|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> #BEGIN OUTFILE1
>
> # Begin Function number 3
> reached_interval := proc()
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_no_eqs,
> glob_relerr,
> years_in_century,
> glob_dump,
> glob_normmax,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_reached_optimal_h,
> days_in_year,
> djd_debug2,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_iter,
> glob_log10_abserr,
> glob_not_yet_finished,
> centuries_in_millinium,
> djd_debug,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_large_float,
> glob_h,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_html_log,
> glob_look_poles,
> glob_hmin_init,
> glob_optimal_done,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_dump_analytic,
> glob_next_display,
> glob_display_flag,
> glob_subiter_method,
> glob_log10abserr,
> glob_neg_h,
> hours_in_day,
> glob_percent_done,
> glob_current_iter,
> glob_optimal_expect_sec,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_display_interval,
> glob_hmax,
> glob_disp_incr,
> sec_in_minute,
> glob_max_minutes,
> glob_iter,
> glob_warned,
> glob_log10_relerr,
> glob_hmin,
> glob_clock_start_sec,
> min_in_hour,
> glob_good_digits,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_y2_init,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_norms,
> array_m1,
> array_pole,
> array_fact_1,
> array_x,
> array_y1_init,
> array_y1_set_initial,
> array_poles,
> array_y2_higher_work2,
> array_y1_higher,
> array_y1_higher_work2,
> array_y2_higher,
> array_complex_pole,
> array_real_pole,
> array_fact_2,
> array_y2_set_initial,
> array_y1_higher_work,
> array_y2_higher_work,
> glob_last;
>
>
>
> local ret;
>
> if ((((array_x[1] >= glob_next_display) and not glob_neg_h) or ((array_x[1] <= glob_next_display) and glob_neg_h)) or (glob_next_display = 0.0)) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1
> ;
> return(ret);
>
> # End Function number 3
> end;
reached_interval := proc()
local ret;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, INFO,
glob_no_eqs, glob_relerr, years_in_century, glob_dump, glob_normmax,
glob_small_float, glob_max_rel_trunc_err, glob_reached_optimal_h,
days_in_year, djd_debug2, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_smallish_float, glob_optimal_start, glob_max_iter, glob_log10_abserr,
glob_not_yet_finished, centuries_in_millinium, djd_debug, glob_start,
glob_warned2, glob_optimal_clock_start_sec, glob_max_hours,
glob_last_good_h, glob_large_float, glob_h, glob_not_yet_start_msg,
glob_clock_sec, glob_almost_1, glob_html_log, glob_look_poles,
glob_hmin_init, glob_optimal_done, glob_curr_iter_when_opt, glob_abserr,
glob_dump_analytic, glob_next_display, glob_display_flag,
glob_subiter_method, glob_log10abserr, glob_neg_h, hours_in_day,
glob_percent_done, glob_current_iter, glob_optimal_expect_sec,
glob_log10relerr, MAX_UNCHANGED, glob_display_interval, glob_hmax,
glob_disp_incr, sec_in_minute, glob_max_minutes, glob_iter, glob_warned,
glob_log10_relerr, glob_hmin, glob_clock_start_sec, min_in_hour,
glob_good_digits, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_initial_pass, glob_log10normmin, array_const_0D0, array_const_1D0,
array_const_1, array_const_5, array_y2, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_y2_init, array_type_pole,
array_1st_rel_error, array_last_rel_error, array_norms, array_m1,
array_pole, array_fact_1, array_x, array_y1_init, array_y1_set_initial,
array_poles, array_y2_higher_work2, array_y1_higher, array_y1_higher_work2,
array_y2_higher, array_complex_pole, array_real_pole, array_fact_2,
array_y2_set_initial, array_y1_higher_work, array_y2_higher_work, glob_last
;
if glob_next_display <= array_x[1] and not glob_neg_h or
array_x[1] <= glob_next_display and glob_neg_h or
glob_next_display = 0. then ret := true
else ret := false
end if;
return ret
end proc
> # Begin Function number 4
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_no_eqs,
> glob_relerr,
> years_in_century,
> glob_dump,
> glob_normmax,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_reached_optimal_h,
> days_in_year,
> djd_debug2,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_iter,
> glob_log10_abserr,
> glob_not_yet_finished,
> centuries_in_millinium,
> djd_debug,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_large_float,
> glob_h,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_html_log,
> glob_look_poles,
> glob_hmin_init,
> glob_optimal_done,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_dump_analytic,
> glob_next_display,
> glob_display_flag,
> glob_subiter_method,
> glob_log10abserr,
> glob_neg_h,
> hours_in_day,
> glob_percent_done,
> glob_current_iter,
> glob_optimal_expect_sec,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_display_interval,
> glob_hmax,
> glob_disp_incr,
> sec_in_minute,
> glob_max_minutes,
> glob_iter,
> glob_warned,
> glob_log10_relerr,
> glob_hmin,
> glob_clock_start_sec,
> min_in_hour,
> glob_good_digits,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_y2_init,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_norms,
> array_m1,
> array_pole,
> array_fact_1,
> array_x,
> array_y1_init,
> array_y1_set_initial,
> array_poles,
> array_y2_higher_work2,
> array_y1_higher,
> array_y1_higher_work2,
> array_y2_higher,
> array_complex_pole,
> array_real_pole,
> array_fact_2,
> array_y2_set_initial,
> array_y1_higher_work,
> array_y2_higher_work,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
>
>
>
>
>
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 1
> if (iter >= 0) then # if number 2
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 4
> glob_good_digits := -trunc(log10(relerr/100.0));
> else
> glob_good_digits := Digits;
> fi;# end if 4
> ;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3
> ;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_y1(ind_var);
> omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 4
> glob_good_digits := -trunc(log10(relerr/100.0));
> else
> glob_good_digits := Digits;
> fi;# end if 4
> ;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3
> ;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 3
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 2
> ;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
>
> # End Function number 4
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, INFO,
glob_no_eqs, glob_relerr, years_in_century, glob_dump, glob_normmax,
glob_small_float, glob_max_rel_trunc_err, glob_reached_optimal_h,
days_in_year, djd_debug2, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_smallish_float, glob_optimal_start, glob_max_iter, glob_log10_abserr,
glob_not_yet_finished, centuries_in_millinium, djd_debug, glob_start,
glob_warned2, glob_optimal_clock_start_sec, glob_max_hours,
glob_last_good_h, glob_large_float, glob_h, glob_not_yet_start_msg,
glob_clock_sec, glob_almost_1, glob_html_log, glob_look_poles,
glob_hmin_init, glob_optimal_done, glob_curr_iter_when_opt, glob_abserr,
glob_dump_analytic, glob_next_display, glob_display_flag,
glob_subiter_method, glob_log10abserr, glob_neg_h, hours_in_day,
glob_percent_done, glob_current_iter, glob_optimal_expect_sec,
glob_log10relerr, MAX_UNCHANGED, glob_display_interval, glob_hmax,
glob_disp_incr, sec_in_minute, glob_max_minutes, glob_iter, glob_warned,
glob_log10_relerr, glob_hmin, glob_clock_start_sec, min_in_hour,
glob_good_digits, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_initial_pass, glob_log10normmin, array_const_0D0, array_const_1D0,
array_const_1, array_const_5, array_y2, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_y2_init, array_type_pole,
array_1st_rel_error, array_last_rel_error, array_norms, array_m1,
array_pole, array_fact_1, array_x, array_y1_init, array_y1_set_initial,
array_poles, array_y2_higher_work2, array_y1_higher, array_y1_higher_work2,
array_y2_higher, array_complex_pole, array_real_pole, array_fact_2,
array_y2_set_initial, array_y1_higher_work, array_y2_higher_work, glob_last
;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y2[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then
glob_good_digits := -trunc(log10(relerr/100.0))
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_y1(ind_var);
omniout_float(ALWAYS, "y1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y1[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then
glob_good_digits := -trunc(log10(relerr/100.0))
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # Begin Function number 5
> adjust_for_pole := proc(h_param)
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_no_eqs,
> glob_relerr,
> years_in_century,
> glob_dump,
> glob_normmax,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_reached_optimal_h,
> days_in_year,
> djd_debug2,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_iter,
> glob_log10_abserr,
> glob_not_yet_finished,
> centuries_in_millinium,
> djd_debug,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_large_float,
> glob_h,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_html_log,
> glob_look_poles,
> glob_hmin_init,
> glob_optimal_done,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_dump_analytic,
> glob_next_display,
> glob_display_flag,
> glob_subiter_method,
> glob_log10abserr,
> glob_neg_h,
> hours_in_day,
> glob_percent_done,
> glob_current_iter,
> glob_optimal_expect_sec,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_display_interval,
> glob_hmax,
> glob_disp_incr,
> sec_in_minute,
> glob_max_minutes,
> glob_iter,
> glob_warned,
> glob_log10_relerr,
> glob_hmin,
> glob_clock_start_sec,
> min_in_hour,
> glob_good_digits,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_y2_init,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_norms,
> array_m1,
> array_pole,
> array_fact_1,
> array_x,
> array_y1_init,
> array_y1_set_initial,
> array_poles,
> array_y2_higher_work2,
> array_y1_higher,
> array_y1_higher_work2,
> array_y2_higher,
> array_complex_pole,
> array_real_pole,
> array_fact_2,
> array_y2_set_initial,
> array_y1_higher_work,
> array_y2_higher_work,
> glob_last;
>
> local hnew, sz2, tmp;
>
>
>
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if ( not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
>
> # End Function number 5
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, INFO,
glob_no_eqs, glob_relerr, years_in_century, glob_dump, glob_normmax,
glob_small_float, glob_max_rel_trunc_err, glob_reached_optimal_h,
days_in_year, djd_debug2, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_smallish_float, glob_optimal_start, glob_max_iter, glob_log10_abserr,
glob_not_yet_finished, centuries_in_millinium, djd_debug, glob_start,
glob_warned2, glob_optimal_clock_start_sec, glob_max_hours,
glob_last_good_h, glob_large_float, glob_h, glob_not_yet_start_msg,
glob_clock_sec, glob_almost_1, glob_html_log, glob_look_poles,
glob_hmin_init, glob_optimal_done, glob_curr_iter_when_opt, glob_abserr,
glob_dump_analytic, glob_next_display, glob_display_flag,
glob_subiter_method, glob_log10abserr, glob_neg_h, hours_in_day,
glob_percent_done, glob_current_iter, glob_optimal_expect_sec,
glob_log10relerr, MAX_UNCHANGED, glob_display_interval, glob_hmax,
glob_disp_incr, sec_in_minute, glob_max_minutes, glob_iter, glob_warned,
glob_log10_relerr, glob_hmin, glob_clock_start_sec, min_in_hour,
glob_good_digits, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_initial_pass, glob_log10normmin, array_const_0D0, array_const_1D0,
array_const_1, array_const_5, array_y2, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_y2_init, array_type_pole,
array_1st_rel_error, array_last_rel_error, array_norms, array_m1,
array_pole, array_fact_1, array_x, array_y1_init, array_y1_set_initial,
array_poles, array_y2_higher_work2, array_y1_higher, array_y1_higher_work2,
array_y2_higher, array_complex_pole, array_real_pole, array_fact_2,
array_y2_set_initial, array_y1_higher_work, array_y2_higher_work, glob_last
;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # Begin Function number 6
> prog_report := proc(x_start,x_end)
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_no_eqs,
> glob_relerr,
> years_in_century,
> glob_dump,
> glob_normmax,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_reached_optimal_h,
> days_in_year,
> djd_debug2,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_iter,
> glob_log10_abserr,
> glob_not_yet_finished,
> centuries_in_millinium,
> djd_debug,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_large_float,
> glob_h,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_html_log,
> glob_look_poles,
> glob_hmin_init,
> glob_optimal_done,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_dump_analytic,
> glob_next_display,
> glob_display_flag,
> glob_subiter_method,
> glob_log10abserr,
> glob_neg_h,
> hours_in_day,
> glob_percent_done,
> glob_current_iter,
> glob_optimal_expect_sec,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_display_interval,
> glob_hmax,
> glob_disp_incr,
> sec_in_minute,
> glob_max_minutes,
> glob_iter,
> glob_warned,
> glob_log10_relerr,
> glob_hmin,
> glob_clock_start_sec,
> min_in_hour,
> glob_good_digits,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_y2_init,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_norms,
> array_m1,
> array_pole,
> array_fact_1,
> array_x,
> array_y1_init,
> array_y1_set_initial,
> array_poles,
> array_y2_higher_work2,
> array_y1_higher,
> array_y1_higher_work2,
> array_y2_higher,
> array_complex_pole,
> array_real_pole,
> array_fact_2,
> array_y2_set_initial,
> array_y1_higher_work,
> array_y2_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 6
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, INFO,
glob_no_eqs, glob_relerr, years_in_century, glob_dump, glob_normmax,
glob_small_float, glob_max_rel_trunc_err, glob_reached_optimal_h,
days_in_year, djd_debug2, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_smallish_float, glob_optimal_start, glob_max_iter, glob_log10_abserr,
glob_not_yet_finished, centuries_in_millinium, djd_debug, glob_start,
glob_warned2, glob_optimal_clock_start_sec, glob_max_hours,
glob_last_good_h, glob_large_float, glob_h, glob_not_yet_start_msg,
glob_clock_sec, glob_almost_1, glob_html_log, glob_look_poles,
glob_hmin_init, glob_optimal_done, glob_curr_iter_when_opt, glob_abserr,
glob_dump_analytic, glob_next_display, glob_display_flag,
glob_subiter_method, glob_log10abserr, glob_neg_h, hours_in_day,
glob_percent_done, glob_current_iter, glob_optimal_expect_sec,
glob_log10relerr, MAX_UNCHANGED, glob_display_interval, glob_hmax,
glob_disp_incr, sec_in_minute, glob_max_minutes, glob_iter, glob_warned,
glob_log10_relerr, glob_hmin, glob_clock_start_sec, min_in_hour,
glob_good_digits, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_initial_pass, glob_log10normmin, array_const_0D0, array_const_1D0,
array_const_1, array_const_5, array_y2, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_y2_init, array_type_pole,
array_1st_rel_error, array_last_rel_error, array_norms, array_m1,
array_pole, array_fact_1, array_x, array_y1_init, array_y1_set_initial,
array_poles, array_y2_higher_work2, array_y1_higher, array_y1_higher_work2,
array_y2_higher, array_complex_pole, array_real_pole, array_fact_2,
array_y2_set_initial, array_y1_higher_work, array_y2_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 7
> check_for_pole := proc()
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_no_eqs,
> glob_relerr,
> years_in_century,
> glob_dump,
> glob_normmax,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_reached_optimal_h,
> days_in_year,
> djd_debug2,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_iter,
> glob_log10_abserr,
> glob_not_yet_finished,
> centuries_in_millinium,
> djd_debug,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_large_float,
> glob_h,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_html_log,
> glob_look_poles,
> glob_hmin_init,
> glob_optimal_done,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_dump_analytic,
> glob_next_display,
> glob_display_flag,
> glob_subiter_method,
> glob_log10abserr,
> glob_neg_h,
> hours_in_day,
> glob_percent_done,
> glob_current_iter,
> glob_optimal_expect_sec,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_display_interval,
> glob_hmax,
> glob_disp_incr,
> sec_in_minute,
> glob_max_minutes,
> glob_iter,
> glob_warned,
> glob_log10_relerr,
> glob_hmin,
> glob_clock_start_sec,
> min_in_hour,
> glob_good_digits,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_y2_init,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_norms,
> array_m1,
> array_pole,
> array_fact_1,
> array_x,
> array_y1_init,
> array_y1_set_initial,
> array_poles,
> array_y2_higher_work2,
> array_y1_higher,
> array_y1_higher_work2,
> array_y2_higher,
> array_complex_pole,
> array_real_pole,
> array_fact_2,
> array_y2_set_initial,
> array_y1_higher_work,
> array_y2_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 ((omniabs(array_y2_higher[1,m]) < glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float) or (omniabs(array_y2_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1];
> rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float) or (omniabs(array_y1_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1];
> rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 5 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y2_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif ((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]);
> rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]);
> rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]);
> rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]);
> rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif ((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]);
> rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]);
> rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]);
> rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]);
> rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * omniabs(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 (reached_interval()) 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 (reached_interval()) 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 (reached_interval()) 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 (reached_interval()) 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
> if (reached_interval()) then # if number 3
> display_pole();
> fi;# end if 3
>
> # End Function number 7
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, INFO,
glob_no_eqs, glob_relerr, years_in_century, glob_dump, glob_normmax,
glob_small_float, glob_max_rel_trunc_err, glob_reached_optimal_h,
days_in_year, djd_debug2, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_smallish_float, glob_optimal_start, glob_max_iter, glob_log10_abserr,
glob_not_yet_finished, centuries_in_millinium, djd_debug, glob_start,
glob_warned2, glob_optimal_clock_start_sec, glob_max_hours,
glob_last_good_h, glob_large_float, glob_h, glob_not_yet_start_msg,
glob_clock_sec, glob_almost_1, glob_html_log, glob_look_poles,
glob_hmin_init, glob_optimal_done, glob_curr_iter_when_opt, glob_abserr,
glob_dump_analytic, glob_next_display, glob_display_flag,
glob_subiter_method, glob_log10abserr, glob_neg_h, hours_in_day,
glob_percent_done, glob_current_iter, glob_optimal_expect_sec,
glob_log10relerr, MAX_UNCHANGED, glob_display_interval, glob_hmax,
glob_disp_incr, sec_in_minute, glob_max_minutes, glob_iter, glob_warned,
glob_log10_relerr, glob_hmin, glob_clock_start_sec, min_in_hour,
glob_good_digits, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_initial_pass, glob_log10normmin, array_const_0D0, array_const_1D0,
array_const_1, array_const_5, array_y2, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_y2_init, array_type_pole,
array_1st_rel_error, array_last_rel_error, array_norms, array_m1,
array_pole, array_fact_1, array_x, array_y1_init, array_y1_set_initial,
array_poles, array_y2_higher_work2, array_y1_higher, array_y1_higher_work2,
array_y2_higher, array_complex_pole, array_real_pole, array_fact_2,
array_y2_set_initial, array_y1_higher_work, array_y2_higher_work, glob_last
;
n := glob_max_terms;
m := n - 6;
while 10 <= m and (omniabs(array_y2_higher[1, m]) < glob_small_float
or omniabs(array_y2_higher[1, m - 1]) < glob_small_float or
omniabs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y1_higher[1, m]) < glob_small_float
or omniabs(array_y1_higher[1, m - 1]) < glob_small_float or
omniabs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 6;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= omniabs(array_y2_higher[1, m]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= omniabs(array_y1_higher[1, m]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(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 reached_interval() 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 reached_interval() 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 reached_interval() 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 reached_interval() 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;
if reached_interval() then display_pole() end if
end proc
> # Begin Function number 8
> get_norms := proc()
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_no_eqs,
> glob_relerr,
> years_in_century,
> glob_dump,
> glob_normmax,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_reached_optimal_h,
> days_in_year,
> djd_debug2,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_iter,
> glob_log10_abserr,
> glob_not_yet_finished,
> centuries_in_millinium,
> djd_debug,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_large_float,
> glob_h,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_html_log,
> glob_look_poles,
> glob_hmin_init,
> glob_optimal_done,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_dump_analytic,
> glob_next_display,
> glob_display_flag,
> glob_subiter_method,
> glob_log10abserr,
> glob_neg_h,
> hours_in_day,
> glob_percent_done,
> glob_current_iter,
> glob_optimal_expect_sec,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_display_interval,
> glob_hmax,
> glob_disp_incr,
> sec_in_minute,
> glob_max_minutes,
> glob_iter,
> glob_warned,
> glob_log10_relerr,
> glob_hmin,
> glob_clock_start_sec,
> min_in_hour,
> glob_good_digits,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_y2_init,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_norms,
> array_m1,
> array_pole,
> array_fact_1,
> array_x,
> array_y1_init,
> array_y1_set_initial,
> array_poles,
> array_y2_higher_work2,
> array_y1_higher,
> array_y1_higher_work2,
> array_y2_higher,
> array_complex_pole,
> array_real_pole,
> array_fact_2,
> array_y2_set_initial,
> array_y1_higher_work,
> array_y2_higher_work,
> glob_last;
>
> local iii;
>
>
>
> if ( not glob_initial_pass) then # if number 3
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2
> ;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 3
> ;
>
> # End Function number 8
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, INFO,
glob_no_eqs, glob_relerr, years_in_century, glob_dump, glob_normmax,
glob_small_float, glob_max_rel_trunc_err, glob_reached_optimal_h,
days_in_year, djd_debug2, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_smallish_float, glob_optimal_start, glob_max_iter, glob_log10_abserr,
glob_not_yet_finished, centuries_in_millinium, djd_debug, glob_start,
glob_warned2, glob_optimal_clock_start_sec, glob_max_hours,
glob_last_good_h, glob_large_float, glob_h, glob_not_yet_start_msg,
glob_clock_sec, glob_almost_1, glob_html_log, glob_look_poles,
glob_hmin_init, glob_optimal_done, glob_curr_iter_when_opt, glob_abserr,
glob_dump_analytic, glob_next_display, glob_display_flag,
glob_subiter_method, glob_log10abserr, glob_neg_h, hours_in_day,
glob_percent_done, glob_current_iter, glob_optimal_expect_sec,
glob_log10relerr, MAX_UNCHANGED, glob_display_interval, glob_hmax,
glob_disp_incr, sec_in_minute, glob_max_minutes, glob_iter, glob_warned,
glob_log10_relerr, glob_hmin, glob_clock_start_sec, min_in_hour,
glob_good_digits, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_initial_pass, glob_log10normmin, array_const_0D0, array_const_1D0,
array_const_1, array_const_5, array_y2, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_y2_init, array_type_pole,
array_1st_rel_error, array_last_rel_error, array_norms, array_m1,
array_pole, array_fact_1, array_x, array_y1_init, array_y1_set_initial,
array_poles, array_y2_higher_work2, array_y1_higher, array_y1_higher_work2,
array_y2_higher, array_complex_pole, array_real_pole, array_fact_2,
array_y2_set_initial, array_y1_higher_work, array_y2_higher_work, glob_last
;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y2[iii]) then
array_norms[iii] := omniabs(array_y2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y1[iii]) then
array_norms[iii] := omniabs(array_y1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 9
> atomall := proc()
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_no_eqs,
> glob_relerr,
> years_in_century,
> glob_dump,
> glob_normmax,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_reached_optimal_h,
> days_in_year,
> djd_debug2,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_iter,
> glob_log10_abserr,
> glob_not_yet_finished,
> centuries_in_millinium,
> djd_debug,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_large_float,
> glob_h,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_html_log,
> glob_look_poles,
> glob_hmin_init,
> glob_optimal_done,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_dump_analytic,
> glob_next_display,
> glob_display_flag,
> glob_subiter_method,
> glob_log10abserr,
> glob_neg_h,
> hours_in_day,
> glob_percent_done,
> glob_current_iter,
> glob_optimal_expect_sec,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_display_interval,
> glob_hmax,
> glob_disp_incr,
> sec_in_minute,
> glob_max_minutes,
> glob_iter,
> glob_warned,
> glob_log10_relerr,
> glob_hmin,
> glob_clock_start_sec,
> min_in_hour,
> glob_good_digits,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_y2_init,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_norms,
> array_m1,
> array_pole,
> array_fact_1,
> array_x,
> array_y1_init,
> array_y1_set_initial,
> array_poles,
> array_y2_higher_work2,
> array_y1_higher,
> array_y1_higher_work2,
> array_y2_higher,
> array_complex_pole,
> array_real_pole,
> array_fact_2,
> array_y2_set_initial,
> array_y1_higher_work,
> array_y2_higher_work,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
>
>
>
>
>
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D0[1] + array_y1[1];
> #emit pre 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] * expt(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 FULL FULL $eq_no = 2 i = 1
> array_tmp3[1] := (array_m1[1] * (array_y2[1]));
> #emit pre add FULL - CONST $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] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp1[2] := array_y1[2];
> #emit pre 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] * expt(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 FULL FULL $eq_no = 2 i = 2
> array_tmp3[2] := ats(2,array_m1,array_y2,1);
> #emit pre add FULL CONST $eq_no = 2 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[2,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp1[3] := array_y1[3];
> #emit pre 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] * expt(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 FULL FULL $eq_no = 2 i = 3
> array_tmp3[3] := ats(3,array_m1,array_y2,1);
> #emit pre add FULL CONST $eq_no = 2 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[2,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp1[4] := array_y1[4];
> #emit pre 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] * expt(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 FULL FULL $eq_no = 2 i = 4
> array_tmp3[4] := ats(4,array_m1,array_y2,1);
> #emit pre add FULL CONST $eq_no = 2 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[2,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp1[5] := array_y1[5];
> #emit pre 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] * expt(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 FULL FULL $eq_no = 2 i = 5
> array_tmp3[5] := ats(5,array_m1,array_y2,1);
> #emit pre add FULL CONST $eq_no = 2 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[2,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp1[kkk] := array_y1[kkk];
> #emit 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] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y2[kkk + order_d] := temporary;
> array_y2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> #emit mult FULL FULL $eq_no = 2
> array_tmp3[kkk] := ats(kkk,array_m1,array_y2,1);
> #emit FULL - NOT FULL add $eq_no = 2
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2
> temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y1[kkk + order_d] := temporary;
> array_y1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
>
> #BOTTOM ATOMALL ???
> # End Function number 9
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, INFO,
glob_no_eqs, glob_relerr, years_in_century, glob_dump, glob_normmax,
glob_small_float, glob_max_rel_trunc_err, glob_reached_optimal_h,
days_in_year, djd_debug2, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_smallish_float, glob_optimal_start, glob_max_iter, glob_log10_abserr,
glob_not_yet_finished, centuries_in_millinium, djd_debug, glob_start,
glob_warned2, glob_optimal_clock_start_sec, glob_max_hours,
glob_last_good_h, glob_large_float, glob_h, glob_not_yet_start_msg,
glob_clock_sec, glob_almost_1, glob_html_log, glob_look_poles,
glob_hmin_init, glob_optimal_done, glob_curr_iter_when_opt, glob_abserr,
glob_dump_analytic, glob_next_display, glob_display_flag,
glob_subiter_method, glob_log10abserr, glob_neg_h, hours_in_day,
glob_percent_done, glob_current_iter, glob_optimal_expect_sec,
glob_log10relerr, MAX_UNCHANGED, glob_display_interval, glob_hmax,
glob_disp_incr, sec_in_minute, glob_max_minutes, glob_iter, glob_warned,
glob_log10_relerr, glob_hmin, glob_clock_start_sec, min_in_hour,
glob_good_digits, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_initial_pass, glob_log10normmin, array_const_0D0, array_const_1D0,
array_const_1, array_const_5, array_y2, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_y2_init, array_type_pole,
array_1st_rel_error, array_last_rel_error, array_norms, array_m1,
array_pole, array_fact_1, array_x, array_y1_init, array_y1_set_initial,
array_poles, array_y2_higher_work2, array_y1_higher, array_y1_higher_work2,
array_y2_higher, array_complex_pole, array_real_pole, array_fact_2,
array_y2_set_initial, array_y1_higher_work, array_y2_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]*expt(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]*expt(glob_h, 1)*factorial_3(0, 1);
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_y1[2];
if not array_y2_set_initial[1, 7] then
if 2 <= glob_max_terms then
temporary := array_tmp1[2]*expt(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];
if not array_y1_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_y1[3];
if not array_y2_set_initial[1, 8] then
if 3 <= glob_max_terms then
temporary := array_tmp1[3]*expt(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];
if not array_y1_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_y1[4];
if not array_y2_set_initial[1, 9] then
if 4 <= glob_max_terms then
temporary := array_tmp1[4]*expt(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];
if not array_y1_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_y1[5];
if not array_y2_set_initial[1, 10] then
if 5 <= glob_max_terms then
temporary := array_tmp1[5]*expt(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];
if not array_y1_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_y1[kkk];
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]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y2[kkk + order_d] := temporary;
array_y2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
array_tmp3[kkk] := ats(kkk, array_m1, array_y2, 1);
array_tmp4[kkk] := array_tmp3[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y1_set_initial[2, kkk + order_d] then
temporary := array_tmp4[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y1[kkk + order_d] := temporary;
array_y1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> fprintf(fd,"
");
> if (secs >= 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_minute;
> sec_int := floor(seconds);
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_minute, years_in_century;
secs := secs_in;
fprintf(fd, "");
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*min_in_hour*
hours_in_day*days_in_year*years_in_century*
centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_minute;
sec_int := floor(seconds);
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs >= 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_minute;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_minute, years_in_century;
secs := convfloat(secs_in);
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*min_in_hour*
hours_in_day*days_in_year*years_in_century*
centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_minute;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
>
>
>
>
>
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats;
>
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
>
>
>
>
>
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
>
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
>
> local good_digits;
>
>
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 11
> if (rel_error <> 0.0) then # if number 12
> good_digits := -trunc(log10(rel_error/100.0));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 12
> ;
> else
> fprintf(file,"Unknown");
> fi;# end if 11
> ;
> fprintf(file," | ");
>
> # End Function number 9
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if rel_error <> 0. then
good_digits := -trunc(log10(rel_error/100.0));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 10
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 10
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 11
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 12
> 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 12
> 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 13
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 13
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 14
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 14
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 15
> not_reached_end := proc(x,x_end)
> global neg_h;
> local ret;
>
>
>
> if ((glob_neg_h and (x > x_end)) or (( not glob_neg_h) and (x < x_end))) then # if number 13
> ret := true;
> else
> ret := false;
> fi;# end if 13
> ;
>
>
> ret;
>
> # End Function number 15
> end;
not_reached_end := proc(x, x_end)
local ret;
global neg_h;
if glob_neg_h and x_end < x or not glob_neg_h and x < x_end then
ret := true
else ret := false
end if;
ret
end proc
> # Begin Function number 16
> 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 16
> 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 17
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
>
>
>
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
>
> # End Function number 17
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # Begin Function number 18
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
>
>
>
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr;
>
> # End Function number 18
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 19
> factorial_2 := proc(nnn)
> local ret;
>
>
>
> ret := nnn!;
>
> # End Function number 19
> end;
factorial_2 := proc(nnn) local ret; ret := nnn! end proc
> # Begin Function number 20
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
>
>
>
> if (nnn <= glob_max_terms) then # if number 13
> if (array_fact_1[nnn] = 0) then # if number 14
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 20
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 21
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
>
>
>
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13
> if (array_fact_2[mmm,nnn] = 0) then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 21
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 22
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 22
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 23
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 23
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> return(1.0 + cos(x));
> end;
exact_soln_y1 := proc(x) return 1.0 + cos(x) end proc
> exact_soln_y2 := proc(x)
> return(1.0 + sin(x));
> end;
exact_soln_y2 := proc(x) return 1.0 + sin(x) end proc
> exact_soln_y2p := proc(x)
> return( cos(x));
> end;
exact_soln_y2p := proc(x) return cos(x) end proc
> exact_soln_y2pp := proc(x)
> return( -sin(x));
> end;
exact_soln_y2pp := proc(x) return -sin(x) end proc
> exact_soln_y2ppp := proc(x)
> return( -cos(x));
> end;
exact_soln_y2ppp := proc(x) return -cos(x) end proc
> exact_soln_y2pppp := proc(x)
> return( sin(x));
> end;
exact_soln_y2pppp := proc(x) return sin(x) end proc
>
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp,subiter;
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_no_eqs,
> glob_relerr,
> years_in_century,
> glob_dump,
> glob_normmax,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_reached_optimal_h,
> days_in_year,
> djd_debug2,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_iter,
> glob_log10_abserr,
> glob_not_yet_finished,
> centuries_in_millinium,
> djd_debug,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_large_float,
> glob_h,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_html_log,
> glob_look_poles,
> glob_hmin_init,
> glob_optimal_done,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_dump_analytic,
> glob_next_display,
> glob_display_flag,
> glob_subiter_method,
> glob_log10abserr,
> glob_neg_h,
> hours_in_day,
> glob_percent_done,
> glob_current_iter,
> glob_optimal_expect_sec,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_display_interval,
> glob_hmax,
> glob_disp_incr,
> sec_in_minute,
> glob_max_minutes,
> glob_iter,
> glob_warned,
> glob_log10_relerr,
> glob_hmin,
> glob_clock_start_sec,
> min_in_hour,
> glob_good_digits,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1D0,
> array_const_1,
> array_const_5,
> #END CONST
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_y2_init,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_norms,
> array_m1,
> array_pole,
> array_fact_1,
> array_x,
> array_y1_init,
> array_y1_set_initial,
> array_poles,
> array_y2_higher_work2,
> array_y1_higher,
> array_y1_higher_work2,
> array_y2_higher,
> array_complex_pole,
> array_real_pole,
> array_fact_2,
> array_y2_set_initial,
> array_y1_higher_work,
> array_y2_higher_work,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> DEBUGL := 3;
> ALWAYS := 1;
> glob_max_terms := 30;
> INFO := 2;
> glob_no_eqs := 0;
> glob_relerr := 0.1e-10;
> years_in_century := 100;
> glob_dump := false;
> glob_normmax := 0.0;
> glob_small_float := 0.1e-50;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_reached_optimal_h := false;
> days_in_year := 365;
> djd_debug2 := true;
> glob_max_opt_iter := 10;
> glob_unchanged_h_cnt := 0;
> glob_smallish_float := 0.1e-100;
> glob_optimal_start := 0.0;
> glob_max_iter := 1000;
> glob_log10_abserr := 0.1e-10;
> glob_not_yet_finished := true;
> centuries_in_millinium := 10;
> djd_debug := true;
> glob_start := 0;
> glob_warned2 := false;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_hours := 0.0;
> glob_last_good_h := 0.1;
> glob_large_float := 9.0e100;
> glob_h := 0.1;
> glob_not_yet_start_msg := true;
> glob_clock_sec := 0.0;
> glob_almost_1 := 0.9990;
> glob_html_log := true;
> glob_look_poles := false;
> glob_hmin_init := 0.001;
> glob_optimal_done := false;
> glob_curr_iter_when_opt := 0;
> glob_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_next_display := 0.0;
> glob_display_flag := true;
> glob_subiter_method := 3;
> glob_log10abserr := 0.0;
> glob_neg_h := false;
> hours_in_day := 24;
> glob_percent_done := 0.0;
> glob_current_iter := 0;
> glob_optimal_expect_sec := 0.1;
> glob_log10relerr := 0.0;
> MAX_UNCHANGED := 10;
> glob_display_interval := 0.0;
> glob_hmax := 1.0;
> glob_disp_incr := 0.1;
> sec_in_minute := 60;
> glob_max_minutes := 0.0;
> glob_iter := 0;
> glob_warned := false;
> glob_log10_relerr := 0.1e-10;
> glob_hmin := 0.00000000001;
> glob_clock_start_sec := 0.0;
> min_in_hour := 60;
> glob_good_digits := 0;
> glob_orig_start_sec := 0.0;
> glob_max_sec := 10000.0;
> glob_max_trunc_err := 0.1e-10;
> glob_initial_pass := true;
> glob_log10normmin := 0.1;
> #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 := 0.005 ;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10000;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return( cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
> omniout_str(ALWAYS,"return( -sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)");
> omniout_str(ALWAYS,"return( -cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)");
> omniout_str(ALWAYS,"return( 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_y2:= Array(0..(max_terms + 1),[]);
> array_y1:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_y2_init:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_y1_init:= Array(0..(max_terms + 1),[]);
> array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_y2_higher_work2 := Array(0..(6+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher := Array(0..(6+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work := Array(0..(6+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_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_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_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_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[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
> ;
> 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 <= 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 <=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 <= max_terms) do # do number 3
> array_y1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=6) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_higher[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 <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=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
> ;
> 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
> ;
> #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_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_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_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
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> 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 := 0.005 ;
> glob_display_interval := 0.1;
> glob_look_poles := true;
> glob_max_iter := 10000;
> glob_max_minutes := 10;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1
> ;
> 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;
> glob_next_display := x_start;
> order_diff := 5;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and not_reached_end(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
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3
> ;
> 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
> if (reached_interval()) then # if number 4
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 4
> ;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y2
> order_diff := 5;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 6;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[6,iii] := array_y2_higher[6,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 6;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 5;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 5;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 5;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 5;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 4;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 4;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 4;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 4;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 5;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 5;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 4;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 6;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 6;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 5;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 5;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 4;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y1
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 4
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 4
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 4
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y2 , x , 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,"2012-09-21T01:24:36-05:00")
> ;
> 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_good_digits(html_log_file,array_last_rel_error[1])
> ;
> 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," 130 | ")
> ;
> logitem_str(html_log_file,"mtest7 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest7 maple results")
> ;
> logitem_str(html_log_file,"c c++ Maple and Maxima")
> ;
> 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)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[2])
> ;
> 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 9
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp, subiter;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, INFO,
glob_no_eqs, glob_relerr, years_in_century, glob_dump, glob_normmax,
glob_small_float, glob_max_rel_trunc_err, glob_reached_optimal_h,
days_in_year, djd_debug2, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_smallish_float, glob_optimal_start, glob_max_iter, glob_log10_abserr,
glob_not_yet_finished, centuries_in_millinium, djd_debug, glob_start,
glob_warned2, glob_optimal_clock_start_sec, glob_max_hours,
glob_last_good_h, glob_large_float, glob_h, glob_not_yet_start_msg,
glob_clock_sec, glob_almost_1, glob_html_log, glob_look_poles,
glob_hmin_init, glob_optimal_done, glob_curr_iter_when_opt, glob_abserr,
glob_dump_analytic, glob_next_display, glob_display_flag,
glob_subiter_method, glob_log10abserr, glob_neg_h, hours_in_day,
glob_percent_done, glob_current_iter, glob_optimal_expect_sec,
glob_log10relerr, MAX_UNCHANGED, glob_display_interval, glob_hmax,
glob_disp_incr, sec_in_minute, glob_max_minutes, glob_iter, glob_warned,
glob_log10_relerr, glob_hmin, glob_clock_start_sec, min_in_hour,
glob_good_digits, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_initial_pass, glob_log10normmin, array_const_0D0, array_const_1D0,
array_const_1, array_const_5, array_y2, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_y2_init, array_type_pole,
array_1st_rel_error, array_last_rel_error, array_norms, array_m1,
array_pole, array_fact_1, array_x, array_y1_init, array_y1_set_initial,
array_poles, array_y2_higher_work2, array_y1_higher, array_y1_higher_work2,
array_y2_higher, array_complex_pole, array_real_pole, array_fact_2,
array_y2_set_initial, array_y1_higher_work, array_y2_higher_work, glob_last
;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
DEBUGL := 3;
ALWAYS := 1;
glob_max_terms := 30;
INFO := 2;
glob_no_eqs := 0;
glob_relerr := 0.1*10^(-10);
years_in_century := 100;
glob_dump := false;
glob_normmax := 0.;
glob_small_float := 0.1*10^(-50);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_reached_optimal_h := false;
days_in_year := 365;
djd_debug2 := true;
glob_max_opt_iter := 10;
glob_unchanged_h_cnt := 0;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_start := 0.;
glob_max_iter := 1000;
glob_log10_abserr := 0.1*10^(-10);
glob_not_yet_finished := true;
centuries_in_millinium := 10;
djd_debug := true;
glob_start := 0;
glob_warned2 := false;
glob_optimal_clock_start_sec := 0.;
glob_max_hours := 0.;
glob_last_good_h := 0.1;
glob_large_float := 0.90*10^101;
glob_h := 0.1;
glob_not_yet_start_msg := true;
glob_clock_sec := 0.;
glob_almost_1 := 0.9990;
glob_html_log := true;
glob_look_poles := false;
glob_hmin_init := 0.001;
glob_optimal_done := false;
glob_curr_iter_when_opt := 0;
glob_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_next_display := 0.;
glob_display_flag := true;
glob_subiter_method := 3;
glob_log10abserr := 0.;
glob_neg_h := false;
hours_in_day := 24;
glob_percent_done := 0.;
glob_current_iter := 0;
glob_optimal_expect_sec := 0.1;
glob_log10relerr := 0.;
MAX_UNCHANGED := 10;
glob_display_interval := 0.;
glob_hmax := 1.0;
glob_disp_incr := 0.1;
sec_in_minute := 60;
glob_max_minutes := 0.;
glob_iter := 0;
glob_warned := false;
glob_log10_relerr := 0.1*10^(-10);
glob_hmin := 0.1*10^(-10);
glob_clock_start_sec := 0.;
min_in_hour := 60;
glob_good_digits := 0;
glob_orig_start_sec := 0.;
glob_max_sec := 10000.0;
glob_max_trunc_err := 0.1*10^(-10);
glob_initial_pass := true;
glob_log10normmin := 0.1;
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 := 0.005 ;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10000;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return(1.0 +\tcos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(1.0 +\tsin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return(\tcos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
omniout_str(ALWAYS, "return( -sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)");
omniout_str(ALWAYS, "return(\t-cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)");
omniout_str(ALWAYS, "return( 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_y2 := Array(0 .. max_terms + 1, []);
array_y1 := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_y2_init := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_y1_init := Array(0 .. max_terms + 1, []);
array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_y2_higher_work2 := Array(0 .. 7, 0 .. max_terms + 1, []);
array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher := Array(0 .. 7, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 3, 0 .. 4, []);
array_real_pole := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work := Array(0 .. 7, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_y1_init[term] := 0.; term := term + 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 <= 3 do array_poles[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 <= max_terms do
array_y1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 6 do
term := 1;
while term <= max_terms do
array_y2_higher[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 <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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;
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;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[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;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.;
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 := 0.005;
glob_display_interval := 0.1;
glob_look_poles := true;
glob_max_iter := 10000;
glob_max_minutes := 10;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
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;
glob_next_display := x_start;
order_diff := 5;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
not_reached_end(array_x[1], x_end) and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
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;
if reached_interval() then
glob_next_display := glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 5;
ord := 6;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[6, iii] := array_y2_higher[6, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 6;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 5;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 5;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 5;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 5;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 4;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 4;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 4;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 3;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 3;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 3;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 5;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 5;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 6;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 6;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 5;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 5;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
term_no := glob_max_terms;
while 1 <= term_no do
array_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
term_no := glob_max_terms;
while 1 <= term_no do
array_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y2 , x , 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, "2012-09-21T01:24:36-05:00");
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_good_digits(html_log_file, array_last_rel_error[1]);
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, " 130 | ");
logitem_str(html_log_file,
"mtest7 diffeq.mxt");
logitem_str(html_log_file,
"mtest7 maple results");
logitem_str(html_log_file, "c c++ Maple and Maxima");
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);
logitem_good_digits(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> main();
##############ECHO OF PROBLEM#################
##############temp/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 := 0.005 ;
glob_display_interval := 0.1;
glob_look_poles := true;
glob_max_iter := 10000;
glob_max_minutes := 10;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(1.0 + cos(x));
end;
exact_soln_y2 := proc(x)
return(1.0 + sin(x));
end;
exact_soln_y2p := proc(x)
return( cos(x));
end;
exact_soln_y2pp := proc(x)
return( -sin(x));
end;
exact_soln_y2ppp := proc(x)
return( -cos(x));
end;
exact_soln_y2pppp := proc(x)
return( 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 %
Correct digits = 32
h = 0.005
y1[1] (analytic) = 2
y1[1] (numeric) = 2
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
x[1] = 0
y2[1] (analytic) = 1
y2[1] (numeric) = 1
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
y1[1] (analytic) = 2
y1[1] (numeric) = 2
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.44
NO POLE
NO POLE
memory used=7.6MB, alloc=4.3MB, time=0.94
memory used=11.4MB, alloc=4.4MB, time=1.43
memory used=15.2MB, alloc=4.4MB, time=1.94
memory used=19.0MB, alloc=4.4MB, time=2.47
memory used=22.8MB, alloc=4.4MB, time=2.98
memory used=26.7MB, alloc=4.5MB, time=3.49
memory used=30.5MB, alloc=4.5MB, time=4.01
memory used=34.3MB, alloc=4.5MB, time=4.53
memory used=38.1MB, alloc=4.5MB, time=5.06
memory used=41.9MB, alloc=4.5MB, time=5.58
memory used=45.7MB, alloc=4.5MB, time=6.10
memory used=49.5MB, alloc=4.5MB, time=6.62
memory used=53.4MB, alloc=4.5MB, time=7.15
memory used=57.2MB, alloc=4.5MB, time=7.67
memory used=61.0MB, alloc=4.5MB, time=8.19
memory used=64.8MB, alloc=4.5MB, time=8.71
memory used=68.6MB, alloc=4.5MB, time=9.23
x[1] = 0.1
y2[1] (analytic) = 1.0998334166468281523068141984106
y2[1] (numeric) = 1.0998334999801011537010088186871
absolute error = 8.33332730013941946202765e-08
relative error = 7.5768995322455883058665598404949e-06 %
Correct digits = 7
h = 0.005
y1[1] (analytic) = 1.9950041652780257660955619878039
y1[1] (numeric) = 1.9950041638891074824746914087479
absolute error = 1.3889182836208705790560e-09
relative error = 6.9619818734930287459518585818897e-08 %
Correct digits = 9
h = 0.005
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.5MB, time=9.76
NO POLE
NO POLE
memory used=76.2MB, alloc=4.5MB, time=10.27
memory used=80.1MB, alloc=4.5MB, time=10.78
memory used=83.9MB, alloc=4.5MB, time=11.30
memory used=87.7MB, alloc=4.5MB, time=11.83
memory used=91.5MB, alloc=4.5MB, time=12.35
memory used=95.3MB, alloc=4.5MB, time=12.88
memory used=99.1MB, alloc=4.5MB, time=13.40
memory used=102.9MB, alloc=4.5MB, time=13.92
memory used=106.8MB, alloc=4.5MB, time=14.45
memory used=110.6MB, alloc=4.5MB, time=14.98
memory used=114.4MB, alloc=4.5MB, time=15.51
memory used=118.2MB, alloc=4.5MB, time=16.02
memory used=122.0MB, alloc=4.5MB, time=16.55
memory used=125.8MB, alloc=4.5MB, time=17.07
memory used=129.7MB, alloc=4.5MB, time=17.59
memory used=133.5MB, alloc=4.5MB, time=18.11
memory used=137.3MB, alloc=4.5MB, time=18.64
x[1] = 0.2
y2[1] (analytic) = 1.1986693307950612154594126271184
y2[1] (numeric) = 1.19867199745936515036545842322
absolute error = 2.6666643039349060457961016e-06
relative error = 0.0002224687188889819634728101130374 %
Correct digits = 5
h = 0.005
y1[1] (analytic) = 1.9800665778412416311241965167482
y1[1] (numeric) = 1.9800664889523670411412545769473
absolute error = 8.88888745899829419398009e-08
relative error = 4.4891861508461813271756948136374e-06 %
Correct digits = 7
h = 0.005
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.5MB, time=19.15
NO POLE
NO POLE
memory used=144.9MB, alloc=4.5MB, time=19.68
memory used=148.7MB, alloc=4.5MB, time=20.21
memory used=152.5MB, alloc=4.5MB, time=20.72
memory used=156.4MB, alloc=4.5MB, time=21.25
memory used=160.2MB, alloc=4.5MB, time=21.77
memory used=164.0MB, alloc=4.5MB, time=22.30
memory used=167.8MB, alloc=4.5MB, time=22.83
memory used=171.6MB, alloc=4.5MB, time=23.36
memory used=175.4MB, alloc=4.5MB, time=23.89
memory used=179.2MB, alloc=4.5MB, time=24.42
memory used=183.1MB, alloc=4.5MB, time=24.90
memory used=186.9MB, alloc=4.5MB, time=25.41
memory used=190.7MB, alloc=4.5MB, time=25.89
memory used=194.5MB, alloc=4.5MB, time=26.38
memory used=198.3MB, alloc=4.5MB, time=26.93
memory used=202.1MB, alloc=4.5MB, time=27.48
memory used=205.9MB, alloc=4.5MB, time=28.02
x[1] = 0.3
y2[1] (analytic) = 1.295520206661339575105320745685
y2[1] (numeric) = 1.2955404566404860698636291595
absolute error = 2.02499791464947583084138150e-05
relative error = 0.0015630770591128480729468577944888 %
Correct digits = 4
h = 0.005
y1[1] (analytic) = 1.955336489125606019642310227568
y1[1] (numeric) = 1.9553354766264958980719010058837
absolute error = 1.0124991101215704092216843e-06
relative error = 5.1781323355467231299480340032307e-05 %
Correct digits = 6
h = 0.005
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.5MB, time=28.55
NO POLE
NO POLE
memory used=213.6MB, alloc=4.5MB, time=29.06
memory used=217.4MB, alloc=4.5MB, time=29.58
memory used=221.2MB, alloc=4.5MB, time=30.09
memory used=225.0MB, alloc=4.5MB, time=30.59
memory used=228.8MB, alloc=4.5MB, time=31.12
memory used=232.7MB, alloc=4.5MB, time=31.65
memory used=236.5MB, alloc=4.5MB, time=32.20
memory used=240.3MB, alloc=4.5MB, time=32.74
memory used=244.1MB, alloc=4.5MB, time=33.27
memory used=247.9MB, alloc=4.5MB, time=33.80
memory used=251.7MB, alloc=4.5MB, time=34.34
memory used=255.5MB, alloc=4.5MB, time=34.86
memory used=259.4MB, alloc=4.5MB, time=35.38
memory used=263.2MB, alloc=4.5MB, time=35.91
memory used=267.0MB, alloc=4.6MB, time=36.43
memory used=270.8MB, alloc=4.6MB, time=36.96
memory used=274.6MB, alloc=4.6MB, time=37.51
x[1] = 0.4
y2[1] (analytic) = 1.3894183423086504916663117567957
y2[1] (numeric) = 1.3895036755416044135386020443452
absolute error = 8.53332329539218722902875495e-05
relative error = 0.0061416515354283148386532866539262 %
Correct digits = 4
h = 0.005
y1[1] (analytic) = 1.9210609940028850827985267320518
y1[1] (numeric) = 1.9210553051200889970661256093334
absolute error = 5.6888827960857324011227184e-06
relative error = 0.00029613233592505021410257572374462 %
Correct digits = 5
h = 0.005
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.6MB, time=38.04
NO POLE
NO POLE
memory used=282.2MB, alloc=4.6MB, time=38.59
memory used=286.1MB, alloc=4.6MB, time=39.12
memory used=289.9MB, alloc=4.6MB, time=39.65
memory used=293.7MB, alloc=4.6MB, time=40.17
memory used=297.5MB, alloc=4.6MB, time=40.69
memory used=301.3MB, alloc=4.6MB, time=41.21
memory used=305.1MB, alloc=4.6MB, time=41.75
memory used=308.9MB, alloc=4.6MB, time=42.29
memory used=312.8MB, alloc=4.6MB, time=42.82
memory used=316.6MB, alloc=4.6MB, time=43.34
memory used=320.4MB, alloc=4.6MB, time=43.88
memory used=324.2MB, alloc=4.6MB, time=44.42
memory used=328.0MB, alloc=4.6MB, time=44.95
memory used=331.8MB, alloc=4.6MB, time=45.47
memory used=335.7MB, alloc=4.6MB, time=46.00
memory used=339.5MB, alloc=4.6MB, time=46.53
memory used=343.3MB, alloc=4.6MB, time=47.07
x[1] = 0.5
y2[1] (analytic) = 1.4794255386042030002732879352156
y2[1] (numeric) = 1.4796859549206291421225339178603
absolute error = 0.0002604163164261418492459826447
relative error = 0.017602529470448200283909450520997 %
Correct digits = 3
h = 0.005
y1[1] (analytic) = 1.8775825618903727161162815826038
y1[1] (numeric) = 1.8775608605279293844449458895512
absolute error = 2.17013624433316713356930526e-05
relative error = 0.0011558140176527032982740810599195 %
Correct digits = 4
h = 0.005
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.6MB, time=47.60
NO POLE
NO POLE
memory used=350.9MB, alloc=4.6MB, time=48.13
memory used=354.7MB, alloc=4.6MB, time=48.66
memory used=358.5MB, alloc=4.6MB, time=49.19
memory used=362.4MB, alloc=4.6MB, time=49.71
memory used=366.2MB, alloc=4.6MB, time=50.23
memory used=370.0MB, alloc=4.6MB, time=50.75
memory used=373.8MB, alloc=4.6MB, time=51.27
memory used=377.6MB, alloc=4.6MB, time=51.80
memory used=381.4MB, alloc=4.6MB, time=52.34
memory used=385.2MB, alloc=4.6MB, time=52.89
memory used=389.1MB, alloc=4.6MB, time=53.44
memory used=392.9MB, alloc=4.6MB, time=53.98
memory used=396.7MB, alloc=4.6MB, time=54.48
memory used=400.5MB, alloc=4.6MB, time=55.00
memory used=404.3MB, alloc=4.6MB, time=55.54
memory used=408.1MB, alloc=4.6MB, time=56.08
memory used=411.9MB, alloc=4.6MB, time=56.63
x[1] = 0.6
y2[1] (analytic) = 1.5646424733950353572009454456587
y2[1] (numeric) = 1.565290472377261598815456535949
absolute error = 0.0006479989822262416145110902903
relative error = 0.041415147117934407508472450921811 %
Correct digits = 3
h = 0.005
y1[1] (analytic) = 1.8253356149096782972409524989554
y1[1] (numeric) = 1.8252708149993534977153018270234
absolute error = 6.47999103247995256506719320e-05
relative error = 0.0035500271728388957469385100941275 %
Correct digits = 4
h = 0.005
TOP MAIN SOLVE Loop
memory used=415.8MB, alloc=4.6MB, time=57.17
NO POLE
NO POLE
memory used=419.6MB, alloc=4.6MB, time=57.71
memory used=423.4MB, alloc=4.6MB, time=58.25
memory used=427.2MB, alloc=4.6MB, time=58.80
memory used=431.0MB, alloc=4.6MB, time=59.29
memory used=434.8MB, alloc=4.6MB, time=59.82
memory used=438.6MB, alloc=4.6MB, time=60.35
memory used=442.5MB, alloc=4.6MB, time=60.86
memory used=446.3MB, alloc=4.6MB, time=61.39
memory used=450.1MB, alloc=4.6MB, time=61.93
memory used=453.9MB, alloc=4.6MB, time=62.46
memory used=457.7MB, alloc=4.6MB, time=63.00
memory used=461.5MB, alloc=4.6MB, time=63.53
memory used=465.4MB, alloc=4.6MB, time=64.03
memory used=469.2MB, alloc=4.6MB, time=64.53
memory used=473.0MB, alloc=4.6MB, time=65.04
memory used=476.8MB, alloc=4.6MB, time=65.52
memory used=480.6MB, alloc=4.6MB, time=66.04
x[1] = 0.7
y2[1] (analytic) = 1.6442176872376910536726143513987
y2[1] (numeric) = 1.6456182678884320911739645399831
absolute error = 0.0014005806507410375013501885844
relative error = 0.085182190996499544042989605885788 %
Correct digits = 3
h = 0.005
y1[1] (analytic) = 1.7648421872844884262558599901919
y1[1] (numeric) = 1.7646787861579365808902402492661
absolute error = 0.0001634011265518453656197409258
relative error = 0.0092586820356592873538590109380614 %
Correct digits = 4
h = 0.005
TOP MAIN SOLVE Loop
memory used=484.4MB, alloc=4.6MB, time=66.55
NO POLE
NO POLE
memory used=488.2MB, alloc=4.6MB, time=67.07
memory used=492.1MB, alloc=4.6MB, time=67.59
memory used=495.9MB, alloc=4.6MB, time=68.12
memory used=499.7MB, alloc=4.6MB, time=68.62
memory used=503.5MB, alloc=4.6MB, time=69.12
memory used=507.3MB, alloc=4.6MB, time=69.61
memory used=511.1MB, alloc=4.6MB, time=70.13
memory used=514.9MB, alloc=4.6MB, time=70.63
memory used=518.8MB, alloc=4.6MB, time=71.14
memory used=522.6MB, alloc=4.6MB, time=71.68
memory used=526.4MB, alloc=4.6MB, time=72.22
memory used=530.2MB, alloc=4.6MB, time=72.76
memory used=534.0MB, alloc=4.6MB, time=73.28
memory used=537.8MB, alloc=4.6MB, time=73.82
memory used=541.6MB, alloc=4.6MB, time=74.31
memory used=545.5MB, alloc=4.6MB, time=74.82
memory used=549.3MB, alloc=4.6MB, time=75.29
x[1] = 0.8
y2[1] (analytic) = 1.7173560908995227616271746105814
y2[1] (numeric) = 1.720086750794118722123567434705
absolute error = 0.0027306598945959604963928241236
relative error = 0.15900370977609459754646691730543 %
Correct digits = 2
h = 0.005
y1[1] (analytic) = 1.6967067093471654209207499816423
y1[1] (numeric) = 1.6963426211630875973621541492889
absolute error = 0.0003640881840778235585958323534
relative error = 0.021458522092949830497102781582383 %
Correct digits = 3
h = 0.005
TOP MAIN SOLVE Loop
memory used=553.1MB, alloc=4.6MB, time=75.81
NO POLE
NO POLE
memory used=556.9MB, alloc=4.6MB, time=76.30
memory used=560.7MB, alloc=4.6MB, time=76.81
memory used=564.5MB, alloc=4.6MB, time=77.30
memory used=568.4MB, alloc=4.6MB, time=77.82
memory used=572.2MB, alloc=4.6MB, time=78.30
memory used=576.0MB, alloc=4.6MB, time=78.80
memory used=579.8MB, alloc=4.6MB, time=79.30
memory used=583.6MB, alloc=4.6MB, time=79.81
memory used=587.4MB, alloc=4.6MB, time=80.29
memory used=591.2MB, alloc=4.6MB, time=80.80
memory used=595.1MB, alloc=4.6MB, time=81.30
memory used=598.9MB, alloc=4.6MB, time=81.82
memory used=602.7MB, alloc=4.6MB, time=82.31
memory used=606.5MB, alloc=4.6MB, time=82.82
memory used=610.3MB, alloc=4.6MB, time=83.31
memory used=614.1MB, alloc=4.6MB, time=83.83
memory used=617.9MB, alloc=4.6MB, time=84.30
x[1] = 0.9
y2[1] (analytic) = 1.7833269096274833884613823157136
y2[1] (numeric) = 1.7882476428038517316251789030819
absolute error = 0.0049207331763683431637965873683
relative error = 0.27592995708208250444326683474787 %
Correct digits = 2
h = 0.005
y1[1] (analytic) = 1.6216099682706644564847161514071
y1[1] (numeric) = 1.620871857581001364000993759838
absolute error = 0.0007381106896630924837223915691
relative error = 0.045517152959428140926267326613768 %
Correct digits = 3
h = 0.005
TOP MAIN SOLVE Loop
memory used=621.8MB, alloc=4.6MB, time=84.78
NO POLE
NO POLE
memory used=625.6MB, alloc=4.6MB, time=85.29
memory used=629.4MB, alloc=4.6MB, time=85.78
memory used=633.2MB, alloc=4.6MB, time=86.28
memory used=637.0MB, alloc=4.6MB, time=86.77
memory used=640.8MB, alloc=4.6MB, time=87.25
memory used=644.6MB, alloc=4.6MB, time=87.73
memory used=648.5MB, alloc=4.6MB, time=88.23
memory used=652.3MB, alloc=4.6MB, time=88.73
memory used=656.1MB, alloc=4.6MB, time=89.20
memory used=659.9MB, alloc=4.6MB, time=89.68
memory used=663.7MB, alloc=4.6MB, time=90.15
memory used=667.5MB, alloc=4.6MB, time=90.68
memory used=671.4MB, alloc=4.6MB, time=91.19
memory used=675.2MB, alloc=4.6MB, time=91.73
memory used=679.0MB, alloc=4.6MB, time=92.22
memory used=682.8MB, alloc=4.6MB, time=92.75
memory used=686.6MB, alloc=4.6MB, time=93.26
x[1] = 1
y2[1] (analytic) = 1.8414709848078965066525023216303
y2[1] (numeric) = 1.8498042768418720946833952867053
absolute error = 0.008333292033975588030892965075
relative error = 0.45253452825078982541049111936971 %
Correct digits = 2
h = 0.005
y1[1] (analytic) = 1.540302305868139717400936607443
y1[1] (numeric) = 1.5389134215183316804714234404889
absolute error = 0.0013888843498080369295131669541
relative error = 0.090169594924110618853967354673302 %
Correct digits = 3
h = 0.005
TOP MAIN SOLVE Loop
memory used=690.4MB, alloc=4.6MB, time=93.78
NO POLE
NO POLE
memory used=694.2MB, alloc=4.6MB, time=94.28
memory used=698.1MB, alloc=4.6MB, time=94.78
memory used=701.9MB, alloc=4.6MB, time=95.28
memory used=705.7MB, alloc=4.6MB, time=95.79
memory used=709.5MB, alloc=4.6MB, time=96.33
memory used=713.3MB, alloc=4.6MB, time=96.83
memory used=717.1MB, alloc=4.6MB, time=97.33
memory used=720.9MB, alloc=4.6MB, time=97.80
memory used=724.8MB, alloc=4.6MB, time=98.31
memory used=728.6MB, alloc=4.6MB, time=98.78
memory used=732.4MB, alloc=4.6MB, time=99.26
memory used=736.2MB, alloc=4.6MB, time=99.74
memory used=740.0MB, alloc=4.6MB, time=100.21
memory used=743.8MB, alloc=4.6MB, time=100.69
memory used=747.6MB, alloc=4.6MB, time=101.16
memory used=751.5MB, alloc=4.6MB, time=101.63
memory used=755.3MB, alloc=4.6MB, time=102.13
x[1] = 1.1
y2[1] (analytic) = 1.8912073600614353399518025778717
y2[1] (numeric) = 1.9046281773746817912017305080047
absolute error = 0.013420817313246451249927930133
relative error = 0.70964282376790664397068259203309 %
Correct digits = 2
h = 0.005
y1[1] (analytic) = 1.4535961214255773877713700517847
y1[1] (numeric) = 1.4511356312031493971694174512809
absolute error = 0.0024604902224279906019526005038
relative error = 0.16926917911798825247141841384614 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
memory used=759.1MB, alloc=4.6MB, time=102.61
NO POLE
NO POLE
memory used=762.9MB, alloc=4.6MB, time=103.13
memory used=766.7MB, alloc=4.6MB, time=103.61
memory used=770.5MB, alloc=4.6MB, time=104.08
memory used=774.4MB, alloc=4.6MB, time=104.55
memory used=778.2MB, alloc=4.6MB, time=105.02
memory used=782.0MB, alloc=4.6MB, time=105.50
memory used=785.8MB, alloc=4.6MB, time=105.98
memory used=789.6MB, alloc=4.6MB, time=106.44
memory used=793.4MB, alloc=4.6MB, time=106.91
memory used=797.2MB, alloc=4.6MB, time=107.39
memory used=801.1MB, alloc=4.6MB, time=107.86
memory used=804.9MB, alloc=4.6MB, time=108.36
memory used=808.7MB, alloc=4.6MB, time=108.86
memory used=812.5MB, alloc=4.6MB, time=109.34
memory used=816.3MB, alloc=4.6MB, time=109.81
memory used=820.1MB, alloc=4.6MB, time=110.32
memory used=823.9MB, alloc=4.6MB, time=110.79
x[1] = 1.2
y2[1] (analytic) = 1.9320390859672263496701344354948
y2[1] (numeric) = 1.9527748541344434811290759848071
absolute error = 0.0207357681672171314589415493123
relative error = 1.0732582129329073704249451385787 %
Correct digits = 1
h = 0.005
y1[1] (analytic) = 1.3623577544766735776383733556231
y1[1] (numeric) = 1.3582105813229841143492922830764
absolute error = 0.0041471731536894632890810725467
relative error = 0.30441146167825270688466162426795 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
memory used=827.8MB, alloc=4.6MB, time=111.29
NO POLE
NO POLE
memory used=831.6MB, alloc=4.6MB, time=111.76
memory used=835.4MB, alloc=4.6MB, time=112.26
memory used=839.2MB, alloc=4.6MB, time=112.73
memory used=843.0MB, alloc=4.6MB, time=113.20
memory used=846.8MB, alloc=4.6MB, time=113.68
memory used=850.6MB, alloc=4.6MB, time=114.19
memory used=854.5MB, alloc=4.6MB, time=114.69
memory used=858.3MB, alloc=4.6MB, time=115.16
memory used=862.1MB, alloc=4.6MB, time=115.64
memory used=865.9MB, alloc=4.6MB, time=116.13
memory used=869.7MB, alloc=4.6MB, time=116.61
memory used=873.5MB, alloc=4.6MB, time=117.12
memory used=877.3MB, alloc=4.6MB, time=117.59
memory used=881.2MB, alloc=4.6MB, time=118.11
memory used=885.0MB, alloc=4.6MB, time=118.58
memory used=888.8MB, alloc=4.6MB, time=119.06
memory used=892.6MB, alloc=4.6MB, time=119.53
memory used=896.4MB, alloc=4.6MB, time=120.00
x[1] = 1.3
y2[1] (analytic) = 1.9635581854171929647013486300396
y2[1] (numeric) = 1.9944987477139275494060033720492
absolute error = 0.0309405622967345847046547420096
relative error = 1.575739518519065952271452263182 %
Correct digits = 1
h = 0.005
y1[1] (analytic) = 1.2674988286245874069979841092929
y1[1] (numeric) = 1.2607949899120528327778453936851
absolute error = 0.0067038387125345742201387156078
relative error = 0.52890295131942425677390160557467 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=900.2MB, alloc=4.6MB, time=120.52
memory used=904.1MB, alloc=4.6MB, time=121.06
memory used=907.9MB, alloc=4.6MB, time=121.62
memory used=911.7MB, alloc=4.6MB, time=122.18
memory used=915.5MB, alloc=4.6MB, time=122.72
memory used=919.3MB, alloc=4.6MB, time=123.21
memory used=923.1MB, alloc=4.6MB, time=123.71
memory used=926.9MB, alloc=4.6MB, time=124.20
memory used=930.8MB, alloc=4.6MB, time=124.67
memory used=934.6MB, alloc=4.6MB, time=125.16
memory used=938.4MB, alloc=4.6MB, time=125.63
memory used=942.2MB, alloc=4.6MB, time=126.11
memory used=946.0MB, alloc=4.6MB, time=126.63
memory used=949.8MB, alloc=4.6MB, time=127.17
memory used=953.6MB, alloc=4.6MB, time=127.69
memory used=957.5MB, alloc=4.6MB, time=128.16
memory used=961.3MB, alloc=4.6MB, time=128.64
memory used=965.1MB, alloc=4.6MB, time=129.12
x[1] = 1.4
y2[1] (analytic) = 1.9854497299884601806594745788061
y2[1] (numeric) = 2.0302672721954696548806249278242
absolute error = 0.0448175422070094742211503490181
relative error = 2.2572992672682759124084250745691 %
Correct digits = 1
h = 0.005
y1[1] (analytic) = 1.1699671429002409386167480352036
y1[1] (numeric) = 1.1595095953981662847500395216948
absolute error = 0.0104575475020746538667085135088
relative error = 0.89383258030232844403527136075346 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
memory used=968.9MB, alloc=4.6MB, time=129.61
NO POLE
NO POLE
memory used=972.7MB, alloc=4.6MB, time=130.09
memory used=976.5MB, alloc=4.6MB, time=130.56
memory used=980.3MB, alloc=4.6MB, time=131.07
memory used=984.2MB, alloc=4.6MB, time=131.60
memory used=988.0MB, alloc=4.6MB, time=132.13
memory used=991.8MB, alloc=4.6MB, time=132.62
memory used=995.6MB, alloc=4.6MB, time=133.11
memory used=999.4MB, alloc=4.6MB, time=133.59
memory used=1003.2MB, alloc=4.6MB, time=134.07
memory used=1007.1MB, alloc=4.6MB, time=134.55
memory used=1010.9MB, alloc=4.6MB, time=135.03
memory used=1014.7MB, alloc=4.6MB, time=135.52
memory used=1018.5MB, alloc=4.6MB, time=136.02
memory used=1022.3MB, alloc=4.6MB, time=136.54
memory used=1026.1MB, alloc=4.6MB, time=137.07
memory used=1029.9MB, alloc=4.6MB, time=137.61
memory used=1033.8MB, alloc=4.6MB, time=138.15
x[1] = 1.5
y2[1] (analytic) = 1.9974949866040544309417233711415
y2[1] (numeric) = 2.0607739066039187827161629644859
absolute error = 0.0632789199998643517744395933444
relative error = 3.1679138332880114621748322377279 %
Correct digits = 1
h = 0.005
y1[1] (analytic) = 1.0707372016677029100881898514343
y1[1] (numeric) = 1.0549171965708819842952880045586
absolute error = 0.0158200050968209257929018468757
relative error = 1.4774871996770849810491870719738 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
memory used=1037.6MB, alloc=4.6MB, time=138.66
NO POLE
NO POLE
memory used=1041.4MB, alloc=4.6MB, time=139.21
memory used=1045.2MB, alloc=4.6MB, time=139.72
memory used=1049.0MB, alloc=4.6MB, time=140.25
memory used=1052.8MB, alloc=4.6MB, time=140.77
memory used=1056.6MB, alloc=4.6MB, time=141.28
memory used=1060.5MB, alloc=4.6MB, time=141.81
memory used=1064.3MB, alloc=4.6MB, time=142.35
memory used=1068.1MB, alloc=4.6MB, time=142.85
memory used=1071.9MB, alloc=4.6MB, time=143.39
memory used=1075.7MB, alloc=4.6MB, time=143.96
memory used=1079.5MB, alloc=4.6MB, time=144.63
memory used=1083.3MB, alloc=4.6MB, time=145.15
memory used=1087.2MB, alloc=4.6MB, time=145.63
memory used=1091.0MB, alloc=4.6MB, time=146.13
memory used=1094.8MB, alloc=4.6MB, time=146.62
memory used=1098.6MB, alloc=4.6MB, time=147.14
memory used=1102.4MB, alloc=4.6MB, time=147.62
x[1] = 1.6
y2[1] (analytic) = 1.9995736030415051643421138255462
y2[1] (numeric) = 2.0869502933431193136873146505928
absolute error = 0.0873766903016141493452008250466
relative error = 4.3697661425769717328258911299933 %
Correct digits = 1
h = 0.005
y1[1] (analytic) = 0.9708004776987112737942295370535
y1[1] (numeric) = 0.9474994327319815747394020001949
absolute error = 0.0233010449667296990548275368586
relative error = 2.4001888649627547373958504293638 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
memory used=1106.2MB, alloc=4.6MB, time=148.11
NO POLE
NO POLE
memory used=1110.0MB, alloc=4.6MB, time=148.62
memory used=1113.9MB, alloc=4.6MB, time=149.16
memory used=1117.7MB, alloc=4.6MB, time=149.69
memory used=1121.5MB, alloc=4.6MB, time=150.21
memory used=1125.3MB, alloc=4.6MB, time=150.73
memory used=1129.1MB, alloc=4.6MB, time=151.28
memory used=1132.9MB, alloc=4.6MB, time=151.83
memory used=1136.8MB, alloc=4.6MB, time=152.37
memory used=1140.6MB, alloc=4.6MB, time=152.91
memory used=1144.4MB, alloc=4.6MB, time=153.45
memory used=1148.2MB, alloc=4.6MB, time=154.00
memory used=1152.0MB, alloc=4.6MB, time=154.56
memory used=1155.8MB, alloc=4.6MB, time=155.08
memory used=1159.6MB, alloc=4.6MB, time=155.59
memory used=1163.5MB, alloc=4.6MB, time=156.10
memory used=1167.3MB, alloc=4.6MB, time=156.62
memory used=1171.1MB, alloc=4.6MB, time=157.16
x[1] = 1.7
y2[1] (analytic) = 1.9916648104524686153461333986479
y2[1] (numeric) = 2.1099773076743452509495120653963
absolute error = 0.1183124972218766356033786667484
relative error = 5.9403819659292103261023801948938 %
Correct digits = 1
h = 0.005
y1[1] (analytic) = 0.87115550570447531591235714266513
y1[1] (numeric) = 0.83763240517360789945409829600588
absolute error = 0.03352310053086741645825884665925
relative error = 3.848118999576128257297929822869 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
memory used=1174.9MB, alloc=4.6MB, time=157.71
NO POLE
NO POLE
memory used=1178.7MB, alloc=4.6MB, time=158.25
memory used=1182.5MB, alloc=4.6MB, time=158.80
memory used=1186.3MB, alloc=4.6MB, time=159.34
memory used=1190.2MB, alloc=4.6MB, time=159.88
memory used=1194.0MB, alloc=4.6MB, time=160.44
memory used=1197.8MB, alloc=4.6MB, time=160.98
memory used=1201.6MB, alloc=4.6MB, time=161.53
memory used=1205.4MB, alloc=4.6MB, time=162.06
memory used=1209.2MB, alloc=4.6MB, time=162.59
memory used=1213.0MB, alloc=4.6MB, time=163.12
memory used=1216.9MB, alloc=4.6MB, time=163.66
memory used=1220.7MB, alloc=4.6MB, time=164.20
memory used=1224.5MB, alloc=4.6MB, time=164.72
memory used=1228.3MB, alloc=4.6MB, time=165.29
memory used=1232.1MB, alloc=4.6MB, time=165.86
memory used=1235.9MB, alloc=4.6MB, time=166.40
memory used=1239.8MB, alloc=4.6MB, time=166.96
x[1] = 1.8
y2[1] (analytic) = 1.9738476308781951865323731788434
y2[1] (numeric) = 2.131295067497474052576081461465
absolute error = 0.1574474366192788660437082826216
relative error = 7.9766763227427072743256438120792 %
Correct digits = 1
h = 0.005
y1[1] (analytic) = 0.77279790530691294468332569346942
y1[1] (numeric) = 0.72556124445665915244844782428591
absolute error = 0.04723666085025379223487786918351
relative error = 6.1124209221936207488986057368415 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
memory used=1243.6MB, alloc=4.6MB, time=167.52
NO POLE
NO POLE
memory used=1247.4MB, alloc=4.6MB, time=168.08
memory used=1251.2MB, alloc=4.6MB, time=168.64
memory used=1255.0MB, alloc=4.6MB, time=169.21
memory used=1258.8MB, alloc=4.6MB, time=169.78
memory used=1262.6MB, alloc=4.6MB, time=170.34
memory used=1266.5MB, alloc=4.6MB, time=170.91
memory used=1270.3MB, alloc=4.6MB, time=171.47
Complex estimate of poles used
memory used=1274.1MB, alloc=4.6MB, time=172.02
memory used=1277.9MB, alloc=4.6MB, time=172.58
memory used=1281.7MB, alloc=4.6MB, time=173.15
memory used=1285.5MB, alloc=4.6MB, time=173.72
memory used=1289.3MB, alloc=4.6MB, time=174.29
memory used=1293.2MB, alloc=4.6MB, time=174.85
memory used=1297.0MB, alloc=4.6MB, time=175.42
memory used=1300.8MB, alloc=4.6MB, time=175.98
memory used=1304.6MB, alloc=4.6MB, time=176.54
memory used=1308.4MB, alloc=4.6MB, time=177.10
x[1] = 1.9
y2[1] (analytic) = 1.946300087687414488489709611635
y2[1] (numeric) = 2.1526118569636457243295280258298
absolute error = 0.2063117692762312358398184141948
relative error = 10.600203462014431972459929143437 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.67671043313649657772116630491969
y1[1] (numeric) = 0.61137373081375278685030980091392
absolute error = 0.06533670232274379087085650400577
relative error = 9.6550458103495773593782441458901 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
memory used=1312.2MB, alloc=4.6MB, time=177.65
NO POLE
NO POLE
memory used=1316.0MB, alloc=4.6MB, time=178.20
memory used=1319.9MB, alloc=4.6MB, time=178.71
memory used=1323.7MB, alloc=4.6MB, time=179.25
memory used=1327.5MB, alloc=4.6MB, time=179.79
memory used=1331.3MB, alloc=4.6MB, time=180.32
memory used=1335.1MB, alloc=4.6MB, time=180.87
memory used=1338.9MB, alloc=4.6MB, time=181.39
memory used=1342.8MB, alloc=4.6MB, time=181.91
memory used=1346.6MB, alloc=4.6MB, time=182.42
memory used=1350.4MB, alloc=4.6MB, time=182.93
memory used=1354.2MB, alloc=4.6MB, time=183.47
memory used=1358.0MB, alloc=4.6MB, time=184.00
memory used=1361.8MB, alloc=4.6MB, time=184.54
memory used=1365.6MB, alloc=4.6MB, time=185.08
memory used=1369.5MB, alloc=4.6MB, time=185.61
memory used=1373.3MB, alloc=4.6MB, time=186.14
memory used=1377.1MB, alloc=4.6MB, time=186.67
memory used=1380.9MB, alloc=4.6MB, time=187.20
x[1] = 2
y2[1] (analytic) = 1.9092974268256816953960198659117
y2[1] (numeric) = 2.1759119405327324641243715983104
absolute error = 0.2666145137070507687283517323987
relative error = 13.964011576253624572803688868895 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.58385316345285761300243177049924
y1[1] (numeric) = 0.49497307748304224132574374588341
absolute error = 0.08888008596981537167668802461583
relative error = 15.223020364261821260051621381543 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1384.7MB, alloc=4.6MB, time=187.73
memory used=1388.5MB, alloc=4.6MB, time=188.25
memory used=1392.3MB, alloc=4.6MB, time=188.77
memory used=1396.2MB, alloc=4.6MB, time=189.30
memory used=1400.0MB, alloc=4.6MB, time=189.84
memory used=1403.8MB, alloc=4.6MB, time=190.38
memory used=1407.6MB, alloc=4.6MB, time=190.92
memory used=1411.4MB, alloc=4.6MB, time=191.45
memory used=1415.2MB, alloc=4.6MB, time=191.96
memory used=1419.0MB, alloc=4.6MB, time=192.50
memory used=1422.9MB, alloc=4.6MB, time=193.02
memory used=1426.7MB, alloc=4.6MB, time=193.56
memory used=1430.5MB, alloc=4.6MB, time=194.09
memory used=1434.3MB, alloc=4.6MB, time=194.63
memory used=1438.1MB, alloc=4.6MB, time=195.17
memory used=1441.9MB, alloc=4.6MB, time=195.70
memory used=1445.7MB, alloc=4.6MB, time=196.23
memory used=1449.6MB, alloc=4.6MB, time=196.76
x[1] = 2.1
y2[1] (analytic) = 1.863209366648873770680759313269
y2[1] (numeric) = 2.2034622457311747004148366650633
absolute error = 0.3402528790823009297340773517943
relative error = 18.261655677175564173975460642911 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.49515389540014254837906147628083
y1[1] (numeric) = 0.37604998902260249545554151726841
absolute error = 0.11910390637754005292351995901242
relative error = 24.053916869883472687897821015391 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
memory used=1453.4MB, alloc=4.6MB, time=197.29
NO POLE
NO POLE
memory used=1457.2MB, alloc=4.6MB, time=197.81
memory used=1461.0MB, alloc=4.6MB, time=198.34
memory used=1464.8MB, alloc=4.6MB, time=198.86
memory used=1468.6MB, alloc=4.6MB, time=199.39
memory used=1472.5MB, alloc=4.6MB, time=199.92
memory used=1476.3MB, alloc=4.6MB, time=200.45
memory used=1480.1MB, alloc=4.6MB, time=200.98
memory used=1483.9MB, alloc=4.6MB, time=201.48
memory used=1487.7MB, alloc=4.6MB, time=202.01
memory used=1491.5MB, alloc=4.6MB, time=202.54
memory used=1495.3MB, alloc=4.6MB, time=203.08
memory used=1499.2MB, alloc=4.6MB, time=203.60
memory used=1503.0MB, alloc=4.6MB, time=204.13
memory used=1506.8MB, alloc=4.6MB, time=204.66
memory used=1510.6MB, alloc=4.6MB, time=205.20
memory used=1514.4MB, alloc=4.6MB, time=205.74
memory used=1518.2MB, alloc=4.6MB, time=206.26
x[1] = 2.2
y2[1] (analytic) = 1.8084964038195901843040369104161
y2[1] (numeric) = 2.2378178927977326678008056581302
absolute error = 0.4293214889781424834967687477141
relative error = 23.739139766681572113186576961722 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.41149888274465429147585738734507
y1[1] (numeric) = 0.2540541088175555749852327020067
absolute error = 0.15744477392709871649062468533837
relative error = 38.261288311880368876009944734444 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
memory used=1522.0MB, alloc=4.6MB, time=206.79
NO POLE
NO POLE
memory used=1525.9MB, alloc=4.6MB, time=207.33
memory used=1529.7MB, alloc=4.6MB, time=207.88
memory used=1533.5MB, alloc=4.6MB, time=208.43
memory used=1537.3MB, alloc=4.6MB, time=208.95
memory used=1541.1MB, alloc=4.6MB, time=209.48
memory used=1544.9MB, alloc=4.6MB, time=210.02
memory used=1548.7MB, alloc=4.6MB, time=210.56
memory used=1552.6MB, alloc=4.6MB, time=211.09
memory used=1556.4MB, alloc=4.6MB, time=211.62
memory used=1560.2MB, alloc=4.6MB, time=212.14
memory used=1564.0MB, alloc=4.6MB, time=212.66
memory used=1567.8MB, alloc=4.6MB, time=213.21
memory used=1571.6MB, alloc=4.6MB, time=213.75
memory used=1575.5MB, alloc=4.6MB, time=214.28
memory used=1579.3MB, alloc=4.6MB, time=214.82
memory used=1583.1MB, alloc=4.6MB, time=215.35
memory used=1586.9MB, alloc=4.6MB, time=215.88
x[1] = 2.3
y2[1] (analytic) = 1.7457052121767201773854062116435
y2[1] (numeric) = 2.2818265473507620543469288513187
absolute error = 0.5361213351740418769615226396752
relative error = 30.710874403906492159704325509764 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.33372397872017580668211942883398
y1[1] (numeric) = 0.12816497225833256430670850566467
absolute error = 0.20555900646184324237541092316931
relative error = 61.595515926112818502515449047823 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
memory used=1590.7MB, alloc=4.6MB, time=216.41
NO POLE
NO POLE
memory used=1594.5MB, alloc=4.6MB, time=216.93
memory used=1598.3MB, alloc=4.6MB, time=217.47
memory used=1602.2MB, alloc=4.6MB, time=218.01
memory used=1606.0MB, alloc=4.6MB, time=218.56
memory used=1609.8MB, alloc=4.6MB, time=219.09
memory used=1613.6MB, alloc=4.6MB, time=219.63
memory used=1617.4MB, alloc=4.6MB, time=220.18
memory used=1621.2MB, alloc=4.6MB, time=220.72
memory used=1625.0MB, alloc=4.6MB, time=221.25
memory used=1628.9MB, alloc=4.6MB, time=221.77
memory used=1632.7MB, alloc=4.6MB, time=222.29
memory used=1636.5MB, alloc=4.6MB, time=222.81
memory used=1640.3MB, alloc=4.6MB, time=223.34
memory used=1644.1MB, alloc=4.6MB, time=223.87
memory used=1647.9MB, alloc=4.6MB, time=224.40
memory used=1651.7MB, alloc=4.6MB, time=224.92
memory used=1655.6MB, alloc=4.6MB, time=225.48
x[1] = 2.4
y2[1] (analytic) = 1.6754631805511509265657715253413
y2[1] (numeric) = 2.3386315678883739011068136037071
absolute error = 0.6631683873372229745410420783658
relative error = 39.581197309216358835499440192757 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.26260628445875450039117777266522
y1[1] (numeric) = -0.0027374153488743420995704993010285
absolute error = 0.26534369980762884249074827196625
relative error = 101.04240283301532578363873363919 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
memory used=1659.4MB, alloc=4.6MB, time=226.00
NO POLE
NO POLE
memory used=1663.2MB, alloc=4.6MB, time=226.52
memory used=1667.0MB, alloc=4.6MB, time=227.03
memory used=1670.8MB, alloc=4.6MB, time=227.57
memory used=1674.6MB, alloc=4.6MB, time=228.09
memory used=1678.5MB, alloc=4.6MB, time=228.61
memory used=1682.3MB, alloc=4.6MB, time=229.15
memory used=1686.1MB, alloc=4.6MB, time=229.68
memory used=1689.9MB, alloc=4.6MB, time=230.20
memory used=1693.7MB, alloc=4.6MB, time=230.71
memory used=1697.5MB, alloc=4.6MB, time=231.26
memory used=1701.3MB, alloc=4.6MB, time=231.79
memory used=1705.2MB, alloc=4.6MB, time=232.32
memory used=1709.0MB, alloc=4.6MB, time=232.86
memory used=1712.8MB, alloc=4.6MB, time=233.39
memory used=1716.6MB, alloc=4.6MB, time=233.92
memory used=1720.4MB, alloc=4.6MB, time=234.45
memory used=1724.2MB, alloc=4.6MB, time=234.97
x[1] = 2.5
y2[1] (analytic) = 1.5984721441039564940518547021862
y2[1] (numeric) = 2.4116739130543854545566845055513
absolute error = 0.8132017689504289605048298033651
relative error = 50.873690351750193253311621938262 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.19885638445306628516649720953265
y1[1] (numeric) = -0.14010225393814322255434410881818
absolute error = 0.33895863839120950772084131835083
relative error = 170.45398835118109900862485023788 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
memory used=1728.0MB, alloc=4.6MB, time=235.49
NO POLE
NO POLE
memory used=1731.9MB, alloc=4.6MB, time=236.00
memory used=1735.7MB, alloc=4.6MB, time=236.51
memory used=1739.5MB, alloc=4.6MB, time=237.04
memory used=1743.3MB, alloc=4.6MB, time=237.57
memory used=1747.1MB, alloc=4.6MB, time=238.09
memory used=1750.9MB, alloc=4.6MB, time=238.61
memory used=1754.7MB, alloc=4.6MB, time=239.15
memory used=1758.6MB, alloc=4.6MB, time=239.67
memory used=1762.4MB, alloc=4.6MB, time=240.19
memory used=1766.2MB, alloc=4.6MB, time=240.71
memory used=1770.0MB, alloc=4.6MB, time=241.23
memory used=1773.8MB, alloc=4.6MB, time=241.74
memory used=1777.6MB, alloc=4.6MB, time=242.27
memory used=1781.4MB, alloc=4.6MB, time=242.81
memory used=1785.3MB, alloc=4.6MB, time=243.34
memory used=1789.1MB, alloc=4.6MB, time=243.85
memory used=1792.9MB, alloc=4.6MB, time=244.39
memory used=1796.7MB, alloc=4.6MB, time=244.91
x[1] = 2.6
y2[1] (analytic) = 1.5155013718214642352577269352094
y2[1] (numeric) = 2.5046927638760672042690130863228
absolute error = 0.9891913920546029690112861511134
relative error = 65.271560319718143309428095465909 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.1431112466310527662022978483548
y1[1] (numeric) = -0.28573775073692027952997982990124
absolute error = 0.42884899736797304573227767825604
relative error = 299.66128271774828367062001119372 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1800.5MB, alloc=4.6MB, time=245.42
memory used=1804.3MB, alloc=4.6MB, time=245.94
memory used=1808.2MB, alloc=4.6MB, time=246.46
memory used=1812.0MB, alloc=4.6MB, time=246.99
memory used=1815.8MB, alloc=4.6MB, time=247.52
memory used=1819.6MB, alloc=4.6MB, time=248.05
memory used=1823.4MB, alloc=4.6MB, time=248.58
memory used=1827.2MB, alloc=4.6MB, time=249.12
memory used=1831.0MB, alloc=4.6MB, time=249.64
memory used=1834.9MB, alloc=4.6MB, time=250.15
memory used=1838.7MB, alloc=4.6MB, time=250.66
memory used=1842.5MB, alloc=4.6MB, time=251.18
memory used=1846.3MB, alloc=4.6MB, time=251.69
memory used=1850.1MB, alloc=4.6MB, time=252.22
memory used=1853.9MB, alloc=4.6MB, time=252.75
memory used=1857.7MB, alloc=4.6MB, time=253.27
memory used=1861.6MB, alloc=4.6MB, time=253.80
memory used=1865.4MB, alloc=4.6MB, time=254.33
x[1] = 2.7
y2[1] (analytic) = 1.4273798802338299345560530858579
y2[1] (numeric) = 2.6217248033089604264302821470715
absolute error = 1.1943449230751304918742290612136
relative error = 83.673935692541482566216736089153 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.09592785798293885201747271805667
y1[1] (numeric) = -0.44184091795126647699198342419184
absolute error = 0.53776877593420532900945614224851
relative error = 560.59708539499508821976520175968 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
memory used=1869.2MB, alloc=4.6MB, time=254.86
NO POLE
NO POLE
memory used=1873.0MB, alloc=4.6MB, time=255.36
memory used=1876.8MB, alloc=4.6MB, time=255.87
memory used=1880.6MB, alloc=4.6MB, time=256.39
memory used=1884.4MB, alloc=4.6MB, time=256.90
memory used=1888.3MB, alloc=4.6MB, time=257.42
memory used=1892.1MB, alloc=4.6MB, time=257.96
memory used=1895.9MB, alloc=4.6MB, time=258.50
memory used=1899.7MB, alloc=4.6MB, time=259.03
memory used=1903.5MB, alloc=4.6MB, time=259.56
memory used=1907.3MB, alloc=4.6MB, time=260.07
memory used=1911.2MB, alloc=4.6MB, time=260.57
memory used=1915.0MB, alloc=4.6MB, time=261.08
memory used=1918.8MB, alloc=4.6MB, time=261.61
memory used=1922.6MB, alloc=4.6MB, time=262.15
memory used=1926.4MB, alloc=4.6MB, time=262.69
memory used=1930.2MB, alloc=4.6MB, time=263.23
memory used=1934.0MB, alloc=4.6MB, time=263.76
x[1] = 2.8
y2[1] (analytic) = 1.3349881501559049195438537527124
y2[1] (numeric) = 2.767102079112201820989331787428
absolute error = 1.4321139289562969014454780347156
relative error = 107.27540381456189475824493971014 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.05777765933134184741321188263385
y1[1] (numeric) = -0.61102722826618798414751235891596
absolute error = 0.66880488759752983156072424154981
relative error = 1157.5492938578294017997570963418 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=1937.9MB, alloc=4.6MB, time=264.30
NO POLE
NO POLE
memory used=1941.7MB, alloc=4.6MB, time=264.84
memory used=1945.5MB, alloc=4.6MB, time=265.36
memory used=1949.3MB, alloc=4.6MB, time=265.88
memory used=1953.1MB, alloc=4.6MB, time=266.43
memory used=1956.9MB, alloc=4.6MB, time=266.96
memory used=1960.7MB, alloc=4.6MB, time=267.49
memory used=1964.6MB, alloc=4.6MB, time=268.03
memory used=1968.4MB, alloc=4.6MB, time=268.57
memory used=1972.2MB, alloc=4.6MB, time=269.10
memory used=1976.0MB, alloc=4.6MB, time=269.63
memory used=1979.8MB, alloc=4.6MB, time=270.16
memory used=1983.6MB, alloc=4.6MB, time=270.69
memory used=1987.4MB, alloc=4.6MB, time=271.21
memory used=1991.3MB, alloc=4.6MB, time=271.75
memory used=1995.1MB, alloc=4.6MB, time=272.29
memory used=1998.9MB, alloc=4.6MB, time=272.82
memory used=2002.7MB, alloc=4.6MB, time=273.36
x[1] = 2.9
y2[1] (analytic) = 1.2392493292139823281842569187396
y2[1] (numeric) = 2.945448356026962224044485359212
absolute error = 1.7061990268129798958602284404724
relative error = 137.68004441004372989953000764272 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.02904183485040947821889333065447
y1[1] (numeric) = -0.79635998197618618686002189360095
absolute error = 0.82540181682659566507891522425542
relative error = 2842.1131828554483727422827915628 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=2006.5MB, alloc=4.6MB, time=273.89
NO POLE
NO POLE
memory used=2010.3MB, alloc=4.6MB, time=274.43
memory used=2014.1MB, alloc=4.6MB, time=274.97
memory used=2018.0MB, alloc=4.6MB, time=275.51
memory used=2021.8MB, alloc=4.6MB, time=276.03
memory used=2025.6MB, alloc=4.6MB, time=276.57
memory used=2029.4MB, alloc=4.6MB, time=277.11
memory used=2033.2MB, alloc=4.6MB, time=277.64
memory used=2037.0MB, alloc=4.6MB, time=278.18
memory used=2040.9MB, alloc=4.6MB, time=278.72
memory used=2044.7MB, alloc=4.6MB, time=279.25
memory used=2048.5MB, alloc=4.6MB, time=279.79
memory used=2052.3MB, alloc=4.6MB, time=280.33
memory used=2056.1MB, alloc=4.6MB, time=280.86
memory used=2059.9MB, alloc=4.6MB, time=281.40
memory used=2063.7MB, alloc=4.6MB, time=281.94
memory used=2067.6MB, alloc=4.6MB, time=282.48
memory used=2071.4MB, alloc=4.6MB, time=283.02
x[1] = 3
y2[1] (analytic) = 1.1411200080598672221007448028081
y2[1] (numeric) = 3.1616738391436389436482046065955
absolute error = 2.0205538310837717215474598037874
relative error = 177.06760172570440699466467589906 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.01000750339955454272842720526874
y1[1] (numeric) = -1.0013792289889433675171153989108
absolute error = 1.0113867323884979102455426041795
relative error = 10106.284175067250918837462556528 %
Correct digits = -2
h = 0.005
TOP MAIN SOLVE Loop
memory used=2075.2MB, alloc=4.6MB, time=283.56
NO POLE
NO POLE
memory used=2079.0MB, alloc=4.6MB, time=284.11
memory used=2082.8MB, alloc=4.6MB, time=284.68
memory used=2086.6MB, alloc=4.6MB, time=285.25
memory used=2090.4MB, alloc=4.6MB, time=285.82
memory used=2094.3MB, alloc=4.6MB, time=286.34
memory used=2098.1MB, alloc=4.6MB, time=286.86
memory used=2101.9MB, alloc=4.6MB, time=287.37
memory used=2105.7MB, alloc=4.6MB, time=287.88
memory used=2109.5MB, alloc=4.6MB, time=288.41
memory used=2113.3MB, alloc=4.6MB, time=288.94
memory used=2117.1MB, alloc=4.6MB, time=289.44
memory used=2121.0MB, alloc=4.6MB, time=289.97
memory used=2124.8MB, alloc=4.6MB, time=290.48
memory used=2128.6MB, alloc=4.6MB, time=291.00
memory used=2132.4MB, alloc=4.6MB, time=291.50
memory used=2136.2MB, alloc=4.6MB, time=292.02
memory used=2140.0MB, alloc=4.6MB, time=292.56
x[1] = 3.1
y2[1] (analytic) = 1.0415806624332905791946982715967
y2[1] (numeric) = 3.4209681219253508346559701178725
absolute error = 2.3793874594920602554612718462758
relative error = 228.44005705073766136735663270732 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.00086484972672053550762394545853
y1[1] (numeric) = -1.2301300757500328871799866471371
absolute error = 1.2309949254767534226876105925956
relative error = 142336.27963838540750860245717939 %
Correct digits = -3
h = 0.005
TOP MAIN SOLVE Loop
memory used=2143.9MB, alloc=4.6MB, time=293.09
NO POLE
NO POLE
memory used=2147.7MB, alloc=4.6MB, time=293.58
memory used=2151.5MB, alloc=4.6MB, time=294.07
memory used=2155.3MB, alloc=4.6MB, time=294.56
memory used=2159.1MB, alloc=4.6MB, time=295.04
memory used=2162.9MB, alloc=4.6MB, time=295.55
memory used=2166.7MB, alloc=4.6MB, time=296.05
memory used=2170.6MB, alloc=4.6MB, time=296.51
memory used=2174.4MB, alloc=4.6MB, time=296.99
memory used=2178.2MB, alloc=4.6MB, time=297.46
memory used=2182.0MB, alloc=4.6MB, time=297.97
memory used=2185.8MB, alloc=4.6MB, time=298.45
memory used=2189.6MB, alloc=4.6MB, time=298.92
Complex estimate of poles used
memory used=2193.4MB, alloc=4.6MB, time=299.39
Complex estimate of poles used
memory used=2197.3MB, alloc=4.6MB, time=299.87
Complex estimate of poles used
memory used=2201.1MB, alloc=4.6MB, time=300.35
Complex estimate of poles used
Complex estimate of poles used
memory used=2204.9MB, alloc=4.6MB, time=300.81
Complex estimate of poles used
memory used=2208.7MB, alloc=4.6MB, time=301.32
Complex estimate of poles used
x[1] = 3.2
y2[1] (analytic) = 0.9416258565724200908627825853809
y2[1] (numeric) = 3.7287911793147641261562949897672
absolute error = 2.7871653227423440352935124043863
relative error = 295.99498604337488235186537513765 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.00170522420524691533833927771642
y1[1] (numeric) = -1.4871901908709928872586789553961
absolute error = 1.4888954150762398025970182331125
relative error = 87313.762641590507457861305870699 %
Correct digits = -2
h = 0.005
TOP MAIN SOLVE Loop
memory used=2212.5MB, alloc=4.6MB, time=301.80
NO POLE
Complex estimate of poles used
Radius of convergence = 0.2492
Order of pole = 1.372
memory used=2216.3MB, alloc=4.6MB, time=302.28
memory used=2220.1MB, alloc=4.6MB, time=302.77
memory used=2224.0MB, alloc=4.6MB, time=303.25
memory used=2227.8MB, alloc=4.6MB, time=303.72
memory used=2231.6MB, alloc=4.6MB, time=304.19
memory used=2235.4MB, alloc=4.6MB, time=304.67
memory used=2239.2MB, alloc=4.6MB, time=305.14
memory used=2243.0MB, alloc=4.6MB, time=305.60
memory used=2246.9MB, alloc=4.6MB, time=306.08
memory used=2250.7MB, alloc=4.6MB, time=306.57
memory used=2254.5MB, alloc=4.6MB, time=307.05
Real estimate of pole used
memory used=2258.3MB, alloc=4.6MB, time=307.55
Real estimate of pole used
memory used=2262.1MB, alloc=4.6MB, time=308.02
Real estimate of pole used
memory used=2265.9MB, alloc=4.6MB, time=308.52
Real estimate of pole used
memory used=2269.7MB, alloc=4.6MB, time=309.00
Real estimate of pole used
memory used=2273.6MB, alloc=4.6MB, time=309.50
Real estimate of pole used
Real estimate of pole used
memory used=2277.4MB, alloc=4.6MB, time=309.98
Real estimate of pole used
x[1] = 3.3
y2[1] (analytic) = 0.84225430585675161798834572239752
y2[1] (numeric) = 4.0908621884023309903164846826801
absolute error = 3.2486078825455793723281389602826
relative error = 385.70392100768838319565227256793 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.01252023009113511606340894889715
y1[1] (numeric) = -1.7776963034304359214048644703975
absolute error = 1.7902165335215710374682734192946
relative error = 14298.591323725947839281777318723 %
Correct digits = -2
h = 0.005
TOP MAIN SOLVE Loop
memory used=2281.2MB, alloc=4.6MB, time=310.47
NO POLE
Real estimate of pole used
Radius of convergence = 14.52
Order of pole = 228.5
memory used=2285.0MB, alloc=4.6MB, time=310.96
memory used=2288.8MB, alloc=4.6MB, time=311.45
memory used=2292.6MB, alloc=4.6MB, time=311.94
memory used=2296.4MB, alloc=4.6MB, time=312.42
memory used=2300.3MB, alloc=4.6MB, time=312.90
memory used=2304.1MB, alloc=4.6MB, time=313.41
memory used=2307.9MB, alloc=4.6MB, time=313.88
memory used=2311.7MB, alloc=4.6MB, time=314.15
memory used=2315.5MB, alloc=4.6MB, time=314.35
memory used=2319.3MB, alloc=4.6MB, time=314.55
memory used=2323.1MB, alloc=4.6MB, time=314.74
memory used=2327.0MB, alloc=4.6MB, time=314.94
memory used=2330.8MB, alloc=4.6MB, time=315.14
memory used=2334.6MB, alloc=4.6MB, time=315.35
memory used=2338.4MB, alloc=4.6MB, time=315.55
memory used=2342.2MB, alloc=4.6MB, time=315.75
memory used=2346.0MB, alloc=4.6MB, time=315.94
memory used=2349.8MB, alloc=4.6MB, time=316.14
x[1] = 3.4
y2[1] (analytic) = 0.74445889797316868075009757063626
y2[1] (numeric) = 4.5131459159977546616023466784255
absolute error = 3.7686870180245859808522491077892
relative error = 506.23171115088406498103092414917 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.03320180742053898571779846023431
y1[1] (numeric) = -2.1073694640532291547250415548768
absolute error = 2.1405712714737681404428400151111
relative error = 6447.1528443044589751656410924808 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2353.7MB, alloc=4.6MB, time=316.34
memory used=2357.5MB, alloc=4.6MB, time=316.55
memory used=2361.3MB, alloc=4.6MB, time=316.75
memory used=2365.1MB, alloc=4.6MB, time=316.95
memory used=2368.9MB, alloc=4.6MB, time=317.14
memory used=2372.7MB, alloc=4.6MB, time=317.35
memory used=2376.6MB, alloc=4.6MB, time=317.55
memory used=2380.4MB, alloc=4.6MB, time=317.75
memory used=2384.2MB, alloc=4.6MB, time=317.95
memory used=2388.0MB, alloc=4.6MB, time=318.15
memory used=2391.8MB, alloc=4.6MB, time=318.34
memory used=2395.6MB, alloc=4.6MB, time=318.54
memory used=2399.4MB, alloc=4.6MB, time=318.74
memory used=2403.3MB, alloc=4.6MB, time=318.94
memory used=2407.1MB, alloc=4.6MB, time=319.14
memory used=2410.9MB, alloc=4.6MB, time=319.34
memory used=2414.7MB, alloc=4.6MB, time=319.54
memory used=2418.5MB, alloc=4.6MB, time=319.73
x[1] = 3.5
y2[1] (analytic) = 0.64921677231038015187963119995636
y2[1] (numeric) = 5.0018363638530687706216126606061
absolute error = 4.3526195915426886187419814606497
relative error = 670.44164248143774550294596739409 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.06354331270920366230134237332824
y1[1] (numeric) = -2.4825388104238625778104760500812
absolute error = 2.5460821231330662401118184234094
relative error = 4006.8451180454269053383711143536 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=2422.3MB, alloc=4.6MB, time=319.93
NO POLE
NO POLE
memory used=2426.1MB, alloc=4.6MB, time=320.13
memory used=2430.0MB, alloc=4.6MB, time=320.32
memory used=2433.8MB, alloc=4.6MB, time=320.52
memory used=2437.6MB, alloc=4.6MB, time=320.72
memory used=2441.4MB, alloc=4.6MB, time=320.92
memory used=2445.2MB, alloc=4.6MB, time=321.12
memory used=2449.0MB, alloc=4.6MB, time=321.32
memory used=2452.8MB, alloc=4.6MB, time=321.52
memory used=2456.7MB, alloc=4.6MB, time=321.72
memory used=2460.5MB, alloc=4.6MB, time=321.92
memory used=2464.3MB, alloc=4.6MB, time=322.12
memory used=2468.1MB, alloc=4.6MB, time=322.32
memory used=2471.9MB, alloc=4.6MB, time=322.52
memory used=2475.7MB, alloc=4.6MB, time=322.72
memory used=2479.6MB, alloc=4.6MB, time=322.92
memory used=2483.4MB, alloc=4.6MB, time=323.12
memory used=2487.2MB, alloc=4.6MB, time=323.32
x[1] = 3.6
y2[1] (analytic) = 0.55747955670514761573327265250731
y2[1] (numeric) = 5.5633373079765432807168462753146
absolute error = 5.0058577512713956649835736228073
relative error = 897.94463152287516444730375075226 %
Correct digits = 0
h = 0.005
y1[1] (analytic) = 0.10324158366585299412970827473406
y1[1] (numeric) = -2.9101635452981772644937359703567
absolute error = 3.0134051289640302586234442450908
relative error = 2918.7901056584718850492959747467 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=2491.0MB, alloc=4.6MB, time=323.52
NO POLE
NO POLE
memory used=2494.8MB, alloc=4.6MB, time=323.72
memory used=2498.6MB, alloc=4.6MB, time=323.92
memory used=2502.4MB, alloc=4.6MB, time=324.11
memory used=2506.3MB, alloc=4.6MB, time=324.32
memory used=2510.1MB, alloc=4.6MB, time=324.53
memory used=2513.9MB, alloc=4.6MB, time=324.73
memory used=2517.7MB, alloc=4.6MB, time=324.93
memory used=2521.5MB, alloc=4.6MB, time=325.14
memory used=2525.3MB, alloc=4.6MB, time=325.35
memory used=2529.1MB, alloc=4.6MB, time=325.55
memory used=2533.0MB, alloc=4.6MB, time=325.75
memory used=2536.8MB, alloc=4.6MB, time=325.94
memory used=2540.6MB, alloc=4.6MB, time=326.14
memory used=2544.4MB, alloc=4.6MB, time=326.34
memory used=2548.2MB, alloc=4.6MB, time=326.54
memory used=2552.0MB, alloc=4.6MB, time=326.74
memory used=2555.8MB, alloc=4.6MB, time=326.94
x[1] = 3.7
y2[1] (analytic) = 0.47016385909150678678922237429879
y2[1] (numeric) = 6.2042393082068037259354828737161
absolute error = 5.7340754491152969391462604994173
relative error = 1219.5908592794004040715971946377 %
Correct digits = -1
h = 0.005
y1[1] (analytic) = 0.1518999682895918411643298936456
y1[1] (numeric) = -3.3978527957587070263986169722329
absolute error = 3.5497527640482988675629468658785
relative error = 2336.9015833372805886161469655273 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=2559.7MB, alloc=4.6MB, time=327.14
NO POLE
NO POLE
memory used=2563.5MB, alloc=4.6MB, time=327.35
memory used=2567.3MB, alloc=4.6MB, time=327.55
memory used=2571.1MB, alloc=4.6MB, time=327.74
memory used=2574.9MB, alloc=4.6MB, time=327.94
memory used=2578.7MB, alloc=4.6MB, time=328.14
memory used=2582.5MB, alloc=4.6MB, time=328.34
memory used=2586.4MB, alloc=4.6MB, time=328.54
memory used=2590.2MB, alloc=4.6MB, time=328.74
memory used=2594.0MB, alloc=4.6MB, time=328.94
memory used=2597.8MB, alloc=4.6MB, time=329.14
memory used=2601.6MB, alloc=4.6MB, time=329.35
memory used=2605.4MB, alloc=4.6MB, time=329.55
memory used=2609.3MB, alloc=4.6MB, time=329.75
memory used=2613.1MB, alloc=4.6MB, time=329.95
memory used=2616.9MB, alloc=4.6MB, time=330.15
memory used=2620.7MB, alloc=4.6MB, time=330.36
memory used=2624.5MB, alloc=4.6MB, time=330.56
x[1] = 3.8
y2[1] (analytic) = 0.38814210905728092426641391388112
y2[1] (numeric) = 6.931292697757618869653334206161
absolute error = 6.5431505887003379453869202922799
relative error = 1685.7615898961166632312575487954 %
Correct digits = -1
h = 0.005
y1[1] (analytic) = 0.20903228808558330000343182564927
y1[1] (numeric) = -3.9538829768053576185462741737667
absolute error = 4.162915264890940918549705999416
relative error = 1991.5178190971790199272777265534 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=2628.3MB, alloc=4.6MB, time=330.76
NO POLE
NO POLE
memory used=2632.1MB, alloc=4.6MB, time=330.97
memory used=2636.0MB, alloc=4.6MB, time=331.16
memory used=2639.8MB, alloc=4.6MB, time=331.36
memory used=2643.6MB, alloc=4.6MB, time=331.56
memory used=2647.4MB, alloc=4.6MB, time=331.76
memory used=2651.2MB, alloc=4.6MB, time=331.96
memory used=2655.0MB, alloc=4.6MB, time=332.16
memory used=2658.8MB, alloc=4.6MB, time=332.37
memory used=2662.7MB, alloc=4.6MB, time=332.57
memory used=2666.5MB, alloc=4.6MB, time=332.77
memory used=2670.3MB, alloc=4.6MB, time=332.97
memory used=2674.1MB, alloc=4.6MB, time=333.17
memory used=2677.9MB, alloc=4.6MB, time=333.36
memory used=2681.7MB, alloc=4.6MB, time=333.56
memory used=2685.5MB, alloc=4.6MB, time=333.76
memory used=2689.4MB, alloc=4.6MB, time=333.96
memory used=2693.2MB, alloc=4.6MB, time=334.16
x[1] = 3.9
y2[1] (analytic) = 0.31223384081602618190911187462131
y2[1] (numeric) = 7.7513759895868857333086019791367
absolute error = 7.4391421487708595513994901045154
relative error = 2382.5547318409142139311994057303 %
Correct digits = -1
h = 0.005
y1[1] (analytic) = 0.27406769579985987062766951538565
y1[1] (numeric) = -4.5872122297554757702896292248173
absolute error = 4.861279925555335640917298740203
relative error = 1773.7515219981723901484989231269 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=2697.0MB, alloc=4.6MB, time=334.36
NO POLE
NO POLE
memory used=2700.8MB, alloc=4.6MB, time=334.56
memory used=2704.6MB, alloc=4.6MB, time=334.76
memory used=2708.4MB, alloc=4.6MB, time=334.96
memory used=2712.3MB, alloc=4.6MB, time=335.15
memory used=2716.1MB, alloc=4.6MB, time=335.35
memory used=2719.9MB, alloc=4.6MB, time=335.55
memory used=2723.7MB, alloc=4.6MB, time=335.75
memory used=2727.5MB, alloc=4.6MB, time=335.95
memory used=2731.3MB, alloc=4.6MB, time=336.16
memory used=2735.1MB, alloc=4.6MB, time=336.36
memory used=2739.0MB, alloc=4.6MB, time=336.56
memory used=2742.8MB, alloc=4.6MB, time=336.76
memory used=2746.6MB, alloc=4.6MB, time=336.97
memory used=2750.4MB, alloc=4.6MB, time=337.17
memory used=2754.2MB, alloc=4.6MB, time=337.38
memory used=2758.0MB, alloc=4.6MB, time=337.58
memory used=2761.8MB, alloc=4.6MB, time=337.78
x[1] = 4
y2[1] (analytic) = 0.24319750469207174862736090548817
y2[1] (numeric) = 8.6714590570026446063177454050553
absolute error = 8.4282615523105728576903844995671
relative error = 3465.6036306713531115886142346809 %
Correct digits = -1
h = 0.005
y1[1] (analytic) = 0.34635637913638808536083181690225
y1[1] (numeric) = -5.3074914456962488865249496092892
absolute error = 5.6538478248326369718857814261914
relative error = 1632.3787189743853082720165154853 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=2765.7MB, alloc=4.6MB, time=337.98
NO POLE
NO POLE
memory used=2769.5MB, alloc=4.6MB, time=338.18
memory used=2773.3MB, alloc=4.6MB, time=338.37
memory used=2777.1MB, alloc=4.6MB, time=338.57
memory used=2780.9MB, alloc=4.6MB, time=338.77
memory used=2784.7MB, alloc=4.6MB, time=338.97
memory used=2788.5MB, alloc=4.6MB, time=339.17
memory used=2792.4MB, alloc=4.6MB, time=339.37
memory used=2796.2MB, alloc=4.6MB, time=339.57
memory used=2800.0MB, alloc=4.6MB, time=339.77
memory used=2803.8MB, alloc=4.6MB, time=339.97
memory used=2807.6MB, alloc=4.6MB, time=340.17
memory used=2811.4MB, alloc=4.6MB, time=340.37
memory used=2815.3MB, alloc=4.6MB, time=340.56
memory used=2819.1MB, alloc=4.6MB, time=340.76
memory used=2822.9MB, alloc=4.6MB, time=340.96
memory used=2826.7MB, alloc=4.6MB, time=341.16
memory used=2830.5MB, alloc=4.6MB, time=341.36
x[1] = 4.1
y2[1] (analytic) = 0.18172288893558949573496297564155
y2[1] (numeric) = 9.6985603597358659195505557512587
absolute error = 9.5168374708002764238155927756172
relative error = 5237.0053803037756006929730225132 %
Correct digits = -1
h = 0.005
y1[1] (analytic) = 0.42517605346673108846497132034021
y1[1] (numeric) = -6.1250713157212725384441442581647
absolute error = 6.5502473691880036269091155785049
relative error = 1540.5964930949582068381072279077 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=2834.3MB, alloc=4.6MB, time=341.56
NO POLE
NO POLE
memory used=2838.1MB, alloc=4.6MB, time=341.76
memory used=2842.0MB, alloc=4.6MB, time=341.95
memory used=2845.8MB, alloc=4.6MB, time=342.16
memory used=2849.6MB, alloc=4.6MB, time=342.36
memory used=2853.4MB, alloc=4.6MB, time=342.56
memory used=2857.2MB, alloc=4.6MB, time=342.77
memory used=2861.0MB, alloc=4.6MB, time=342.98
memory used=2864.8MB, alloc=4.6MB, time=343.17
memory used=2868.7MB, alloc=4.6MB, time=343.38
memory used=2872.5MB, alloc=4.6MB, time=343.57
memory used=2876.3MB, alloc=4.6MB, time=343.77
memory used=2880.1MB, alloc=4.6MB, time=343.98
memory used=2883.9MB, alloc=4.6MB, time=344.19
memory used=2887.7MB, alloc=4.6MB, time=344.39
memory used=2891.5MB, alloc=4.6MB, time=344.59
memory used=2895.4MB, alloc=4.6MB, time=344.79
memory used=2899.2MB, alloc=4.6MB, time=344.99
x[1] = 4.2
y2[1] (analytic) = 0.12842422758641193998142290209118
y2[1] (numeric) = 10.839697393657395904485668049094
absolute error = 10.711273166070983964504245147003
relative error = 8340.539294942429889120103718451 %
Correct digits = -1
h = 0.005
y1[1] (analytic) = 0.50973917865930042234445511862287
y1[1] (numeric) = -7.0510047722111584743972432876165
absolute error = 7.5607439508704588967416984062394
relative error = 1483.2573730660617912445181394133 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=2903.0MB, alloc=4.6MB, time=345.20
NO POLE
NO POLE
memory used=2906.8MB, alloc=4.6MB, time=345.40
memory used=2910.6MB, alloc=4.6MB, time=345.60
memory used=2914.4MB, alloc=4.6MB, time=345.80
memory used=2918.2MB, alloc=4.6MB, time=346.00
memory used=2922.1MB, alloc=4.6MB, time=346.19
memory used=2925.9MB, alloc=4.6MB, time=346.39
memory used=2929.7MB, alloc=4.6MB, time=346.59
memory used=2933.5MB, alloc=4.6MB, time=346.79
memory used=2937.3MB, alloc=4.6MB, time=346.99
memory used=2941.1MB, alloc=4.6MB, time=347.20
memory used=2945.0MB, alloc=4.6MB, time=347.40
memory used=2948.8MB, alloc=4.6MB, time=347.60
memory used=2952.6MB, alloc=4.6MB, time=347.80
memory used=2956.4MB, alloc=4.6MB, time=348.00
memory used=2960.2MB, alloc=4.6MB, time=348.20
memory used=2964.0MB, alloc=4.6MB, time=348.39
memory used=2967.8MB, alloc=4.6MB, time=348.59
x[1] = 4.3
y2[1] (analytic) = 0.08383406325054501596829063971536
y2[1] (numeric) = 12.101829442304960602054934089456
absolute error = 12.017995379054415586086643449741
relative error = 14335.456153589555449493589037509 %
Correct digits = -2
h = 0.005
y1[1] (analytic) = 0.59920082792002470309323760366397
y1[1] (numeric) = -8.0970440982934789284898010976385
absolute error = 8.6962449262135036315830387013025
relative error = 1451.307228062473721457425176378 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=2971.7MB, alloc=4.6MB, time=348.81
NO POLE
NO POLE
memory used=2975.5MB, alloc=4.6MB, time=349.01
memory used=2979.3MB, alloc=4.6MB, time=349.22
memory used=2983.1MB, alloc=4.6MB, time=349.43
memory used=2986.9MB, alloc=4.6MB, time=349.62
memory used=2990.7MB, alloc=4.6MB, time=349.82
memory used=2994.5MB, alloc=4.6MB, time=350.03
memory used=2998.4MB, alloc=4.6MB, time=350.23
memory used=3002.2MB, alloc=4.6MB, time=350.43
memory used=3006.0MB, alloc=4.6MB, time=350.63
memory used=3009.8MB, alloc=4.6MB, time=350.83
memory used=3013.6MB, alloc=4.6MB, time=351.04
memory used=3017.4MB, alloc=4.6MB, time=351.25
memory used=3021.2MB, alloc=4.6MB, time=351.45
memory used=3025.1MB, alloc=4.6MB, time=351.64
memory used=3028.9MB, alloc=4.6MB, time=351.84
memory used=3032.7MB, alloc=4.6MB, time=352.05
memory used=3036.5MB, alloc=4.6MB, time=352.25
x[1] = 4.4
y2[1] (analytic) = 0.04839792611048404596460766661961
y2[1] (numeric) = 13.491791601368619317155102479935
absolute error = 13.443393675258135271190494813315
relative error = 27776.796973839759445720098849673 %
Correct digits = -2
h = 0.005
y1[1] (analytic) = 0.69266713002158031688086025778229
y1[1] (numeric) = -9.2756318851415106433440816817333
absolute error = 9.9682990151630909602249419395156
relative error = 1439.1182406551505747935952050695 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=3040.3MB, alloc=4.6MB, time=352.45
NO POLE
NO POLE
memory used=3044.1MB, alloc=4.6MB, time=352.64
memory used=3048.0MB, alloc=4.6MB, time=352.84
memory used=3051.8MB, alloc=4.6MB, time=353.04
memory used=3055.6MB, alloc=4.6MB, time=353.24
memory used=3059.4MB, alloc=4.6MB, time=353.44
memory used=3063.2MB, alloc=4.6MB, time=353.64
memory used=3067.0MB, alloc=4.6MB, time=353.84
memory used=3070.8MB, alloc=4.6MB, time=354.04
memory used=3074.7MB, alloc=4.6MB, time=354.24
memory used=3078.5MB, alloc=4.6MB, time=354.44
memory used=3082.3MB, alloc=4.6MB, time=354.64
memory used=3086.1MB, alloc=4.6MB, time=354.86
memory used=3089.9MB, alloc=4.6MB, time=355.05
memory used=3093.7MB, alloc=4.6MB, time=355.25
memory used=3097.5MB, alloc=4.6MB, time=355.45
memory used=3101.4MB, alloc=4.6MB, time=355.65
memory used=3105.2MB, alloc=4.6MB, time=355.85
x[1] = 4.5
y2[1] (analytic) = 0.02246988233490294461086498550137
y2[1] (numeric) = 15.016218933262421117543703167889
absolute error = 14.993749050927518172932838182388
relative error = 66728.204569355531925799177619662 %
Correct digits = -2
h = 0.005
y1[1] (analytic) = 0.78920420056922029401951817520617
y1[1] (numeric) = -10.599884908243251210505281089932
absolute error = 11.389089108812471504524799265138
relative error = 1443.1105537195561513250493292834 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=3109.0MB, alloc=4.6MB, time=356.05
NO POLE
NO POLE
memory used=3112.8MB, alloc=4.6MB, time=356.25
memory used=3116.6MB, alloc=4.6MB, time=356.45
memory used=3120.4MB, alloc=4.6MB, time=356.65
memory used=3124.2MB, alloc=4.6MB, time=356.85
memory used=3128.1MB, alloc=4.6MB, time=357.05
memory used=3131.9MB, alloc=4.6MB, time=357.24
memory used=3135.7MB, alloc=4.6MB, time=357.44
memory used=3139.5MB, alloc=4.6MB, time=357.64
memory used=3143.3MB, alloc=4.6MB, time=357.84
memory used=3147.1MB, alloc=4.6MB, time=358.06
memory used=3151.0MB, alloc=4.6MB, time=358.26
memory used=3154.8MB, alloc=4.6MB, time=358.45
memory used=3158.6MB, alloc=4.6MB, time=358.66
memory used=3162.4MB, alloc=4.6MB, time=358.86
memory used=3166.2MB, alloc=4.6MB, time=359.07
memory used=3170.0MB, alloc=4.6MB, time=359.26
memory used=3173.8MB, alloc=4.6MB, time=359.47
x[1] = 4.6
y2[1] (analytic) = 0.00630899636653554386189534009117
y2[1] (numeric) = 16.681459487946649243297685099114
absolute error = 16.675150491580113699435789759023
relative error = 264307.49873354152940780445442824 %
Correct digits = -3
h = 0.005
y1[1] (analytic) = 0.88784747306494548257009217877081
y1[1] (numeric) = -12.083569873494224017854645847681
absolute error = 12.971417346559169500424738026452
relative error = 1460.9961440539368978232671749453 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=3177.7MB, alloc=4.6MB, time=359.66
NO POLE
NO POLE
memory used=3181.5MB, alloc=4.6MB, time=359.87
memory used=3185.3MB, alloc=4.6MB, time=360.06
memory used=3189.1MB, alloc=4.6MB, time=360.26
memory used=3192.9MB, alloc=4.6MB, time=360.46
memory used=3196.7MB, alloc=4.6MB, time=360.68
memory used=3200.5MB, alloc=4.6MB, time=360.87
memory used=3204.4MB, alloc=4.6MB, time=361.07
memory used=3208.2MB, alloc=4.6MB, time=361.27
memory used=3212.0MB, alloc=4.6MB, time=361.47
memory used=3215.8MB, alloc=4.6MB, time=361.67
memory used=3219.6MB, alloc=4.6MB, time=361.87
memory used=3223.4MB, alloc=4.6MB, time=362.08
memory used=3227.2MB, alloc=4.6MB, time=362.28
memory used=3231.1MB, alloc=4.6MB, time=362.48
memory used=3234.9MB, alloc=4.6MB, time=362.68
memory used=3238.7MB, alloc=4.6MB, time=362.87
memory used=3242.5MB, alloc=4.6MB, time=363.07
x[1] = 4.7
y2[1] (analytic) = 7.674243589911582046345842503e-05
y2[1] (numeric) = 18.493474798385597351254914445133
absolute error = 18.493398055949698235434450986708
relative error = 24098007.626785231986081268030449 %
Correct digits = -5
h = 0.005
y1[1] (analytic) = 0.98761133653710926284949170367289
y1[1] (numeric) = -13.741069851251134517338000431797
absolute error = 14.72868118778824378018749213547
relative error = 1491.3438761681141416495342747521 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=3246.3MB, alloc=4.6MB, time=363.28
NO POLE
NO POLE
memory used=3250.1MB, alloc=4.6MB, time=363.48
memory used=3253.9MB, alloc=4.6MB, time=363.68
memory used=3257.8MB, alloc=4.6MB, time=363.88
memory used=3261.6MB, alloc=4.6MB, time=364.09
memory used=3265.4MB, alloc=4.6MB, time=364.29
memory used=3269.2MB, alloc=4.6MB, time=364.49
memory used=3273.0MB, alloc=4.6MB, time=364.69
memory used=3276.8MB, alloc=4.6MB, time=364.90
memory used=3280.7MB, alloc=4.6MB, time=365.10
memory used=3284.5MB, alloc=4.6MB, time=365.30
memory used=3288.3MB, alloc=4.6MB, time=365.50
memory used=3292.1MB, alloc=4.6MB, time=365.70
memory used=3295.9MB, alloc=4.6MB, time=365.91
memory used=3299.7MB, alloc=4.6MB, time=366.11
memory used=3303.5MB, alloc=4.6MB, time=366.30
memory used=3307.4MB, alloc=4.6MB, time=366.50
memory used=3311.2MB, alloc=4.6MB, time=366.69
x[1] = 4.8
y2[1] (analytic) = 0.00383539116415932821840353349637
y2[1] (numeric) = 20.457726324633128748177736949919
absolute error = 20.453890933468969419959333416423
relative error = 533293.47797963697928131686118836 %
Correct digits = -3
h = 0.005
y1[1] (analytic) = 1.0874989834394465693202152576495
y1[1] (numeric) = -15.587340070656344313808720767872
absolute error = 16.674839054095790883128936025522
relative error = 1533.3199670088950227005858671689 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=3315.0MB, alloc=4.6MB, time=366.91
NO POLE
NO POLE
memory used=3318.8MB, alloc=4.6MB, time=367.11
memory used=3322.6MB, alloc=4.6MB, time=367.31
memory used=3326.4MB, alloc=4.6MB, time=367.51
memory used=3330.2MB, alloc=4.6MB, time=367.71
memory used=3334.1MB, alloc=4.6MB, time=367.91
memory used=3337.9MB, alloc=4.6MB, time=368.11
memory used=3341.7MB, alloc=4.6MB, time=368.31
memory used=3345.5MB, alloc=4.6MB, time=368.51
memory used=3349.3MB, alloc=4.6MB, time=368.70
memory used=3353.1MB, alloc=4.6MB, time=368.92
memory used=3356.9MB, alloc=4.6MB, time=369.12
memory used=3360.8MB, alloc=4.6MB, time=369.32
memory used=3364.6MB, alloc=4.6MB, time=369.52
memory used=3368.4MB, alloc=4.6MB, time=369.72
memory used=3372.2MB, alloc=4.6MB, time=369.94
memory used=3376.0MB, alloc=4.6MB, time=370.13
memory used=3379.8MB, alloc=4.6MB, time=370.33
x[1] = 4.9
y2[1] (analytic) = 0.01754738737566748772362275008167
y2[1] (numeric) = 22.579046179822472557862211879271
absolute error = 22.561498792446805070138589129189
relative error = 128574.68926532195396755733391693 %
Correct digits = -3
h = 0.005
y1[1] (analytic) = 1.1865123694225754044943291441219
y1[1] (numeric) = -17.637851586957795088720560667931
absolute error = 18.824363956380370493214889812053
relative error = 1586.5290949761762452135965591142 %
Correct digits = -1
h = 0.005
TOP MAIN SOLVE Loop
memory used=3383.7MB, alloc=4.6MB, time=370.53
NO POLE
NO POLE
memory used=3387.5MB, alloc=4.6MB, time=370.73
memory used=3391.3MB, alloc=4.6MB, time=370.94
memory used=3395.1MB, alloc=4.6MB, time=371.14
memory used=3398.9MB, alloc=4.6MB, time=371.34
memory used=3402.7MB, alloc=4.6MB, time=371.54
memory used=3406.5MB, alloc=4.6MB, time=371.74
memory used=3410.4MB, alloc=4.6MB, time=371.95
memory used=3414.2MB, alloc=4.6MB, time=372.15
memory used=3418.0MB, alloc=4.6MB, time=372.35
memory used=3421.8MB, alloc=4.6MB, time=372.56
memory used=3425.6MB, alloc=4.6MB, time=372.76
memory used=3429.4MB, alloc=4.6MB, time=372.96
memory used=3433.2MB, alloc=4.6MB, time=373.16
memory used=3437.1MB, alloc=4.6MB, time=373.36
memory used=3440.9MB, alloc=4.6MB, time=373.56
memory used=3444.7MB, alloc=4.6MB, time=373.76
memory used=3448.5MB, alloc=4.6MB, time=373.95
x[1] = 5
y2[1] (analytic) = 0.04107572533686153110684559384401
y2[1] (numeric) = 24.861490324687842441977478643714
absolute error = 24.82041459935098091087063304987
relative error = 60425.99222728036646352676839435 %
Correct digits = -2
h = 0.005
y1[1] (analytic) = 1.2836621854632262644666391715136
y1[1] (numeric) = -19.908521160591744195835438943151
absolute error = 21.192183346054970460302078114665
relative error = 1650.9159174465744915925186766895 %
Correct digits = -1
h = 0.005
Finished!
diff ( y2 , x , 5 ) = y1 ;
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
Iterations = 1000
Total Elapsed Time = 6 Minutes 14 Seconds
Elapsed Time(since restart) = 6 Minutes 14 Seconds
Time to Timeout = 3 Minutes 45 Seconds
Percent Done = 100.1 %
> quit
memory used=3452.3MB, alloc=4.6MB, time=374.14