.1957422499999998e-15
relative error = 1.1925224433151174322788677526042e-13 %
h = 0.0001
y1[1] (analytic) = 1.999996355002214336961916057547
y1[1] (numeric) = 1.9999963550022143364238294200487
absolute error = 5.380866374983e-19
relative error = 2.6904380908119417365096989123237e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0028
y2[1] (analytic) = 1.0027999963413347675303989498603
y2[1] (numeric) = 1.0027999963413362017277322831934
absolute error = 1.4341973333333331e-15
relative error = 1.4301927987294872042680181966792e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999960800025610659973746714787
y1[1] (numeric) = 1.9999960800025610653280798603694
absolute error = 6.692948111093e-19
relative error = 3.3464806146442194238135512738309e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.5MB, time=5.01
NO POLE
NO POLE
x[1] = 0.0029
y2[1] (analytic) = 1.0028999959351683759287410739227
y2[1] (numeric) = 1.0028999959351700851911577405892
absolute error = 1.7092624166666665e-15
relative error = 1.7043198958963405228569955017006e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999957950029470033405232893468
y1[1] (numeric) = 1.9999957950029470025143769685155
absolute error = 8.261463208313e-19
relative error = 4.1307402890318710367935493275877e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.5MB, time=5.22
NO POLE
NO POLE
x[1] = 0.003
y2[1] (analytic) = 1.0029999955000020249995660714828
y2[1] (numeric) = 1.0029999955000040499995660714826
absolute error = 2.0249999999999998e-15
relative error = 2.0189431795466002189438070592242e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999955000033749989875001627232
y1[1] (numeric) = 1.9999955000033749979749972460588
absolute error = 1.0125029166644e-18
relative error = 5.0625259739968984830033703538339e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.5MB, time=5.43
NO POLE
NO POLE
x[1] = 0.0031
y2[1] (analytic) = 1.0030999950348357190953707815389
y2[1] (numeric) = 1.003099995034838104857954114872
absolute error = 2.3857625833333331e-15
relative error = 2.3783895874214217182138781136047e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999951950038480029340228768083
y1[1] (numeric) = 1.999995195003848001701375861533
absolute error = 1.2326470152753e-18
relative error = 6.1632498835724871810829010093894e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.5MB, time=5.65
NO POLE
NO POLE
x[1] = 0.0032
y2[1] (analytic) = 1.0031999945386694628686515925897
y2[1] (numeric) = 1.0031999945386722590713182592561
absolute error = 2.7962026666666664e-15
relative error = 2.7872833750886585047948773992425e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999948800043690651753588504741
y1[1] (numeric) = 1.9999948800043690636840476504768
absolute error = 1.4913111999973e-18
relative error = 7.4565750888024382029678320672934e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.5MB, time=5.86
NO POLE
NO POLE
x[1] = 0.0033
y2[1] (analytic) = 1.0032999940105032612819043961006
y2[1] (numeric) = 1.0032999940105065225646543961003
absolute error = 3.2612827499999997e-15
relative error = 3.2505559348840764188267976136501e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999945550049413357062948363116
y1[1] (numeric) = 1.9999945550049413339125861154813
absolute error = 1.7937087208303e-18
relative error = 8.9685680210557789716598618739910e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.5MB, time=6.08
NO POLE
NO POLE
x[1] = 0.0034
y2[1] (analytic) = 1.0033999934493371196176245368708
y2[1] (numeric) = 1.0033999934493409059029578702038
absolute error = 3.7862853333333330e-15
relative error = 3.7734556089814317206750410782961e-13 %
h = 0.0001
y1[1] (analytic) = 1.999994220005568064521105420683
y1[1] (numeric) = 1.9999942200055680623755404262418
absolute error = 2.1455649944412e-18
relative error = 1.0727855975679903017796865410566e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.5MB, time=6.29
NO POLE
NO POLE
x[1] = 0.0035
y2[1] (analytic) = 1.0034999928541710434883067601998
y2[1] (numeric) = 1.0034999928541754203112234268661
absolute error = 4.3768229166666663e-15
relative error = 4.3615574965955258143128642451123e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999938750062526016135205237785
y1[1] (numeric) = 1.9999938750062525990603704196154
absolute error = 2.5531501041631e-18
relative error = 1.2765789616006289320885592975992e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=122.0MB, alloc=4.5MB, time=6.50
x[1] = 0.0036
y2[1] (analytic) = 1.0035999922240050388464451557542
y2[1] (numeric) = 1.0035999922240100776944451557537
absolute error = 5.0388479999999995e-15
relative error = 5.0207732553223465867687301162054e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999935200069983969766918996799
y1[1] (numeric) = 1.9999935200069983939533795996838
absolute error = 3.0233122999961e-18
relative error = 1.5116610477745551875055433397859e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0037
y2[1] (analytic) = 1.0036999915578391119945330980341
y2[1] (numeric) = 1.0036999915578448906576164313669
absolute error = 5.7786630833333328e-15
relative error = 5.7573608966204042837310584382446e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999931550078090006031586364283
y1[1] (numeric) = 1.9999931550078089970396461378214
absolute error = 3.5635124986069e-18
relative error = 1.7817623473781270100170112123683e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.5MB, time=6.71
NO POLE
NO POLE
x[1] = 0.0038
y2[1] (analytic) = 1.0037999908546732695950631833404
y2[1] (numeric) = 1.0037999908546798725257298500065
absolute error = 6.6029306666666661e-15
relative error = 6.5779345754373650165393341439498e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999927800086880624848116560991
y1[1] (numeric) = 1.9999927800086880583029518727703
absolute error = 4.1818597833288e-18
relative error = 2.0909374399394750839400398841273e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.5MB, time=6.92
NO POLE
NO POLE
x[1] = 0.0039
y2[1] (analytic) = 1.0038999901135075186805271631411
y2[1] (numeric) = 1.0038999901135150373637771631405
absolute error = 7.5186832499999994e-15
relative error = 7.4894743739860857530115573469562e-13 %
h = 0.0001
y1[1] (analytic) = 1.999992395009639332612857214883
y1[1] (numeric) = 1.9999923950096393277257093107213
absolute error = 4.8871479041617e-18
relative error = 2.4435832437943572722164584177831e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.5MB, time=7.12
NO POLE
NO POLE
x[1] = 0.004
y2[1] (analytic) = 1.0039999893333418666634158737383
y2[1] (numeric) = 1.003999989333350399996749207071
absolute error = 8.5333333333333327e-15
relative error = 8.4993360796741484285033196543085e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999920000106666609777794031743
y1[1] (numeric) = 1.9999920000106666552888866254019
absolute error = 5.6888927777724e-18
relative error = 2.8444577667020963750539888155551e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.5MB, time=7.32
NO POLE
NO POLE
x[1] = 0.0041
y2[1] (analytic) = 1.0040999885131763213462191621347
y2[1] (numeric) = 1.0040999885131859760296358288007
absolute error = 9.6546834166666660e-15
relative error = 9.6152609571909901797596690867590e-13 %
h = 0.0001
y1[1] (analytic) = 1.9999915950117739975693016456656
y1[1] (numeric) = 1.9999915950117739909719306581714
absolute error = 6.5973709874942e-18
relative error = 3.2986993565117263014270687631785e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.5MB, time=7.53
NO POLE
NO POLE
x[1] = 0.0042
y2[1] (analytic) = 1.0041999876520108909314258080007
y2[1] (numeric) = 1.0041999876520217818674258079999
absolute error = 1.08909359999999992e-14
relative error = 1.0845385514756723182499591904629e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999911800129653923763472014509
y1[1] (numeric) = 1.9999911800129653847526879181238
absolute error = 7.6236592833271e-18
relative error = 3.8118464518816917557971265574465e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.5MB, time=7.73
NO POLE
NO POLE
x[1] = 0.0043
y2[1] (analytic) = 1.0042999867488455840315234416408
y2[1] (numeric) = 1.0042999867488578347351067749733
absolute error = 1.22507035833333325e-14
relative error = 1.2198251264536735647873163310447e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999907550142449953869986641364
y1[1] (numeric) = 1.9999907550142449866073235821986
absolute error = 8.7796750819378e-18
relative error = 4.3898578330554665466033841377331e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.5MB, time=7.94
NO POLE
NO POLE
x[1] = 0.0044
y2[1] (analytic) = 1.0043999858026804096789984578608
y2[1] (numeric) = 1.0043999858026941526976651245266
absolute error = 1.37430186666666658e-14
relative error = 1.3682814477226160721078041630669e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999903200156170565884564619595
y1[1] (numeric) = 1.9999903200156170465102384952999
absolute error = 1.00782179666596e-17
relative error = 5.0391333726959756330029774752740e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0045
y2[1] (analytic) = 1.0044999848125153773363359256343
y2[1] (numeric) = 1.0044999848125307546800859256333
absolute error = 1.53773437499999990e-14
relative error = 1.5308455930808300692758023928823e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999898750170859259669963579171
y1[1] (numeric) = 1.9999898750170859144339841704246
absolute error = 1.15330121874925e-17
relative error = 5.7665352867818760357494173587131e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.5MB, time=8.16
NO POLE
NO POLE
x[1] = 0.0046
y2[1] (analytic) = 1.0045999837773504969060194934696
y2[1] (numeric) = 1.0045999837773676604873528268018
absolute error = 1.71635813333333322e-14
relative error = 1.7084990653491088328909521570372e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999894200186560535079259499027
y1[1] (numeric) = 1.9999894200186560403491757887996
absolute error = 1.31587501611031e-17
relative error = 6.5794098855684717457776639838701e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.5MB, time=8.38
NO POLE
NO POLE
x[1] = 0.0047
y2[1] (analytic) = 1.0046999826961857787405312903764
y2[1] (numeric) = 1.0046999826962048908244479570419
absolute error = 1.91120839166666655e-14
relative error = 1.9022677660825665107823179178635e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999889550203319891955401708534
y1[1] (numeric) = 1.9999889550203319742244032000286
absolute error = 1.49711369708248e-17
relative error = 7.4856098246165577759022508171977e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.5MB, time=8.59
NO POLE
NO POLE
x[1] = 0.0048
y2[1] (analytic) = 1.0047999815680212336523518223331
y2[1] (numeric) = 1.0047999815680424673163518223318
absolute error = 2.12336639999999987e-14
relative error = 2.1132229687011154037192474481902e-12 %
h = 0.0001
y1[1] (analytic) = 1.999988480022118383013075788907
y1[1] (numeric) = 1.9999884800221183660261399222495
absolute error = 1.69869358666575e-17
relative error = 8.4935168558919085079196893811784e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.5MB, time=8.80
NO POLE
NO POLE
x[1] = 0.0049
y2[1] (analytic) = 1.0048999803918568729239598641532
y2[1] (numeric) = 1.004899980391880412528043197485
absolute error = 2.35396040833333318e-14
relative error = 2.3424822910389702610539566972553e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999879950240199849426649075699
y1[1] (numeric) = 1.9999879950240199657186501423018
absolute error = 1.92240147652681e-17
relative error = 9.6120650789392455035891173670958e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.5MB, time=9.02
NO POLE
NO POLE
x[1] = 0.005
y2[1] (analytic) = 1.0049999791666927083178323466521
y2[1] (numeric) = 1.0049999791667187499844990133171
absolute error = 2.60416666666666650e-14
relative error = 2.5912106673135866563470252450608e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999875000260416449652874658951
y1[1] (numeric) = 1.9999875000260416232638937159054
absolute error = 2.17013937499897e-17
relative error = 1.0850764692132889949704984919429e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.5MB, time=9.24
NO POLE
NO POLE
x[1] = 0.0051
y2[1] (analytic) = 1.0050999778915287520864442390147
y2[1] (numeric) = 1.0050999778915575041906942390128
absolute error = 2.87521042499999981e-14
relative error = 2.8606213195144403578286157982192e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999869950281883130607227386734
y1[1] (numeric) = 1.999986995028188288621429167851
absolute error = 2.44392935708224e-17
relative error = 1.2219726244008874933268027682964e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.5MB, time=9.46
NO POLE
NO POLE
x[1] = 0.0052
y2[1] (analytic) = 1.0051999765653650169822684262613
y2[1] (numeric) = 1.0051999765653967006516017595926
absolute error = 3.16836693333333313e-14
relative error = 3.1519767282120545469717330248179e-12 %
h = 0.0001
y1[1] (analytic) = 1.999986480030465039207499836635
y1[1] (numeric) = 1.9999864800304650117483146922021
absolute error = 2.74591851444329e-17
relative error = 1.3729685384680512738490647548033e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=179.2MB, alloc=4.5MB, time=9.68
x[1] = 0.0053
y2[1] (analytic) = 1.0052999751872015162677755817155
y2[1] (numeric) = 1.00529997518723636589219224838
absolute error = 3.48496244166666645e-14
relative error = 3.4665896027876809805750171702298e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999859550328769733828472066644
y1[1] (numeric) = 1.9999859550328769425990071525099
absolute error = 3.07838400541545e-17
relative error = 1.5392028117341682382603592687184e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0054
y2[1] (analytic) = 1.0053999737560382637254340343706
y2[1] (numeric) = 1.0053999737560765274774340343682
absolute error = 3.82637519999999976e-14
relative error = 3.8058238510840414589722457431803e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999854200354293655626411320282
y1[1] (numeric) = 1.9999854200354293311252590820411
absolute error = 3.44373820499871e-17
relative error = 1.7218816549861172614897819295252e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.5MB, time=9.89
NO POLE
NO POLE
x[1] = 0.0055
y2[1] (analytic) = 1.0054999722708752736677096310567
y2[1] (numeric) = 1.0054999722709172140322929643874
absolute error = 4.19403645833333307e-14
relative error = 4.1710955484775353348413441945193e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999848750381275657213532326165
y1[1] (numeric) = 1.999984875038127527276013684019
absolute error = 3.84453395485975e-17
relative error = 1.9222815146471835619333606570829e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.5MB, time=10.11
NO POLE
NO POLE
x[1] = 0.0056
y2[1] (analytic) = 1.0055999707307125609470655933077
y2[1] (numeric) = 1.0055999707307584552617322599715
absolute error = 4.58943146666666638e-14
relative error = 4.5638739063723185970612099519909e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999843200409770238319969651979
y1[1] (numeric) = 1.9999843200409769809972978318789
absolute error = 4.28346991333190e-17
relative error = 2.1417517479557726670486072340473e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.5MB, time=10.33
NO POLE
NO POLE
x[1] = 0.0057
y2[1] (analytic) = 1.0056999691345501409659623688285
y2[1] (numeric) = 1.0056999691346002819707123688253
absolute error = 5.01410047499999968e-14
relative error = 4.9856822401166599138881035059122e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999837550439832898660731236897
y1[1] (numeric) = 1.9999837550439832422321130695382
absolute error = 4.76339600541515e-17
relative error = 2.3817173481543575015173420215803e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.5MB, time=10.54
NO POLE
NO POLE
x[1] = 0.0058
y2[1] (analytic) = 1.0057999674813880296868574774616
y2[1] (numeric) = 1.0057999674814427260841908107915
absolute error = 5.46963973333333299e-14
relative error = 5.4380989363419786807292065613294e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999831800471520137935143394429
y1[1] (numeric) = 1.9999831800471519609203246116811
absolute error = 5.28731897277618e-17
relative error = 2.6436817196890251262450924101240e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.5MB, time=10.75
NO POLE
NO POLE
x[1] = 0.0059
y2[1] (analytic) = 1.005899965770226243642205351555
y2[1] (numeric) = 1.0058999657702858206671220182179
absolute error = 5.95770249166666629e-14
relative error = 5.9227584197249696895804070831147e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999825950504889455826285815429
y1[1] (numeric) = 1.9999825950504888869985483440596
absolute error = 5.85840802374833e-17
relative error = 2.9292295034199716578047515000881e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.5MB, time=10.97
NO POLE
NO POLE
x[1] = 0.006
y2[1] (analytic) = 1.0059999640000647999444571706286
y2[1] (numeric) = 1.0059999640001295999444571706244
absolute error = 6.47999999999999958e-14
relative error = 6.4413521191732191560400975293425e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999820000539999352000416571262
y1[1] (numeric) = 1.9999820000539998704000358238105
absolute error = 6.48000058333157e-17
relative error = 3.2400294518433709001152167772152e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.5MB, time=11.17
NO POLE
NO POLE
x[1] = 0.0061
y2[1] (analytic) = 1.0060999621699037162960606902414
y2[1] (numeric) = 1.0060999621699740993211440235701
absolute error = 7.03830250833333287e-14
relative error = 6.9956294334347161335339919302886e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999813950576909326106387117147
y1[1] (numeric) = 1.9999813950576908610545572797888
absolute error = 7.15560814319259e-17
relative error = 3.5778373543250792221993674875799e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0062
y2[1] (analytic) = 1.0061999602787430109994600649592
y2[1] (numeric) = 1.0061999602788193554021267316208
absolute error = 7.63444026666666616e-14
relative error = 7.5873986961316633343802585841497e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999807800615679877775047295666
y1[1] (numeric) = 1.9999807800615679088882826129193
absolute error = 7.88892221166473e-17
relative error = 3.9444990123464462158578716551545e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.5MB, time=11.37
NO POLE
NO POLE
x[1] = 0.0063
y2[1] (analytic) = 1.0062999583255827029670956653213
y2[1] (numeric) = 1.0062999583256654060123456653158
absolute error = 8.27030452499999945e-14
relative error = 8.2185281402189910890330804026445e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999801550656372506618640340453
y1[1] (numeric) = 1.9999801550656371638236603965657
absolute error = 8.68382036374796e-17
relative error = 4.3419532647627526710127122780338e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.5MB, time=11.59
NO POLE
NO POLE
x[1] = 0.0064
y2[1] (analytic) = 1.0063999563094228117314038887082
y2[1] (numeric) = 1.0063999563095122902167372220355
absolute error = 8.94784853333333273e-14
relative error = 8.8909468618679778172072063205117e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999795200699049712230187880081
y1[1] (numeric) = 1.9999795200699048757792948769183
absolute error = 9.54437239110898e-17
relative error = 4.7722350630747344079034766518640e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.6MB, time=11.80
NO POLE
NO POLE
x[1] = 0.0065
y2[1] (analytic) = 1.0064999542292633574548169640085
y2[1] (numeric) = 1.0064999542293600483402336306686
absolute error = 9.66908854166666601e-14
relative error = 9.6066457837753802259314308182967e-12 %
h = 0.0001
y1[1] (analytic) = 1.9999788750743774994182864942121
y1[1] (numeric) = 1.9999788750743773946698209734011
absolute error = 1.047484655208110e-16
relative error = 5.2374785967134525052019148063640e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.6MB, time=12.01
NO POLE
NO POLE
x[1] = 0.0066
y2[1] (analytic) = 1.0065999520841043609397627499864
y2[1] (numeric) = 1.0065999520842087219877627499793
absolute error = 1.043610479999999929e-13
relative error = 1.0367678617898476022789246030280e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999782200790612852029364957421
y1[1] (numeric) = 1.9999782200790611704057772790987
absolute error = 1.147971592166434e-16
relative error = 5.7399204683391674689389688745672e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.6MB, time=12.22
NO POLE
NO POLE
x[1] = 0.0067
y2[1] (analytic) = 1.0066999498729458436386645272492
y2[1] (numeric) = 1.0066999498730583540642478605748
absolute error = 1.125104255833333256e-13
relative error = 1.1176162827616421853820219271128e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999775550839628785301254764571
y1[1] (numeric) = 1.9999775550839627528934770612037
absolute error = 1.256366484152534e-16
relative error = 6.2819029191544568850228890170383e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.6MB, time=12.43
NO POLE
NO POLE
x[1] = 0.0068
y2[1] (analytic) = 1.0067999475947878276639407837147
y2[1] (numeric) = 1.0067999475949089887946074503729
absolute error = 1.211611306666666582e-13
relative error = 1.2034280589318328808752929056974e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999768800890889293508319614595
y1[1] (numeric) = 1.999976880089088792034877261485
absolute error = 1.373159546999745e-16
relative error = 6.8658771042322131042482659277667e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.6MB, time=12.64
NO POLE
NO POLE
x[1] = 0.0069
y2[1] (analytic) = 1.0068999452486303357980049934784
y2[1] (numeric) = 1.0068999452487606717437549934692
absolute error = 1.303359457499999908e-13
relative error = 1.2944279753418457539238669465442e-11 %
h = 0.0001
y1[1] (analytic) = 1.999976195094446187613789817585
y1[1] (numeric) = 1.9999761950944460377274454967783
absolute error = 1.498863443208067e-16
relative error = 7.4944064178588145072421304081198e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=236.5MB, alloc=4.6MB, time=12.85
x[1] = 0.007
y2[1] (analytic) = 1.0069999428334733915032653889815
y2[1] (numeric) = 1.0069999428336134498365987223049
absolute error = 1.400583333333333234e-13
relative error = 1.3908474804798934808485336287345e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999755001000415032654207539152
y1[1] (numeric) = 1.9999755001000413398640250594986
absolute error = 1.634013956944166e-16
relative error = 8.1701698688930459020033465887451e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0071
y2[1] (analytic) = 1.007099940348317018932124726378
y2[1] (numeric) = 1.007099940348467371378041393034
absolute error = 1.503524459166666560e-13
relative error = 1.4929247822680393073506738244690e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999747951058818262497658223139
y1[1] (numeric) = 1.9999747951058816483326979181762
absolute error = 1.779170679041377e-16
relative error = 8.8959655061412156076471182416502e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.6MB, time=13.07
NO POLE
NO POLE
x[1] = 0.0072
y2[1] (analytic) = 1.007199937792161242936980044003
y2[1] (numeric) = 1.0071999377923224860729800439914
absolute error = 1.612431359999999884e-13
relative error = 1.6009049439920934325309303940514e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999740801119742065084159179862
y1[1] (numeric) = 1.9999740801119740130166457180164
absolute error = 1.934917701999698e-16
relative error = 9.6747138937488937799391483663972e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.6MB, time=13.28
NO POLE
NO POLE
x[1] = 0.0073
y2[1] (analytic) = 1.0072999351640060890802224138395
y2[1] (numeric) = 1.0072999351641788450463057471603
absolute error = 1.727559660833333208e-13
relative error = 1.7150399801743819314704685594827e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999733551183257939804412800631
y1[1] (numeric) = 1.9999733551183255837940087814835
absolute error = 2.101864324985796e-16
relative error = 1.0509461636609863538677569054610e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.6MB, time=13.51
NO POLE
NO POLE
x[1] = 0.0074
y2[1] (analytic) = 1.0073999324628515836442366858868
y2[1] (numeric) = 1.00739993246303650086290335254
absolute error = 1.849172186666666532e-13
relative error = 1.8355889523894282717369567468105e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999726201249438386023199922106
y1[1] (numeric) = 1.9999726201249436105377431089101
absolute error = 2.280645768833005e-16
relative error = 1.1403384955792678457049734852635e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.6MB, time=13.72
NO POLE
NO POLE
x[1] = 0.0075
y2[1] (analytic) = 1.0074999296876977536414012253283
y2[1] (numeric) = 1.0074999296878955075476512253138
absolute error = 1.977539062499999855e-13
relative error = 1.9628180650225874912961951940621e-11 %
h = 0.0001
y1[1] (analytic) = 1.999971875131835690307865483265
y1[1] (numeric) = 1.9999718751318354431154753791326
absolute error = 2.471923901041324e-16
relative error = 1.2359793313985366977417219306128e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.6MB, time=13.94
NO POLE
NO POLE
x[1] = 0.0076
y2[1] (analytic) = 1.0075999268375446268240876423992
y2[1] (numeric) = 1.0075999268377559206054209757169
absolute error = 2.112937813333333177e-13
relative error = 2.0970007609716730538963460406821e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999711201390087990281530278951
y1[1] (numeric) = 1.9999711201390085313893559501529
absolute error = 2.676387970777422e-16
relative error = 1.3382133090958826320747525708520e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.6MB, time=14.15
NO POLE
NO POLE
x[1] = 0.0077
y2[1] (analytic) = 1.0076999239113922316946605148542
y2[1] (numeric) = 1.0076999239116177970410771815041
absolute error = 2.255653464166666499e-13
relative error = 2.2384178172916163744050448850895e-11 %
h = 0.0001
y1[1] (analytic) = 1.999970355146470714691445247291
y1[1] (numeric) = 1.999970355146470425215909859828
absolute error = 2.894755353874630e-16
relative error = 1.4473991309049320457815375404080e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.6MB, time=14.38
NO POLE
NO POLE
x[1] = 0.0078
y2[1] (analytic) = 1.0077999209082405975154771029362
y2[1] (numeric) = 1.0077999209084811953794771029182
absolute error = 2.405978639999999820e-13
relative error = 2.3873574407821989820171402200075e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999695801542290872231166098821
y1[1] (numeric) = 1.9999695801542287744458858265871
absolute error = 3.127772307832950e-16
relative error = 1.5639099408660753716669365150982e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0079
y2[1] (analytic) = 1.0078999178270897543188870567438
y2[1] (numeric) = 1.0078999178273461756854703900578
absolute error = 2.564213665833333140e-13
relative error = 2.5441153635188972726428443788922e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999687951622916665455769320828
y1[1] (numeric) = 1.9999687951622913289241032501782
absolute error = 3.376214736819046e-16
relative error = 1.6881337073787073599204562992268e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.6MB, time=14.59
NO POLE
NO POLE
x[1] = 0.008
y2[1] (analytic) = 1.0079999146669397329172321158996
y2[1] (numeric) = 1.0079999146672127995838987825456
absolute error = 2.730666666666666460e-13
relative error = 2.7089949383268797574105121669222e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999680001706663025781938790692
y1[1] (numeric) = 1.9999680001706659384892972124439
absolute error = 3.640888966666253e-16
relative error = 1.8204736107555518387850084816154e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.6MB, time=14.81
NO POLE
NO POLE
x[1] = 0.0081
y2[1] (analytic) = 1.0080999114267905649128458014187
y2[1] (numeric) = 1.0080999114270811302795958013966
absolute error = 2.905653667499999779e-13
relative error = 2.8823072341981966966607236283276e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999671951793609452372144655848
y1[1] (numeric) = 1.9999671951793605529739614781278
absolute error = 3.922632529874570e-16
relative error = 1.9613484357791082121320130547420e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.6MB, time=15.03
NO POLE
NO POLE
x[1] = 0.0082
y2[1] (analytic) = 1.0081999081056422827080530996768
y2[1] (numeric) = 1.0081999081059512325773864329865
absolute error = 3.089498693333333097e-13
relative error = 3.0643711316522019912618376007546e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999663801883836444356855567786
y1[1] (numeric) = 1.9999663801883832222041894957121
absolute error = 4.222314960610665e-16
relative error = 2.1111929692602886526241258889800e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.6MB, time=15.25
NO POLE
NO POLE
x[1] = 0.0083
y2[1] (analytic) = 1.0082999047024949195151701383786
y2[1] (numeric) = 1.00829990470282317290208680502
absolute error = 3.282533869166666414e-13
relative error = 3.2555134180392471577721806775211e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999655551977425500833733690744
y1[1] (numeric) = 1.9999655551977420959995133982873
absolute error = 4.540838599707871e-16
relative error = 2.2704584025992911490977122221572e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.6MB, time=15.47
NO POLE
NO POLE
x[1] = 0.0084
y2[1] (analytic) = 1.0083999012163485093665038544264
y2[1] (numeric) = 1.0083999012166970193185038543994
absolute error = 3.485099519999999730e-13
relative error = 3.4560688827876872024216170004293e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999647202074459120866819710734
y1[1] (numeric) = 1.9999647202074454241727410044546
absolute error = 4.879139409666188e-16
relative error = 2.4396127393487722674165498329405e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.6MB, time=15.69
NO POLE
NO POLE
x[1] = 0.0085
y2[1] (analytic) = 1.0084998976462030871243516535888
y2[1] (numeric) = 1.0084998976465728415514349868933
absolute error = 3.697544270833333045e-13
relative error = 3.6663804125942381765154995796006e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999638752175020803485707844898
y1[1] (numeric) = 1.9999638752175015565297908192617
absolute error = 5.238187799652281e-16
relative error = 2.6191412077793716841917048987247e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.6MB, time=15.90
NO POLE
NO POLE
x[1] = 0.0086
y2[1] (analytic) = 1.008599893991058688491001061869
y2[1] (numeric) = 1.008599893991450711005667728505
absolute error = 3.920225146666666360e-13
relative error = 3.8867990865577261714503066931100e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999630202279195047684710851221
y1[1] (numeric) = 1.9999630202279189428695250351735
absolute error = 5.618989460499486e-16
relative error = 2.8095466784476522533023176717412e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=293.7MB, alloc=4.6MB, time=16.13
x[1] = 0.0087
y2[1] (analytic) = 1.0086998902499153500187293684742
y2[1] (numeric) = 1.0086998902503307007859793684415
absolute error = 4.153507672499999673e-13
relative error = 4.1176842712562674782113571436123e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999621552387067352422015038579
y1[1] (numeric) = 1.9999621552387061329835805330778
absolute error = 6.022586209707801e-16
relative error = 3.0113500867665025652031140287421e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0088
y2[1] (analytic) = 1.0087998864217731091198032602839
y2[1] (numeric) = 1.0087998864222128857171365935824
absolute error = 4.397765973333332985e-13
relative error = 4.3594037157679196306849517594624e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999612802498724216618825277167
y1[1] (numeric) = 1.9999612802498717766561978833273
absolute error = 6.450056846443894e-16
relative error = 3.2250908605780771598676905933017e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.6MB, time=16.34
NO POLE
NO POLE
x[1] = 0.0089
y2[1] (analytic) = 1.0088998825056320040764784477192
y2[1] (numeric) = 1.0088998825060973423638951143488
absolute error = 4.653382874166666296e-13
relative error = 4.6123336466348429910735705334739e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999603952614253139158500009278
y1[1] (numeric) = 1.9999603952614246236640483468181
absolute error = 6.902518016541097e-16
relative error = 3.4513273527293187540278157764480e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.6MB, time=16.56
NO POLE
NO POLE
x[1] = 0.009
y2[1] (analytic) = 1.0089998785004920740509992819119
y2[1] (numeric) = 1.0089998785009841490509992818725
absolute error = 4.920749999999999606e-13
relative error = 4.8768588627710125440845080505987e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999595002733742618885676260481
y1[1] (numeric) = 1.9999595002733735237760588761069
absolute error = 7.381125087499412e-16
relative error = 3.6906372786501360442801902618781e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.6MB, time=16.78
NO POLE
NO POLE
x[1] = 0.0091
y2[1] (analytic) = 1.0090998744053533590955983630738
y2[1] (numeric) = 1.0090998744058733858831816963651
absolute error = 5.200267875833332913e-13
relative error = 5.1533728303135195174550421493766e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999585952857282154605384651164
y1[1] (numeric) = 1.9999585952857274267532351165661
absolute error = 7.887073033485503e-16
relative error = 3.9436181589342853475373736381911e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.6MB, time=17.00
NO POLE
NO POLE
x[1] = 0.0092
y2[1] (analytic) = 1.0091998702192159001624961399656
y2[1] (numeric) = 1.0091998702197651347651628065876
absolute error = 5.492346026666666220e-13
relative error = 5.4422777774175024399171527790927e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999576802984962245082154408494
y1[1] (numeric) = 1.9999576802984953823484824075789
absolute error = 8.421597330332705e-16
relative error = 4.2108877669230335412625552189053e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.6MB, time=17.21
NO POLE
NO POLE
x[1] = 0.0093
y2[1] (analytic) = 1.0092998659410797391139005003671
y2[1] (numeric) = 1.0092998659416594794216505003196
absolute error = 5.797403077499999525e-13
relative error = 5.7439847889947471837803233099110e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999567553116874389039108378768
y1[1] (numeric) = 1.999956755311686540306424783775
absolute error = 8.985974860541018e-16
relative error = 4.4930845812916489657190389371959e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.6MB, time=17.43
NO POLE
NO POLE
x[1] = 0.0094
y2[1] (analytic) = 1.0093998615699449187320063524461
y2[1] (numeric) = 1.0093998615705565054173396857289
absolute error = 6.115866853333332828e-13
relative error = 6.0589139013959955725262733646664e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999558203253111085157048040181
y1[1] (numeric) = 1.9999558203253101503632219763073
absolute error = 9.581524828277108e-16
relative error = 4.7908682436387946514284380499451e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.6MB, time=17.65
NO POLE
NO POLE
x[1] = 0.0095
y2[1] (analytic) = 1.0094998571048114827289951969284
y2[1] (numeric) = 1.0094998571054563001769118635415
absolute error = 6.448174479166666131e-13
relative error = 6.3874941970370020501010325712645e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999548753393765832073528516022
y1[1] (numeric) = 1.9999548753393755622463844141714
absolute error = 1.0209609684374308e-15
relative error = 5.1049200210788844351797889956717e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.0096
y2[1] (analytic) = 1.0095998525446794757570346899679
y2[1] (numeric) = 1.009599852545358953005034689911
absolute error = 6.794772479999999431e-13
relative error = 6.7301638989683779061716654647213e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999539203538933128381923588301
y1[1] (numeric) = 1.9999539203538922256745862255681
absolute error = 1.0871636061332620e-15
relative error = 5.4359432738374672284555284442083e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.6MB, time=17.87
NO POLE
NO POLE
x[1] = 0.0097
y2[1] (analytic) = 1.0096998478885489434182781966159
y2[1] (numeric) = 1.009699847889264555106361529889
absolute error = 7.156116880833332731e-13
relative error = 7.0873704653892625501848373960108e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999529553688708472630480711808
y1[1] (numeric) = 1.9999529553688696903574762393099
absolute error = 1.1569055718318709e-15
relative error = 5.7846639278497004024787620242754e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.6MB, time=18.09
NO POLE
NO POLE
x[1] = 0.0098
y2[1] (analytic) = 1.0097998431354199322748643347922
y2[1] (numeric) = 1.009799843136173199605531001395
absolute error = 7.532673306666666028e-13
relative error = 7.4595706841048612355141317611547e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999519803843188363321366028639
y1[1] (numeric) = 1.9999519803843176059954869862731
absolute error = 1.2303366496165908e-15
relative error = 6.1518309523619879548689069547701e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.6MB, time=18.31
NO POLE
NO POLE
x[1] = 0.0099
y2[1] (analytic) = 1.0098998382842924898589165096544
y2[1] (numeric) = 1.0098998382850849815671665095867
absolute error = 7.924917082499999323e-13
relative error = 7.8472307669278886940197484999298e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999509954002470298909699383174
y1[1] (numeric) = 1.9999509954002457222796417008956
absolute error = 1.3076113282374218e-15
relative error = 6.5382168425368423229747753795773e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=335.7MB, alloc=4.6MB, time=18.52
NO POLE
NO POLE
x[1] = 0.01
y2[1] (analytic) = 1.0099998333341666646825424382691
y2[1] (numeric) = 1.0099998333349999980158757715307
absolute error = 8.333333333333332616e-13
relative error = 8.2508264440239580339871125591238e-11 %
h = 0.0001
y1[1] (analytic) = 1.9999500004166652777802579337522
y1[1] (numeric) = 1.9999500004166638888913593227217
absolute error = 1.3888888986110305e-15
relative error = 6.9446181070610384096320425011773e-14 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y2 , x , 5 ) = y1 ;
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
Iterations = 100
Total Elapsed Time = 18 Seconds
Elapsed Time(since restart) = 18 Seconds
Expected Time Remaining = 2 Hours 33 Minutes 2 Seconds
Optimized Time Remaining = 2 Hours 32 Minutes 58 Seconds
Time to Timeout = 14 Minutes 41 Seconds
Percent Done = 0.202 %
> quit
memory used=337.7MB, alloc=4.6MB, time=18.64