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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_log10_relerr,
> glob_look_poles,
> glob_large_float,
> hours_in_day,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_hmin,
> glob_optimal_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_clock_sec,
> min_in_hour,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_iter,
> glob_last_good_h,
> glob_hmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_dump_analytic,
> glob_h,
> djd_debug2,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_relerr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_optimal_expect_sec,
> glob_max_sec,
> glob_smallish_float,
> glob_max_hours,
> years_in_century,
> glob_subiter_method,
> glob_reached_optimal_h,
> glob_initial_pass,
> centuries_in_millinium,
> glob_log10normmin,
> glob_html_log,
> glob_max_minutes,
> glob_small_float,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> glob_almost_1,
> glob_good_digits,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_3,
> array_const_0D0,
> #END CONST
> array_x,
> array_y1_init,
> array_m1,
> array_last_rel_error,
> array_y2_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_y2,
> array_y1,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_y2_higher_work2,
> array_poles,
> array_y2_higher,
> array_complex_pole,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y2_set_initial,
> array_y2_higher_work,
> array_fact_2,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
>
>
>
>
>
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 3
> glob_good_digits := -trunc(log10(relerr/100.0));
> else
> glob_good_digits := Digits;
> fi;# end if 3
> ;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 2
> ;
> if (glob_iter = 1) then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> 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 2
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 3
> glob_good_digits := -trunc(log10(relerr/100.0));
> else
> glob_good_digits := Digits;
> fi;# end if 3
> ;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 2
> ;
> if (glob_iter = 1) then # if number 2
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
>
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_max_iter, glob_log10_relerr, glob_look_poles, glob_large_float,
hours_in_day, glob_log10relerr, glob_max_trunc_err, glob_hmin_init,
glob_hmin, glob_optimal_done, glob_normmax, glob_curr_iter_when_opt,
glob_start, glob_warned2, glob_unchanged_h_cnt, glob_clock_sec, min_in_hour,
glob_max_opt_iter, glob_log10abserr, glob_iter, glob_last_good_h, glob_hmax,
MAX_UNCHANGED, glob_current_iter, glob_warned, glob_optimal_clock_start_sec,
glob_abserr, glob_dump_analytic, glob_h, djd_debug2, glob_orig_start_sec,
glob_optimal_start, glob_relerr, glob_disp_incr, days_in_year,
sec_in_minute, glob_display_flag, djd_debug, glob_dump,
glob_optimal_expect_sec, glob_max_sec, glob_smallish_float, glob_max_hours,
years_in_century, glob_subiter_method, glob_reached_optimal_h,
glob_initial_pass, centuries_in_millinium, glob_log10normmin, glob_html_log,
glob_max_minutes, glob_small_float, glob_log10_abserr,
glob_not_yet_start_msg, glob_almost_1, glob_good_digits, glob_no_eqs,
glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
glob_percent_done, array_const_1D0, array_const_1, array_const_3,
array_const_0D0, array_x, array_y1_init, array_m1, array_last_rel_error,
array_y2_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_pole, array_y2, array_y1,
array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_y2_higher_work2, array_poles, array_y2_higher, array_complex_pole,
array_y1_higher_work, array_y1_higher_work2, array_y2_set_initial,
array_y2_higher_work, array_fact_2, array_y1_set_initial, array_real_pole,
array_y1_higher, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := 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 proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_log10_relerr,
> glob_look_poles,
> glob_large_float,
> hours_in_day,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_hmin,
> glob_optimal_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_clock_sec,
> min_in_hour,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_iter,
> glob_last_good_h,
> glob_hmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_dump_analytic,
> glob_h,
> djd_debug2,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_relerr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_optimal_expect_sec,
> glob_max_sec,
> glob_smallish_float,
> glob_max_hours,
> years_in_century,
> glob_subiter_method,
> glob_reached_optimal_h,
> glob_initial_pass,
> centuries_in_millinium,
> glob_log10normmin,
> glob_html_log,
> glob_max_minutes,
> glob_small_float,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> glob_almost_1,
> glob_good_digits,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_3,
> array_const_0D0,
> #END CONST
> array_x,
> array_y1_init,
> array_m1,
> array_last_rel_error,
> array_y2_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_y2,
> array_y1,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_y2_higher_work2,
> array_poles,
> array_y2_higher,
> array_complex_pole,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y2_set_initial,
> array_y2_higher_work,
> array_fact_2,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> glob_last;
>
> local hnew, sz2, tmp;
>
>
>
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if ( not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
>
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_max_iter, glob_log10_relerr, glob_look_poles, glob_large_float,
hours_in_day, glob_log10relerr, glob_max_trunc_err, glob_hmin_init,
glob_hmin, glob_optimal_done, glob_normmax, glob_curr_iter_when_opt,
glob_start, glob_warned2, glob_unchanged_h_cnt, glob_clock_sec, min_in_hour,
glob_max_opt_iter, glob_log10abserr, glob_iter, glob_last_good_h, glob_hmax,
MAX_UNCHANGED, glob_current_iter, glob_warned, glob_optimal_clock_start_sec,
glob_abserr, glob_dump_analytic, glob_h, djd_debug2, glob_orig_start_sec,
glob_optimal_start, glob_relerr, glob_disp_incr, days_in_year,
sec_in_minute, glob_display_flag, djd_debug, glob_dump,
glob_optimal_expect_sec, glob_max_sec, glob_smallish_float, glob_max_hours,
years_in_century, glob_subiter_method, glob_reached_optimal_h,
glob_initial_pass, centuries_in_millinium, glob_log10normmin, glob_html_log,
glob_max_minutes, glob_small_float, glob_log10_abserr,
glob_not_yet_start_msg, glob_almost_1, glob_good_digits, glob_no_eqs,
glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
glob_percent_done, array_const_1D0, array_const_1, array_const_3,
array_const_0D0, array_x, array_y1_init, array_m1, array_last_rel_error,
array_y2_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_pole, array_y2, array_y1,
array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_y2_higher_work2, array_poles, array_y2_higher, array_complex_pole,
array_y1_higher_work, array_y1_higher_work2, array_y2_set_initial,
array_y2_higher_work, array_fact_2, array_y1_set_initial, array_real_pole,
array_y1_higher, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_log10_relerr,
> glob_look_poles,
> glob_large_float,
> hours_in_day,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_hmin,
> glob_optimal_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_clock_sec,
> min_in_hour,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_iter,
> glob_last_good_h,
> glob_hmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_dump_analytic,
> glob_h,
> djd_debug2,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_relerr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_optimal_expect_sec,
> glob_max_sec,
> glob_smallish_float,
> glob_max_hours,
> years_in_century,
> glob_subiter_method,
> glob_reached_optimal_h,
> glob_initial_pass,
> centuries_in_millinium,
> glob_log10normmin,
> glob_html_log,
> glob_max_minutes,
> glob_small_float,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> glob_almost_1,
> glob_good_digits,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_3,
> array_const_0D0,
> #END CONST
> array_x,
> array_y1_init,
> array_m1,
> array_last_rel_error,
> array_y2_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_y2,
> array_y1,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_y2_higher_work2,
> array_poles,
> array_y2_higher,
> array_complex_pole,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y2_set_initial,
> array_y2_higher_work,
> array_fact_2,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
>
>
>
>
>
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
>
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_max_iter, glob_log10_relerr, glob_look_poles, glob_large_float,
hours_in_day, glob_log10relerr, glob_max_trunc_err, glob_hmin_init,
glob_hmin, glob_optimal_done, glob_normmax, glob_curr_iter_when_opt,
glob_start, glob_warned2, glob_unchanged_h_cnt, glob_clock_sec, min_in_hour,
glob_max_opt_iter, glob_log10abserr, glob_iter, glob_last_good_h, glob_hmax,
MAX_UNCHANGED, glob_current_iter, glob_warned, glob_optimal_clock_start_sec,
glob_abserr, glob_dump_analytic, glob_h, djd_debug2, glob_orig_start_sec,
glob_optimal_start, glob_relerr, glob_disp_incr, days_in_year,
sec_in_minute, glob_display_flag, djd_debug, glob_dump,
glob_optimal_expect_sec, glob_max_sec, glob_smallish_float, glob_max_hours,
years_in_century, glob_subiter_method, glob_reached_optimal_h,
glob_initial_pass, centuries_in_millinium, glob_log10normmin, glob_html_log,
glob_max_minutes, glob_small_float, glob_log10_abserr,
glob_not_yet_start_msg, glob_almost_1, glob_good_digits, glob_no_eqs,
glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
glob_percent_done, array_const_1D0, array_const_1, array_const_3,
array_const_0D0, array_x, array_y1_init, array_m1, array_last_rel_error,
array_y2_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_pole, array_y2, array_y1,
array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_y2_higher_work2, array_poles, array_y2_higher, array_complex_pole,
array_y1_higher_work, array_y1_higher_work2, array_y2_set_initial,
array_y2_higher_work, array_fact_2, array_y1_set_initial, array_real_pole,
array_y1_higher, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_log10_relerr,
> glob_look_poles,
> glob_large_float,
> hours_in_day,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_hmin,
> glob_optimal_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_clock_sec,
> min_in_hour,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_iter,
> glob_last_good_h,
> glob_hmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_dump_analytic,
> glob_h,
> djd_debug2,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_relerr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_optimal_expect_sec,
> glob_max_sec,
> glob_smallish_float,
> glob_max_hours,
> years_in_century,
> glob_subiter_method,
> glob_reached_optimal_h,
> glob_initial_pass,
> centuries_in_millinium,
> glob_log10normmin,
> glob_html_log,
> glob_max_minutes,
> glob_small_float,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> glob_almost_1,
> glob_good_digits,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_3,
> array_const_0D0,
> #END CONST
> array_x,
> array_y1_init,
> array_m1,
> array_last_rel_error,
> array_y2_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_y2,
> array_y1,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_y2_higher_work2,
> array_poles,
> array_y2_higher,
> array_complex_pole,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y2_set_initial,
> array_y2_higher_work,
> array_fact_2,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
>
>
>
>
>
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 3 - 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 - 3 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y2_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif ((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]);
> rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]);
> rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]);
> rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]);
> rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif ((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]);
> rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]);
> rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]);
> rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]);
> rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4
> ;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3
> ;
> #BOTTOM RADII COMPLEX EQ = 2
> found := false;
> #TOP WHICH RADII EQ = 1
> if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found ) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 2
> if ( not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float)))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if ( not found ) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 2
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if (array_pole[1] > array_poles[2,1]) then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 2
> #BOTTOM CHECK FOR POLE
> display_pole();
>
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_max_iter, glob_log10_relerr, glob_look_poles, glob_large_float,
hours_in_day, glob_log10relerr, glob_max_trunc_err, glob_hmin_init,
glob_hmin, glob_optimal_done, glob_normmax, glob_curr_iter_when_opt,
glob_start, glob_warned2, glob_unchanged_h_cnt, glob_clock_sec, min_in_hour,
glob_max_opt_iter, glob_log10abserr, glob_iter, glob_last_good_h, glob_hmax,
MAX_UNCHANGED, glob_current_iter, glob_warned, glob_optimal_clock_start_sec,
glob_abserr, glob_dump_analytic, glob_h, djd_debug2, glob_orig_start_sec,
glob_optimal_start, glob_relerr, glob_disp_incr, days_in_year,
sec_in_minute, glob_display_flag, djd_debug, glob_dump,
glob_optimal_expect_sec, glob_max_sec, glob_smallish_float, glob_max_hours,
years_in_century, glob_subiter_method, glob_reached_optimal_h,
glob_initial_pass, centuries_in_millinium, glob_log10normmin, glob_html_log,
glob_max_minutes, glob_small_float, glob_log10_abserr,
glob_not_yet_start_msg, glob_almost_1, glob_good_digits, glob_no_eqs,
glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
glob_percent_done, array_const_1D0, array_const_1, array_const_3,
array_const_0D0, array_x, array_y1_init, array_m1, array_last_rel_error,
array_y2_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_pole, array_y2, array_y1,
array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_y2_higher_work2, array_poles, array_y2_higher, array_complex_pole,
array_y1_higher_work, array_y1_higher_work2, array_y2_set_initial,
array_y2_higher_work, array_fact_2, array_y1_set_initial, array_real_pole,
array_y1_higher, glob_last;
n := glob_max_terms;
m := n - 4;
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 - 4;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= omniabs(array_y2_higher[1, m]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= omniabs(array_y1_higher[1, m]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[2, 1] := rad_c;
array_complex_pole[2, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_log10_relerr,
> glob_look_poles,
> glob_large_float,
> hours_in_day,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_hmin,
> glob_optimal_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_clock_sec,
> min_in_hour,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_iter,
> glob_last_good_h,
> glob_hmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_dump_analytic,
> glob_h,
> djd_debug2,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_relerr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_optimal_expect_sec,
> glob_max_sec,
> glob_smallish_float,
> glob_max_hours,
> years_in_century,
> glob_subiter_method,
> glob_reached_optimal_h,
> glob_initial_pass,
> centuries_in_millinium,
> glob_log10normmin,
> glob_html_log,
> glob_max_minutes,
> glob_small_float,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> glob_almost_1,
> glob_good_digits,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_3,
> array_const_0D0,
> #END CONST
> array_x,
> array_y1_init,
> array_m1,
> array_last_rel_error,
> array_y2_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_y2,
> array_y1,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_y2_higher_work2,
> array_poles,
> array_y2_higher,
> array_complex_pole,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y2_set_initial,
> array_y2_higher_work,
> array_fact_2,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> glob_last;
>
> local iii;
>
>
>
> if ( not glob_initial_pass) then # if number 3
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2
> ;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 3
> ;
>
> # End Function number 7
> end;
get_norms := proc()
local iii;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_max_iter, glob_log10_relerr, glob_look_poles, glob_large_float,
hours_in_day, glob_log10relerr, glob_max_trunc_err, glob_hmin_init,
glob_hmin, glob_optimal_done, glob_normmax, glob_curr_iter_when_opt,
glob_start, glob_warned2, glob_unchanged_h_cnt, glob_clock_sec, min_in_hour,
glob_max_opt_iter, glob_log10abserr, glob_iter, glob_last_good_h, glob_hmax,
MAX_UNCHANGED, glob_current_iter, glob_warned, glob_optimal_clock_start_sec,
glob_abserr, glob_dump_analytic, glob_h, djd_debug2, glob_orig_start_sec,
glob_optimal_start, glob_relerr, glob_disp_incr, days_in_year,
sec_in_minute, glob_display_flag, djd_debug, glob_dump,
glob_optimal_expect_sec, glob_max_sec, glob_smallish_float, glob_max_hours,
years_in_century, glob_subiter_method, glob_reached_optimal_h,
glob_initial_pass, centuries_in_millinium, glob_log10normmin, glob_html_log,
glob_max_minutes, glob_small_float, glob_log10_abserr,
glob_not_yet_start_msg, glob_almost_1, glob_good_digits, glob_no_eqs,
glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
glob_percent_done, array_const_1D0, array_const_1, array_const_3,
array_const_0D0, array_x, array_y1_init, array_m1, array_last_rel_error,
array_y2_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_pole, array_y2, array_y1,
array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_y2_higher_work2, array_poles, array_y2_higher, array_complex_pole,
array_y1_higher_work, array_y1_higher_work2, array_y2_set_initial,
array_y2_higher_work, array_fact_2, array_y1_set_initial, array_real_pole,
array_y1_higher, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y2[iii]) then
array_norms[iii] := omniabs(array_y2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y1[iii]) then
array_norms[iii] := omniabs(array_y1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_log10_relerr,
> glob_look_poles,
> glob_large_float,
> hours_in_day,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_hmin,
> glob_optimal_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_clock_sec,
> min_in_hour,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_iter,
> glob_last_good_h,
> glob_hmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_dump_analytic,
> glob_h,
> djd_debug2,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_relerr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_optimal_expect_sec,
> glob_max_sec,
> glob_smallish_float,
> glob_max_hours,
> years_in_century,
> glob_subiter_method,
> glob_reached_optimal_h,
> glob_initial_pass,
> centuries_in_millinium,
> glob_log10normmin,
> glob_html_log,
> glob_max_minutes,
> glob_small_float,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> glob_almost_1,
> glob_good_digits,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_3,
> array_const_0D0,
> #END CONST
> array_x,
> array_y1_init,
> array_m1,
> array_last_rel_error,
> array_y2_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_y2,
> array_y1,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_y2_higher_work2,
> array_poles,
> array_y2_higher,
> array_complex_pole,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y2_set_initial,
> array_y2_higher_work,
> array_fact_2,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
>
>
>
>
>
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre cos 1 $eq_no = 1
> array_tmp1[1] := cos(array_x[1]);
> array_tmp1_g[1] := sin(array_x[1]);
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp2[1] := (array_m1[1] * (array_tmp1[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[1,4]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[1] * expt(glob_h , (3)) * factorial_3(0,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,2] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> # emit pre mult FULL FULL $eq_no = 2 i = 1
> array_tmp5[1] := (array_m1[1] * (array_y2[1]));
> #emit pre add FULL - CONST $eq_no = 2 i = 1
> array_tmp6[1] := array_tmp5[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_tmp6[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 cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := -array_tmp1_g[1] * array_x[2] / 1;
> array_tmp1_g[2] := array_tmp1[1] * array_x[2] / 1;
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_m1,array_tmp1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[1,5]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[2] * expt(glob_h , (3)) * factorial_3(1,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,3] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> # emit pre mult FULL FULL $eq_no = 2 i = 2
> array_tmp5[2] := ats(2,array_m1,array_y2,1);
> #emit pre add FULL CONST $eq_no = 2 i = 2
> array_tmp6[2] := array_tmp5[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_tmp6[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 cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := -array_tmp1_g[2] * array_x[2] / 2;
> array_tmp1_g[3] := array_tmp1[2] * array_x[2] / 2;
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_m1,array_tmp1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[1,6]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[3] * expt(glob_h , (3)) * factorial_3(2,5);
> 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
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> # emit pre mult FULL FULL $eq_no = 2 i = 3
> array_tmp5[3] := ats(3,array_m1,array_y2,1);
> #emit pre add FULL CONST $eq_no = 2 i = 3
> array_tmp6[3] := array_tmp5[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_tmp6[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 cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := -array_tmp1_g[3] * array_x[2] / 3;
> array_tmp1_g[4] := array_tmp1[3] * array_x[2] / 3;
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_m1,array_tmp1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[1,7]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[4] * expt(glob_h , (3)) * factorial_3(3,6);
> 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
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> # emit pre mult FULL FULL $eq_no = 2 i = 4
> array_tmp5[4] := ats(4,array_m1,array_y2,1);
> #emit pre add FULL CONST $eq_no = 2 i = 4
> array_tmp6[4] := array_tmp5[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_tmp6[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 cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := -array_tmp1_g[4] * array_x[2] / 4;
> array_tmp1_g[5] := array_tmp1[4] * array_x[2] / 4;
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_m1,array_tmp1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[1,8]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[5] * expt(glob_h , (3)) * factorial_3(4,7);
> 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
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> # emit pre mult FULL FULL $eq_no = 2 i = 5
> array_tmp5[5] := ats(5,array_m1,array_y2,1);
> #emit pre add FULL CONST $eq_no = 2 i = 5
> array_tmp6[5] := array_tmp5[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_tmp6[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 cos LINEAR $eq_no = 1
> array_tmp1[kkk] := -array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp1_g[kkk] := array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
> #emit mult FULL FULL $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_m1,array_tmp1,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 3;
> 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_tmp3[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_tmp5[kkk] := ats(kkk,array_m1,array_y2,1);
> #emit FULL - NOT FULL add $eq_no = 2
> array_tmp6[kkk] := array_tmp5[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_tmp6[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y1[kkk + order_d] := temporary;
> array_y1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
>
> #BOTTOM ATOMALL ???
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_max_iter, glob_log10_relerr, glob_look_poles, glob_large_float,
hours_in_day, glob_log10relerr, glob_max_trunc_err, glob_hmin_init,
glob_hmin, glob_optimal_done, glob_normmax, glob_curr_iter_when_opt,
glob_start, glob_warned2, glob_unchanged_h_cnt, glob_clock_sec, min_in_hour,
glob_max_opt_iter, glob_log10abserr, glob_iter, glob_last_good_h, glob_hmax,
MAX_UNCHANGED, glob_current_iter, glob_warned, glob_optimal_clock_start_sec,
glob_abserr, glob_dump_analytic, glob_h, djd_debug2, glob_orig_start_sec,
glob_optimal_start, glob_relerr, glob_disp_incr, days_in_year,
sec_in_minute, glob_display_flag, djd_debug, glob_dump,
glob_optimal_expect_sec, glob_max_sec, glob_smallish_float, glob_max_hours,
years_in_century, glob_subiter_method, glob_reached_optimal_h,
glob_initial_pass, centuries_in_millinium, glob_log10normmin, glob_html_log,
glob_max_minutes, glob_small_float, glob_log10_abserr,
glob_not_yet_start_msg, glob_almost_1, glob_good_digits, glob_no_eqs,
glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
glob_percent_done, array_const_1D0, array_const_1, array_const_3,
array_const_0D0, array_x, array_y1_init, array_m1, array_last_rel_error,
array_y2_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_pole, array_y2, array_y1,
array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_y2_higher_work2, array_poles, array_y2_higher, array_complex_pole,
array_y1_higher_work, array_y1_higher_work2, array_y2_set_initial,
array_y2_higher_work, array_fact_2, array_y1_set_initial, array_real_pole,
array_y1_higher, glob_last;
array_tmp1[1] := cos(array_x[1]);
array_tmp1_g[1] := sin(array_x[1]);
array_tmp2[1] := array_m1[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
if not array_y2_set_initial[1, 4] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*expt(glob_h, 3)*factorial_3(0, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 2] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 1] := temporary
end if
end if;
kkk := 2;
array_tmp5[1] := array_m1[1]*array_y2[1];
array_tmp6[1] := array_tmp5[1] + array_const_1D0[1];
if not array_y1_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp6[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_tmp1_g[1]*array_x[2];
array_tmp1_g[2] := array_tmp1[1]*array_x[2];
array_tmp2[2] := ats(2, array_m1, array_tmp1, 1);
array_tmp3[2] := array_tmp2[2];
if not array_y2_set_initial[1, 5] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*expt(glob_h, 3)*factorial_3(1, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 3] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 2] := temporary
end if
end if;
kkk := 3;
array_tmp5[2] := ats(2, array_m1, array_y2, 1);
array_tmp6[2] := array_tmp5[2];
if not array_y1_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp6[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] := -1/2*array_tmp1_g[2]*array_x[2];
array_tmp1_g[3] := 1/2*array_tmp1[2]*array_x[2];
array_tmp2[3] := ats(3, array_m1, array_tmp1, 1);
array_tmp3[3] := array_tmp2[3];
if not array_y2_set_initial[1, 6] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*expt(glob_h, 3)*factorial_3(2, 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
end if
end if;
kkk := 4;
array_tmp5[3] := ats(3, array_m1, array_y2, 1);
array_tmp6[3] := array_tmp5[3];
if not array_y1_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp6[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] := -1/3*array_tmp1_g[3]*array_x[2];
array_tmp1_g[4] := 1/3*array_tmp1[3]*array_x[2];
array_tmp2[4] := ats(4, array_m1, array_tmp1, 1);
array_tmp3[4] := array_tmp2[4];
if not array_y2_set_initial[1, 7] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*expt(glob_h, 3)*factorial_3(3, 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
end if
end if;
kkk := 5;
array_tmp5[4] := ats(4, array_m1, array_y2, 1);
array_tmp6[4] := array_tmp5[4];
if not array_y1_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp6[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] := -1/4*array_tmp1_g[4]*array_x[2];
array_tmp1_g[5] := 1/4*array_tmp1[4]*array_x[2];
array_tmp2[5] := ats(5, array_m1, array_tmp1, 1);
array_tmp3[5] := array_tmp2[5];
if not array_y2_set_initial[1, 8] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*expt(glob_h, 3)*factorial_3(4, 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
end if
end if;
kkk := 6;
array_tmp5[5] := ats(5, array_m1, array_y2, 1);
array_tmp6[5] := array_tmp5[5];
if not array_y1_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp6[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_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2[kkk] := ats(kkk, array_m1, array_tmp1, 1);
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 3;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := array_tmp3[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_tmp5[kkk] := ats(kkk, array_m1, array_y2, 1);
array_tmp6[kkk] := array_tmp5[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_tmp6[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y1[kkk + order_d] := temporary;
array_y1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs >= 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_minute;
> sec_int := floor(seconds);
> fprintf(fd,"| ");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_minute, years_in_century;
secs := secs_in;
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*min_in_hour*
hours_in_day*days_in_year*years_in_century*
centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_minute;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs >= 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_minute;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_minute, years_in_century;
secs := convfloat(secs_in);
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*min_in_hour*
hours_in_day*days_in_year*years_in_century*
centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_minute;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
>
>
>
>
>
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats;
>
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
>
>
>
>
>
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
>
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 11
> fprintf(file,"NA");
> elif (pole = 1) then # if number 12
> fprintf(file,"Real");
> elif (pole = 2) then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
>
>
>
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
>
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
>
>
>
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
>
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
>
>
>
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr;
>
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 17
> factorial_2 := proc(nnn)
> local ret;
>
>
>
> ret := nnn!;
>
> # End Function number 17
> end;
factorial_2 := proc(nnn) local ret; ret := nnn! end proc
> # Begin Function number 18
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
>
>
>
> if (nnn <= glob_max_terms) then # if number 13
> if (array_fact_1[nnn] = 0) then # if number 14
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 18
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 19
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
>
>
>
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13
> if (array_fact_2[mmm,nnn] = 0) then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 19
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 20
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 21
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 21
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y2 := proc(x)
> return(1.0 + cos(x));
> end;
exact_soln_y2 := proc(x) return 1.0 + cos(x) end proc
> exact_soln_y2p := proc(x)
> return( -sin(x));
> end;
exact_soln_y2p := proc(x) return -sin(x) end proc
> exact_soln_y2pp := proc(x)
> return( -cos(x));
> end;
exact_soln_y2pp := proc(x) return -cos(x) end proc
> exact_soln_y1 := proc(x)
> return( 1.0 - sin(x));
> end;
exact_soln_y1 := proc(x) return 1.0 - 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
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_log10_relerr,
> glob_look_poles,
> glob_large_float,
> hours_in_day,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_hmin_init,
> glob_hmin,
> glob_optimal_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_clock_sec,
> min_in_hour,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_iter,
> glob_last_good_h,
> glob_hmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_dump_analytic,
> glob_h,
> djd_debug2,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_relerr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_optimal_expect_sec,
> glob_max_sec,
> glob_smallish_float,
> glob_max_hours,
> years_in_century,
> glob_subiter_method,
> glob_reached_optimal_h,
> glob_initial_pass,
> centuries_in_millinium,
> glob_log10normmin,
> glob_html_log,
> glob_max_minutes,
> glob_small_float,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> glob_almost_1,
> glob_good_digits,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_3,
> array_const_0D0,
> #END CONST
> array_x,
> array_y1_init,
> array_m1,
> array_last_rel_error,
> array_y2_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_pole,
> array_y2,
> array_y1,
> array_type_pole,
> array_fact_1,
> array_1st_rel_error,
> array_norms,
> array_y2_higher_work2,
> array_poles,
> array_y2_higher,
> array_complex_pole,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y2_set_initial,
> array_y2_higher_work,
> array_fact_2,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> glob_iolevel := 5;
> DEBUGL := 3;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_max_iter := 1000;
> glob_log10_relerr := 0.1e-10;
> glob_look_poles := false;
> glob_large_float := 9.0e100;
> hours_in_day := 24;
> glob_log10relerr := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_hmin := 0.00000000001;
> glob_optimal_done := false;
> glob_normmax := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_start := 0;
> glob_warned2 := false;
> glob_unchanged_h_cnt := 0;
> glob_clock_sec := 0.0;
> min_in_hour := 60;
> glob_max_opt_iter := 10;
> glob_log10abserr := 0.0;
> glob_iter := 0;
> glob_last_good_h := 0.1;
> glob_hmax := 1.0;
> MAX_UNCHANGED := 10;
> glob_current_iter := 0;
> glob_warned := false;
> glob_optimal_clock_start_sec := 0.0;
> glob_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_h := 0.1;
> djd_debug2 := true;
> glob_orig_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_relerr := 0.1e-10;
> glob_disp_incr := 0.1;
> days_in_year := 365;
> sec_in_minute := 60;
> glob_display_flag := true;
> djd_debug := true;
> glob_dump := false;
> glob_optimal_expect_sec := 0.1;
> glob_max_sec := 10000.0;
> glob_smallish_float := 0.1e-100;
> glob_max_hours := 0.0;
> years_in_century := 100;
> glob_subiter_method := 3;
> glob_reached_optimal_h := false;
> glob_initial_pass := true;
> centuries_in_millinium := 10;
> glob_log10normmin := 0.1;
> glob_html_log := true;
> glob_max_minutes := 0.0;
> glob_small_float := 0.1e-50;
> glob_log10_abserr := 0.1e-10;
> glob_not_yet_start_msg := true;
> glob_almost_1 := 0.9990;
> glob_good_digits := 0;
> glob_no_eqs := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_not_yet_finished := true;
> glob_clock_start_sec := 0.0;
> glob_percent_done := 0.0;
> #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/mtest4postode.ode#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 3 ) = m1 * cos(x) ;");
> 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 := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0;");
> omniout_str(ALWAYS,"glob_h := 0.00001;");
> 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,"glob_max_iter := 20;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 1;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return( -sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
> omniout_str(ALWAYS,"return( -cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return( 1.0 - 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_x:= Array(0..(max_terms + 1),[]);
> array_y1_init:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_y2_init:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= 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_tmp5:= Array(0..(max_terms + 1),[]);
> array_tmp6:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_y2:= Array(0..(max_terms + 1),[]);
> array_y1:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_y2_higher_work2 := Array(0..(4+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_y2_higher := Array(0..(4+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work := Array(0..(4+ 1) ,(0..max_terms+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> 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
> ;
> 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_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_y2_init[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_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=4) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=4) 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 <= 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 <=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 <=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 <=4) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=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_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_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 <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_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_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_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_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_3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3[1] := 3;
> 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_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 := 0.1;
> x_end := 5.0;
> glob_h := 0.00001;
> 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);
> glob_max_iter := 20;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 1;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y2_set_initial[1,1] := true;
> array_y2_set_initial[1,2] := true;
> array_y2_set_initial[1,3] := true;
> array_y2_set_initial[1,4] := false;
> array_y2_set_initial[1,5] := false;
> array_y2_set_initial[1,6] := false;
> array_y2_set_initial[1,7] := false;
> array_y2_set_initial[1,8] := false;
> array_y2_set_initial[1,9] := false;
> array_y2_set_initial[1,10] := false;
> array_y2_set_initial[1,11] := false;
> array_y2_set_initial[1,12] := false;
> array_y2_set_initial[1,13] := false;
> array_y2_set_initial[1,14] := false;
> array_y2_set_initial[1,15] := false;
> array_y2_set_initial[1,16] := false;
> array_y2_set_initial[1,17] := false;
> array_y2_set_initial[1,18] := false;
> array_y2_set_initial[1,19] := false;
> array_y2_set_initial[1,20] := false;
> array_y2_set_initial[1,21] := false;
> array_y2_set_initial[1,22] := false;
> array_y2_set_initial[1,23] := false;
> array_y2_set_initial[1,24] := false;
> array_y2_set_initial[1,25] := false;
> array_y2_set_initial[1,26] := false;
> array_y2_set_initial[1,27] := false;
> array_y2_set_initial[1,28] := false;
> array_y2_set_initial[1,29] := false;
> array_y2_set_initial[1,30] := false;
> array_y1_set_initial[2,1] := true;
> array_y1_set_initial[2,2] := false;
> array_y1_set_initial[2,3] := false;
> array_y1_set_initial[2,4] := false;
> array_y1_set_initial[2,5] := false;
> array_y1_set_initial[2,6] := false;
> array_y1_set_initial[2,7] := false;
> array_y1_set_initial[2,8] := false;
> array_y1_set_initial[2,9] := false;
> array_y1_set_initial[2,10] := false;
> array_y1_set_initial[2,11] := false;
> array_y1_set_initial[2,12] := false;
> array_y1_set_initial[2,13] := false;
> array_y1_set_initial[2,14] := false;
> array_y1_set_initial[2,15] := false;
> array_y1_set_initial[2,16] := false;
> array_y1_set_initial[2,17] := false;
> array_y1_set_initial[2,18] := false;
> array_y1_set_initial[2,19] := false;
> array_y1_set_initial[2,20] := false;
> array_y1_set_initial[2,21] := false;
> array_y1_set_initial[2,22] := false;
> array_y1_set_initial[2,23] := false;
> array_y1_set_initial[2,24] := false;
> array_y1_set_initial[2,25] := false;
> array_y1_set_initial[2,26] := false;
> array_y1_set_initial[2,27] := false;
> array_y1_set_initial[2,28] := false;
> array_y1_set_initial[2,29] := false;
> array_y1_set_initial[2,30] := false;
> if (glob_html_log) then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 3;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> if (glob_subiter_method = 1 ) then # if number 3
> atomall();
> elif (glob_subiter_method = 2 ) then # if number 4
> subiter := 1;
> while (subiter <= 4) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while (subiter <= 4 + glob_max_terms) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> fi;# end if 4
> ;
> if (glob_look_poles) then # if number 4
> #left paren 0004C
> check_for_pole();
> fi;# end if 4
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y2
> order_diff := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #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 := 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 := 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 := 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 , 3 ) = m1 * cos(x) ;");
> 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,"2012-08-21T18:01:00-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest4")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 3 ) = m1 * cos(x) ;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_good_digits)
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 5
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 5
> ;
> log_revs(html_log_file," 123 | ")
> ;
> logitem_str(html_log_file,"mtest4 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest4 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_integer(html_log_file,glob_good_digits)
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logditto(html_log_file)
> ;
> if (glob_percent_done < 100.0) then # if number 5
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 5
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 4
> ;
> if (glob_html_log) then # if number 4
> fclose(html_log_file);
> fi;# end if 4
> ;
> ;;
> #END OUTFILEMAIN
>
> # End Function number 8
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp, subiter;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_max_iter, glob_log10_relerr, glob_look_poles, glob_large_float,
hours_in_day, glob_log10relerr, glob_max_trunc_err, glob_hmin_init,
glob_hmin, glob_optimal_done, glob_normmax, glob_curr_iter_when_opt,
glob_start, glob_warned2, glob_unchanged_h_cnt, glob_clock_sec, min_in_hour,
glob_max_opt_iter, glob_log10abserr, glob_iter, glob_last_good_h, glob_hmax,
MAX_UNCHANGED, glob_current_iter, glob_warned, glob_optimal_clock_start_sec,
glob_abserr, glob_dump_analytic, glob_h, djd_debug2, glob_orig_start_sec,
glob_optimal_start, glob_relerr, glob_disp_incr, days_in_year,
sec_in_minute, glob_display_flag, djd_debug, glob_dump,
glob_optimal_expect_sec, glob_max_sec, glob_smallish_float, glob_max_hours,
years_in_century, glob_subiter_method, glob_reached_optimal_h,
glob_initial_pass, centuries_in_millinium, glob_log10normmin, glob_html_log,
glob_max_minutes, glob_small_float, glob_log10_abserr,
glob_not_yet_start_msg, glob_almost_1, glob_good_digits, glob_no_eqs,
glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
glob_percent_done, array_const_1D0, array_const_1, array_const_3,
array_const_0D0, array_x, array_y1_init, array_m1, array_last_rel_error,
array_y2_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_pole, array_y2, array_y1,
array_type_pole, array_fact_1, array_1st_rel_error, array_norms,
array_y2_higher_work2, array_poles, array_y2_higher, array_complex_pole,
array_y1_higher_work, array_y1_higher_work2, array_y2_set_initial,
array_y2_higher_work, array_fact_2, array_y1_set_initial, array_real_pole,
array_y1_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
glob_iolevel := 5;
DEBUGL := 3;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_max_iter := 1000;
glob_log10_relerr := 0.1*10^(-10);
glob_look_poles := false;
glob_large_float := 0.90*10^101;
hours_in_day := 24;
glob_log10relerr := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_hmin := 0.1*10^(-10);
glob_optimal_done := false;
glob_normmax := 0.;
glob_curr_iter_when_opt := 0;
glob_start := 0;
glob_warned2 := false;
glob_unchanged_h_cnt := 0;
glob_clock_sec := 0.;
min_in_hour := 60;
glob_max_opt_iter := 10;
glob_log10abserr := 0.;
glob_iter := 0;
glob_last_good_h := 0.1;
glob_hmax := 1.0;
MAX_UNCHANGED := 10;
glob_current_iter := 0;
glob_warned := false;
glob_optimal_clock_start_sec := 0.;
glob_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_h := 0.1;
djd_debug2 := true;
glob_orig_start_sec := 0.;
glob_optimal_start := 0.;
glob_relerr := 0.1*10^(-10);
glob_disp_incr := 0.1;
days_in_year := 365;
sec_in_minute := 60;
glob_display_flag := true;
djd_debug := true;
glob_dump := false;
glob_optimal_expect_sec := 0.1;
glob_max_sec := 10000.0;
glob_smallish_float := 0.1*10^(-100);
glob_max_hours := 0.;
years_in_century := 100;
glob_subiter_method := 3;
glob_reached_optimal_h := false;
glob_initial_pass := true;
centuries_in_millinium := 10;
glob_log10normmin := 0.1;
glob_html_log := true;
glob_max_minutes := 0.;
glob_small_float := 0.1*10^(-50);
glob_log10_abserr := 0.1*10^(-10);
glob_not_yet_start_msg := true;
glob_almost_1 := 0.9990;
glob_good_digits := 0;
glob_no_eqs := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_not_yet_finished := true;
glob_clock_start_sec := 0.;
glob_percent_done := 0.;
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/mtest4postode.ode#################");
omniout_str(ALWAYS, "diff ( y2 , x , 3 ) = m1 * cos(x) ;");
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 := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0;");
omniout_str(ALWAYS, "glob_h := 0.00001;");
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, "glob_max_iter := 20;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 1;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(1.0 + cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return( -sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
omniout_str(ALWAYS, "return( -cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return( 1.0 - 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_x := Array(0 .. max_terms + 1, []);
array_y1_init := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_y2_init := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1_g := 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_tmp5 := Array(0 .. max_terms + 1, []);
array_tmp6 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_y2 := Array(0 .. max_terms + 1, []);
array_y1 := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_y2_higher_work2 := Array(0 .. 5, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_y2_higher := Array(0 .. 5, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 3, 0 .. 4, []);
array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y2_higher_work := Array(0 .. 5, 0 .. max_terms + 1, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 3, 0 .. 4, []);
array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
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;
term := 1;
while term <= max_terms do array_m1[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_y2_init[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_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 4 do
term := 1;
while term <= max_terms do
array_y2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 4 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 <= max_terms do
array_y1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work2[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 <= 4 do
term := 1;
while term <= max_terms do
array_y2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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_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_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1
end do;
array_const_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_3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3[term] := 0.; term := term + 1
end do;
array_const_3[1] := 3;
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_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 := 0.1;
x_end := 5.0;
glob_h := 0.00001;
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);
glob_max_iter := 20;
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 1;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
chk_data();
array_y2_set_initial[1, 1] := true;
array_y2_set_initial[1, 2] := true;
array_y2_set_initial[1, 3] := true;
array_y2_set_initial[1, 4] := false;
array_y2_set_initial[1, 5] := false;
array_y2_set_initial[1, 6] := false;
array_y2_set_initial[1, 7] := false;
array_y2_set_initial[1, 8] := false;
array_y2_set_initial[1, 9] := false;
array_y2_set_initial[1, 10] := false;
array_y2_set_initial[1, 11] := false;
array_y2_set_initial[1, 12] := false;
array_y2_set_initial[1, 13] := false;
array_y2_set_initial[1, 14] := false;
array_y2_set_initial[1, 15] := false;
array_y2_set_initial[1, 16] := false;
array_y2_set_initial[1, 17] := false;
array_y2_set_initial[1, 18] := false;
array_y2_set_initial[1, 19] := false;
array_y2_set_initial[1, 20] := false;
array_y2_set_initial[1, 21] := false;
array_y2_set_initial[1, 22] := false;
array_y2_set_initial[1, 23] := false;
array_y2_set_initial[1, 24] := false;
array_y2_set_initial[1, 25] := false;
array_y2_set_initial[1, 26] := false;
array_y2_set_initial[1, 27] := false;
array_y2_set_initial[1, 28] := false;
array_y2_set_initial[1, 29] := false;
array_y2_set_initial[1, 30] := false;
array_y1_set_initial[2, 1] := true;
array_y1_set_initial[2, 2] := false;
array_y1_set_initial[2, 3] := false;
array_y1_set_initial[2, 4] := false;
array_y1_set_initial[2, 5] := false;
array_y1_set_initial[2, 6] := false;
array_y1_set_initial[2, 7] := false;
array_y1_set_initial[2, 8] := false;
array_y1_set_initial[2, 9] := false;
array_y1_set_initial[2, 10] := false;
array_y1_set_initial[2, 11] := false;
array_y1_set_initial[2, 12] := false;
array_y1_set_initial[2, 13] := false;
array_y1_set_initial[2, 14] := false;
array_y1_set_initial[2, 15] := false;
array_y1_set_initial[2, 16] := false;
array_y1_set_initial[2, 17] := false;
array_y1_set_initial[2, 18] := false;
array_y1_set_initial[2, 19] := false;
array_y1_set_initial[2, 20] := false;
array_y1_set_initial[2, 21] := false;
array_y1_set_initial[2, 22] := false;
array_y1_set_initial[2, 23] := false;
array_y1_set_initial[2, 24] := false;
array_y1_set_initial[2, 25] := false;
array_y1_set_initial[2, 26] := false;
array_y1_set_initial[2, 27] := false;
array_y1_set_initial[2, 28] := false;
array_y1_set_initial[2, 29] := false;
array_y1_set_initial[2, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 3;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 4 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 4 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 3;
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 := 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 := 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 := 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 , 3 ) = m1 * cos(x) ;");
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, "2012-08-21T18:01:00-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest4")
;
logitem_str(html_log_file, "diff ( y2 , x , 3 ) = m1 * cos(x) ;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_good_digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 123 | ");
logitem_str(html_log_file,
"mtest4 diffeq.mxt");
logitem_str(html_log_file,
"mtest4 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_integer(html_log_file, glob_good_digits);
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/mtest4postode.ode#################
diff ( y2 , x , 3 ) = m1 * cos(x) ;
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 := 0.1;
x_end := 5.0;
glob_h := 0.00001;
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);
glob_max_iter := 20;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 1;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y2 := proc(x)
return(1.0 + cos(x));
end;
exact_soln_y2p := proc(x)
return( -sin(x));
end;
exact_soln_y2pp := proc(x)
return( -cos(x));
end;
exact_soln_y1 := proc(x)
return( 1.0 - sin(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y2[1] (analytic) = 1.9950041652780257660955619878039
y2[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 1e-05
y1[1] (analytic) = 0.90016658335317184769318580158938
y1[1] (numeric) = 0.90016658335317184769318580158938
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 1e-05
x[1] = 0.1
y2[1] (analytic) = 1.9950041652780257660955619878039
y2[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 1e-05
y1[1] (analytic) = 0.90016658335317184769318580158938
y1[1] (numeric) = 0.90016658335317184769318580158938
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 1e-05
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.1MB, time=0.50
NO POLE
NO POLE
x[1] = 0.10001
y2[1] (analytic) = 1.9950031668941091061894549908141
y2[1] (numeric) = 1.9950031668941089237161516831056
absolute error = 1.824733033077085e-16
relative error = 9.1465169747970544739062974516909e-15 %
Correct digits = 16
h = 1e-05
y1[1] (analytic) = 0.90015663331651090410185220183636
y1[1] (numeric) = 0.90015663331651090410230838490809
absolute error = 4.5618307173e-22
relative error = 5.0678188089249797117950947755126e-20 %
Correct digits = 21
h = 1e-05
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=1.10
NO POLE
NO POLE
x[1] = 0.10002
y2[1] (analytic) = 1.9950021684106921295947662525112
y2[1] (numeric) = 1.9950021684106906698053559102442
absolute error = 1.4597894103422670e-15
relative error = 7.3172321988261319651481711015104e-14 %
Correct digits = 15
h = 1e-05
y1[1] (analytic) = 0.90014668328983429717878430886759
y1[1] (numeric) = 0.90014668328983429718608324995145
absolute error = 7.29894108386e-21
relative error = 8.1086129842571956182090945643575e-19 %
Correct digits = 20
h = 1e-05
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.4MB, time=1.70
NO POLE
NO POLE
x[1] = 0.10003
y2[1] (analytic) = 1.9950011698277749361598374697225
y2[1] (numeric) = 1.9950011698277700093605070168191
absolute error = 4.9267993304529034e-15
relative error = 2.4695721511171974006331268617216e-13 %
Correct digits = 14
h = 1e-05
y1[1] (analytic) = 0.90013673327314302192664977508368
y1[1] (numeric) = 0.90013673327314302196360072474447
absolute error = 3.695094966079e-20
relative error = 4.1050374120858566007892438959806e-18 %
Correct digits = 19
h = 1e-05
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.4MB, time=2.30
NO POLE
NO POLE
x[1] = 0.10004
y2[1] (analytic) = 1.9950001711453576257429603609593
y2[1] (numeric) = 1.9950001711453459473799358835967
absolute error = 1.16783630244773626e-14
relative error = 5.8538155501874720742004025825138e-13 %
Correct digits = 14
h = 1e-05
y1[1] (analytic) = 0.90012678326643807334711771971817
y1[1] (numeric) = 0.90012678326643807346390115899611
absolute error = 1.1678343927794e-19
relative error = 1.2974110030827960731830244916530e-17 %
Correct digits = 18
h = 1e-05
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.4MB, time=2.90
NO POLE
NO POLE
x[1] = 0.10005
y2[1] (analytic) = 1.994999172363440298212376656431
y2[1] (numeric) = 1.9949991723634174888629720240107
absolute error = 2.28093494046324203e-14
relative error = 1.1433262590084479460986606794714e-12 %
Correct digits = 13
h = 1e-05
y1[1] (analytic) = 0.90011683326972044644085862933734
y1[1] (numeric) = 0.90011683326972044672597491411343
absolute error = 2.8511628477609e-19
relative error = 3.1675475253627966174658901464378e-17 %
Correct digits = 18
h = 1e-05
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=3.51
NO POLE
NO POLE
x[1] = 0.10006
y2[1] (analytic) = 1.9949981734820230534462780880586
y2[1] (numeric) = 1.9949981734819836388099436836622
absolute error = 3.94146363344043964e-14
relative error = 1.9756728030287373114668616356807e-12 %
Correct digits = 13
h = 1e-05
y1[1] (analytic) = 0.90010688328299113620754425834015
y1[1] (numeric) = 0.90010688328299113679876235321478
absolute error = 5.9121809487463e-19
relative error = 6.5683098958010373526096098120097e-17 %
Correct digits = 18
h = 1e-05
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.4MB, time=4.09
NO POLE
NO POLE
x[1] = 0.10007
y2[1] (analytic) = 1.994997174501105991332806379486
y2[1] (numeric) = 1.9949971745010434022221779398195
absolute error = 6.25891106284396665e-14
relative error = 3.1373032216996239258725900940723e-12 %
Correct digits = 13
h = 1e-05
y1[1] (analytic) = 0.90009693330625113764584752945827
y1[1] (numeric) = 0.90009693330625113874115383114199
absolute error = 1.09530630168372e-18
relative error = 1.2168759398617463782020021941938e-16 %
Correct digits = 17
h = 1e-05
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.4MB, time=4.70
NO POLE
NO POLE
x[1] = 0.10008
y2[1] (analytic) = 1.9949961754206892117700532360923
y2[1] (numeric) = 1.9949961754205957841020008009181
absolute error = 9.34276680524351742e-14
relative error = 4.6831001083364922876524663730903e-12 %
Correct digits = 13
h = 1e-05
y1[1] (analytic) = 0.90008698333950144575344243425622
y1[1] (numeric) = 0.90008698333950144762198968447154
absolute error = 1.86854725021532e-18
relative error = 2.0759629733591287467979755134928e-16 %
Correct digits = 17
h = 1e-05
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=5.30
NO POLE
NO POLE
x[1] = 0.10009
y2[1] (analytic) = 1.994995176240772814666060335001
y2[1] (numeric) = 1.9949951762406397894527373060604
absolute error = 1.330252133230289406e-13
relative error = 6.6679466149733856727229643388036e-12 %
Correct digits = 13
h = 1e-05
y1[1] (analytic) = 0.90007703338274305552700393363162
y1[1] (numeric) = 0.90007703338274305852006022152474
absolute error = 2.99305628789312e-18
relative error = 3.3253334735632252330586748983754e-16 %
Correct digits = 17
h = 1e-05
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.4MB, time=5.91
NO POLE
NO POLE
x[1] = 0.1001
y2[1] (analytic) = 1.99499417696135689993881931509
y2[1] (numeric) = 1.9949941769611744232787116245154
absolute error = 1.824766601076905746e-13
relative error = 9.1467264523862895092208640632915e-12 %
Correct digits = 13
h = 1e-05
y1[1] (analytic) = 0.90006708343597696196220785831547
y1[1] (numeric) = 0.90006708343597696652410571237697
absolute error = 4.56189785406150e-18
relative error = 5.0683976094832871564984892090619e-16 %
Correct digits = 17
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=41.9MB, alloc=4.4MB, time=6.52
x[1] = 0.10011
y2[1] (analytic) = 1.9949931775824415675162717669993
y2[1] (numeric) = 1.9949931775821986905852471552182
absolute error = 2.428769310246117811e-13
relative error = 1.2174323890116415079844556120856e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.90005713349920416005373080937263
y1[1] (numeric) = 0.90005713349920416673281637886582
absolute error = 6.67908556949319e-18
relative error = 7.4207351076997999454546734119207e-16 %
Correct digits = 17
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=45.7MB, alloc=4.4MB, time=7.12
x[1] = 0.10012
y2[1] (analytic) = 1.9949921781040269173363092231383
y2[1] (numeric) = 1.9949921781037115963786666262696
absolute error = 3.153209576425968687e-13
relative error = 1.5805623756493483632111988721992e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.90004718357242564479525005870233
y1[1] (numeric) = 0.90004718357242565425483238459835
absolute error = 9.45958232589602e-18
relative error = 1.0510096024465610161612248351388e-15 %
Correct digits = 16
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.10013
y2[1] (analytic) = 1.994991178526113049346773147692
y2[1] (numeric) = 1.9949911785257121456662921944353
absolute error = 4.009036804809532567e-13
relative error = 2.0095511438659010886525407760526e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.90003723365564241117944344953882
y1[1] (numeric) = 0.90003723365564242420874382495727
absolute error = 1.302930037541845e-17
relative error = 1.4476401517854881014274518172528e-15 %
Correct digits = 16
h = 1e-05
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.4MB, time=7.74
NO POLE
NO POLE
x[1] = 0.10014
y2[1] (analytic) = 1.9949901788487000635054549266265
y2[1] (numeric) = 1.9949901788481993434564455446454
absolute error = 5.007200490093819811e-13
relative error = 2.5098872882589591927620444042410e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.90002728374885545419798929695208
y1[1] (numeric) = 0.90002728374885547172309071710616
absolute error = 1.752510142015408e-17
relative error = 1.9471744619960101630155275641936e-15 %
Correct digits = 16
h = 1e-05
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.4MB, time=8.34
NO POLE
NO POLE
x[1] = 0.10015
y2[1] (analytic) = 1.9949891790717880597800958576928
y2[1] (numeric) = 1.9949891790711721947584479894933
absolute error = 6.158650216478681995e-13
relative error = 3.0870594593120186472902159081228e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.90001733385206576884156628834866
y1[1] (numeric) = 0.90001733385206579193636298999371
absolute error = 2.309479670164505e-17
relative error = 2.5660391009137053148313557837658e-15 %
Correct digits = 16
h = 1e-05
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.4MB, time=8.94
NO POLE
NO POLE
x[1] = 0.10016
y2[1] (analytic) = 1.9949881791953771381483871404304
y2[1] (numeric) = 1.9949881791946297045826205687349
absolute error = 7.474335657665716955e-13
relative error = 3.7465563633967404549758568299528e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.90000738396527435009985338397263
y1[1] (numeric) = 0.90000738396527437999700047435692
absolute error = 2.989714709038429e-17
relative error = 3.3218779782297690256316983967040e-15 %
Correct digits = 16
h = 1e-05
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.4MB, time=9.55
NO POLE
NO POLE
x[1] = 0.10017
y2[1] (analytic) = 1.9949871792194673985979698661691
y2[1] (numeric) = 1.9949871792185708779402841487876
absolute error = 8.965206576857173815e-13
relative error = 4.4938667627752792525228701216665e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.89999743408848219296152971740658
y1[1] (numeric) = 0.89999743408848223106339289272334
absolute error = 3.810186317531676e-17
relative error = 4.2335524227251096780567990126029e-15 %
Correct digits = 16
h = 1e-05
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.4MB, time=10.16
NO POLE
NO POLE
x[1] = 0.10018
y2[1] (analytic) = 1.9949861791440589411264350080307
y2[1] (numeric) = 1.9949861791429947198437595222292
absolute error = 1.0642212826754858015e-12
relative error = 5.3344794756026119568841320926865e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.89998748422169029241427449607279
y1[1] (numeric) = 0.89998748422169034030387984941232
absolute error = 4.788960535333953e-17
relative error = 5.3211412595092351730990703021418e-15 %
Correct digits = 16
h = 1e-05
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.4MB, time=10.78
NO POLE
NO POLE
x[1] = 0.10019
y2[1] (analytic) = 1.9949851789691518657413234109289
y2[1] (numeric) = 1.9949851789679002353063675072965
absolute error = 1.2516304349559036324e-12
relative error = 6.2738833759288664473351121565153e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.89997753436489964344476690173442
y1[1] (numeric) = 0.89997753436489970289675082053522
absolute error = 5.945198391880080e-17
relative error = 6.6059408872639419970456512051513e-15 %
Correct digits = 16
h = 1e-05
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.4MB, time=11.40
NO POLE
NO POLE
x[1] = 0.1002
y2[1] (analytic) = 1.9949841786947462724601257815688
y2[1] (numeric) = 1.9949841786932864293424290473841
absolute error = 1.4598431176967341847e-12
relative error = 7.3175673937016502878500627216799e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.89996758451811124103868599099689
y1[1] (numeric) = 0.89996758451811131403024514399469
absolute error = 7.299155915299780e-17
relative error = 8.1104653554918003905181497566264e-15 %
Correct digits = 16
h = 1e-05
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.4MB, time=12.02
NO POLE
NO POLE
x[1] = 0.10021
y2[1] (analytic) = 1.9949831783208422613102826784449
y2[1] (numeric) = 1.9949831783191523069672653105429
absolute error = 1.6899543430173679020e-12
relative error = 8.4710205147683794867747593106137e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.89995763468132608018071059580924
y1[1] (numeric) = 0.89995763468132616890255200948291
absolute error = 8.872184141367367e-17
relative error = 9.8584464417694470372788111224329e-15 %
Correct digits = 16
h = 1e-05
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.4MB, time=12.65
NO POLE
NO POLE
x[1] = 0.10022
y2[1] (analytic) = 1.9949821778474399323291845018386
y2[1] (numeric) = 1.9949821778454968731971977889787
absolute error = 1.9430591319867128599e-12
relative error = 9.7397317808786072968048502910565e-11 %
Correct digits = 12
h = 1e-05
y1[1] (analytic) = 0.89994768485454515585451922396577
y1[1] (numeric) = 0.89994768485454526272181044847882
absolute error = 1.0686729122451305e-16
relative error = 1.1874833729005655577975086333363e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.4MB, time=13.28
NO POLE
NO POLE
x[1] = 0.10023
y2[1] (analytic) = 1.9949811772745393855641714838142
y2[1] (numeric) = 1.9949811772723191330495483985504
absolute error = 2.2202525146230852638e-12
relative error = 1.1129190289686353052765051221643e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89993773503776946304278995960755
y1[1] (numeric) = 0.89993773503776959070610932424443
absolute error = 1.2766331936463688e-16
relative error = 1.4185794682704240812836896827315e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.4MB, time=13.89
NO POLE
NO POLE
x[1] = 0.10024
y2[1] (analytic) = 1.9949801766021407210725336782145
y2[1] (numeric) = 1.9949801765996180915426395782683
absolute error = 2.5226295298940999462e-12
relative error = 1.2644885194752431050198248043722e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89992778523099999672720036372425
y1[1] (numeric) = 0.89992778523100014808348732182003
absolute error = 1.5135628695809578e-16
relative error = 1.6818714728231726896645106398240e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.4MB, time=14.51
NO POLE
NO POLE
x[1] = 0.10025
y2[1] (analytic) = 1.9949791758302440389215109506547
y2[1] (numeric) = 1.9949791758273927536957943897923
absolute error = 2.8512852257165608624e-12
relative error = 1.4292305705546779459252193249631e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89991783543423775188842737465592
y1[1] (numeric) = 0.89991783543423793009193293801852
absolute error = 1.7820350556336260e-16
relative error = 1.9802197328089845391050886581039e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.4MB, time=15.13
NO POLE
NO POLE
x[1] = 0.10026
y2[1] (analytic) = 1.994978174958849439188292968516
y2[1] (numeric) = 1.9949781749556421245293366169301
absolute error = 3.2073146589563515859e-12
relative error = 1.6076941087450789280381663862948e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89990788564748372350614720859495
y1[1] (numeric) = 0.89990788564748393197938447141863
absolute error = 2.0847323726282368e-16
relative error = 2.3166064059192812366536722607317e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=15.76
NO POLE
NO POLE
x[1] = 0.10027
y2[1] (analytic) = 1.9949771739879570219600191909375
y2[1] (numeric) = 1.9949771739843652090645908651349
absolute error = 3.5918128954283258026e-12
relative error = 1.8004280661759633337356281156636e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89989793587073890655903526008807
y1[1] (numeric) = 0.89989793587073914900373001235723
absolute error = 2.4244469475226916e-16
relative error = 2.6941354690149422640779985262332e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.4MB, time=16.39
NO POLE
NO POLE
x[1] = 0.10028
y2[1] (analytic) = 1.994976172917566887333778858808
y2[1] (numeric) = 1.9949761729135610123238826610035
absolute error = 4.0058750098961978045e-12
relative error = 2.0079813805684595311084319877990e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89988798610400429602476600253851
y1[1] (numeric) = 0.89988798610400457643280743292063
absolute error = 2.8040804143038212e-16
relative error = 3.1160327258549937013575361896289e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.5MB, time=17.00
NO POLE
NO POLE
x[1] = 0.10029
y2[1] (analytic) = 1.994975171747679135416610984756
y2[1] (numeric) = 1.994975171743228539330538551774
absolute error = 4.4505960860724329820e-12
relative error = 2.2309029952355398809742698932041e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89987803634728088688001288870823
y1[1] (numeric) = 0.89987803634728120954440437693484
absolute error = 3.2266439148822661e-16
relative error = 3.5856458148257769471658687253041e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.5MB, time=17.62
NO POLE
NO POLE
x[1] = 0.1003
y2[1] (analytic) = 1.9949741704782938663255043431386
y2[1] (numeric) = 1.9949741704733667951088862048233
absolute error = 4.9270712166181383153e-12
relative error = 2.4697418590822536477720962117780e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89986808660056967410044825122023
y1[1] (numeric) = 0.89986808660057004362625824995488
absolute error = 3.6952580999873465e-16
relative error = 4.1064442166705983559933341603784e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.5MB, time=18.21
NO POLE
NO POLE
x[1] = 0.10031
y2[1] (analytic) = 1.9949731691094111801873974600309
y2[1] (numeric) = 1.994973169103974784684254507165
absolute error = 5.4363955031429528659e-12
relative error = 2.7250469266059599148393366979532e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89985813686387165266074320306103
y1[1] (numeric) = 0.89985813686387207397605620925308
absolute error = 4.2131531300619205e-16
relative error = 4.6820192622198581556823280683573e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.5MB, time=18.80
NO POLE
NO POLE
x[1] = 0.10032
y2[1] (analytic) = 1.9949721676410311771391786032119
y2[1] (numeric) = 1.9949721676350515130829736649465
absolute error = 5.9796640562049382654e-12
relative error = 2.9973671578965605026685335216376e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89984818713718781753456753808314
y1[1] (numeric) = 0.89984818713718829590143515380639
absolute error = 4.7836686761572325e-16
relative error = 5.3160841401216608985473026417137e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.5MB, time=19.41
NO POLE
NO POLE
x[1] = 0.10033
y2[1] (analytic) = 1.9949711660731539573276857721521
y2[1] (numeric) = 1.9949711660665959853323753029466
absolute error = 6.5579719953104692055e-12
relative error = 3.2872515186367328920984907063305e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89983823742051916369458963150774
y1[1] (numeric) = 0.89983823742051970471998171428269
absolute error = 5.4102539208277495e-16
relative error = 6.0124739045729049208135151922797e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.5MB, time=20.00
NO POLE
NO POLE
x[1] = 0.10034
y2[1] (analytic) = 1.9949701644057796209097066879979
y2[1] (numeric) = 1.9949701643986072064607925640728
absolute error = 7.1724144489141239251e-12
relative error = 3.5952489801021631503849070263300e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.8998282877138666861124763404274
y1[1] (numeric) = 0.89982828771386729575923224302611
absolute error = 6.0964675590259871e-16
relative error = 6.7751454830508528413094607937169e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.5MB, time=20.61
NO POLE
NO POLE
x[1] = 0.10035
y2[1] (analytic) = 1.9949691626389082680519787835564
y2[1] (numeric) = 1.9949691626310841814975602088583
absolute error = 7.8240865544185746981e-12
relative error = 3.9219085191617788619551839576073e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.8998183380172313797588929043089
y1[1] (numeric) = 0.89981833801723206435667280404133
absolute error = 6.8459777989973243e-16
relative error = 7.6081776840451821299212987971491e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=133.5MB, alloc=4.5MB, time=21.21
x[1] = 0.10036
y2[1] (analytic) = 1.9949681607725399989311891932786
y2[1] (numeric) = 1.9949681607640259154730147149591
absolute error = 8.5140834581744783195e-12
relative error = 4.2677791182779820626445367326765e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.8998083883306142396035028454962
y1[1] (numeric) = 0.89980838833061500585973916297694
absolute error = 7.6625623631748074e-16
relative error = 8.5157712047905161098484649914594e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.10037
y2[1] (analytic) = 1.9949671588066749137339747432416
y2[1] (numeric) = 1.9949671587974314134184943766511
absolute error = 9.2435003154803665905e-12
relative error = 4.6334097655068821777644420126236e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89979843865401626061496786971342
y1[1] (numeric) = 0.89979843865401711562581677710774
absolute error = 8.5501084890739432e-16
relative error = 9.5022486389994356465952448711523e-14 %
Correct digits = 15
h = 1e-05
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.5MB, time=21.78
NO POLE
NO POLE
x[1] = 0.10038
y2[1] (analytic) = 1.9949661567413131126569219411302
y2[1] (numeric) = 1.9949661567312996803663394043268
absolute error = 1.00134322905825368034e-11
relative error = 5.0193494544985289644045832660808e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89978848898743843776094776656803
y1[1] (numeric) = 0.89978848898743938902224078531609
absolute error = 9.5126129301874806e-16
relative error = 1.0572054484595970554145312660888e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.5MB, time=22.37
NO POLE
NO POLE
x[1] = 0.10039
y2[1] (analytic) = 1.9949651545764546959065669662171
y2[1] (numeric) = 1.9949651545656297213498920239923
absolute error = 1.08249745566749422248e-11
relative error = 5.4261471844971454572165542174641e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89977853933088176600810031005403
y1[1] (numeric) = 0.89977853933088282142629599807226
absolute error = 1.05541819568801823e-15
relative error = 1.1729755151449572638279777077364e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.5MB, time=22.94
NO POLE
NO POLE
x[1] = 0.1004
y2[1] (analytic) = 1.9949641523120997636993956593421
y2[1] (numeric) = 1.9949641523004205414034965767636
absolute error = 1.16792222958990825785e-11
relative error = 5.8543519603413609183812379145709e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89976858968434724032208115905533
y1[1] (numeric) = 0.89976858968434840822521688741376
absolute error = 1.16790313572835843e-15
relative error = 1.2980038969109567851580997997501e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.5MB, time=23.51
NO POLE
NO POLE
x[1] = 0.10041
y2[1] (analytic) = 1.9949631499482484162618435128908
y2[1] (numeric) = 1.9949631499356711455624996183635
absolute error = 1.25772706993438945273e-11
relative error = 6.3045127924644437913590045275964e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89975864004783585566754375784915
y1[1] (numeric) = 0.8997586400478371448161875769237
absolute error = 1.28914864381907455e-15
relative error = 1.4327716194540090146922569086022e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.5MB, time=24.11
NO POLE
NO POLE
x[1] = 0.10042
y2[1] (analytic) = 1.9949621474849007538302956607716
y2[1] (numeric) = 1.9949621474713805388632500186179
absolute error = 1.35202149670456421537e-11
relative error = 6.7771786968945346584228794984955e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.8997486904213486070081392366096
y1[1] (numeric) = 0.89974869042135002660634183170815
absolute error = 1.41959820259509855e-15
relative error = 1.5777719019855494948503968673619e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.5MB, time=24.69
NO POLE
NO POLE
x[1] = 0.10043
y2[1] (analytic) = 1.9949611449220568766510868683922
y2[1] (numeric) = 1.9949611449075477263430990609522
absolute error = 1.45091503079878074400e-11
relative error = 7.2728986952548792022254651108189e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89973874080488648930651631191125
y1[1] (numeric) = 0.89973874080488804901276304837248
absolute error = 1.55970624673646123e-15
relative error = 1.7335101580056254160465156544627e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.5MB, time=25.28
NO POLE
NO POLE
x[1] = 0.10044
y2[1] (analytic) = 1.9949601422597168849805015226352
y2[1] (numeric) = 1.9949601422441717130404005418876
absolute error = 1.55451719401009807476e-11
relative error = 7.7922218147640611712995153580955e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89972879119845049752432118723292
y1[1] (numeric) = 0.89972879119845220746248424499677
absolute error = 1.70993816305776385e-15
relative error = 1.9005039960765331187802919168531e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.5MB, time=25.86
NO POLE
NO POLE
x[1] = 0.10045
y2[1] (analytic) = 1.994959139497880879084773621832
y2[1] (numeric) = 1.9949591394812515039945108705372
absolute error = 1.66293750902627512948e-11
relative error = 8.3356970882362353491414318897758e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.8997188416020416266221974534615
y1[1] (numeric) = 0.89971884160204349739248805111013
absolute error = 1.87077029059764863e-15
relative error = 2.0792832205965036333654365895105e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.5MB, time=26.45
NO POLE
NO POLE
x[1] = 0.10046
y2[1] (analytic) = 1.9949581366365489592400867657366
y2[1] (numeric) = 1.9949581366187861042457891681022
absolute error = 1.77628549942975976344e-11
relative error = 8.9038735540813605275294747091226e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.89970889201566087155978598939585
y1[1] (numeric) = 0.89970889201566291424970669766412
absolute error = 2.04268992070826827e-15
relative error = 2.2703898325734364159662249903844e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.5MB, time=27.03
NO POLE
NO POLE
x[1] = 0.10047
y2[1] (analytic) = 1.9949571336757212257325741454977
y2[1] (numeric) = 1.9949571336567745188355973673676
absolute error = 1.89467068969767781301e-11
relative error = 9.4973002563054324835755769436102e-10 %
Correct digits = 11
h = 1e-05
y1[1] (analytic) = 0.8996989424393092272957248622509
y1[1] (numeric) = 0.8996989424393114534910220070051
absolute error = 2.22619529714475420e-15
relative error = 2.4743780303986809616900025905599e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.5MB, time=27.60
NO POLE
NO POLE
x[1] = 0.10048
y2[1] (analytic) = 1.9949561306153977788583185336303
y2[1] (numeric) = 1.9949561305952157528063003121983
absolute error = 2.01820260520182214320e-11
relative error = 1.0116526244510716960661294398289e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89968899287298768878764922816175
y1[1] (numeric) = 0.89968899287299011058326538284564
absolute error = 2.42179561615468389e-15
relative error = 2.6918142106208666645821750596453e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.5MB, time=28.21
NO POLE
NO POLE
x[1] = 0.10049
y2[1] (analytic) = 1.9949551274555787189233522739858
y2[1] (numeric) = 1.9949551274341088112012658570349
absolute error = 2.14699077220864169509e-11
relative error = 1.0762100573895982653107662566375e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.8996790433166972509921912326879
y1[1] (numeric) = 0.89967904331669988100321780023489
absolute error = 2.63001102656754699e-15
relative error = 2.9232769687197806719586549950406e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.5MB, time=28.81
NO POLE
NO POLE
x[1] = 0.1005
y2[1] (analytic) = 1.994954124196264146243657271722
y2[1] (numeric) = 1.994954124173452699064864966389
absolute error = 2.28114471787923053330e-11
relative error = 1.1434572305256734195381136023150e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89966909377043890886497991131759
y1[1] (numeric) = 0.89966909377044176023760979552799
absolute error = 2.85137262988421040e-15
relative error = 3.1693570998802938472898604447076e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.5MB, time=29.43
NO POLE
NO POLE
x[1] = 0.10051
y2[1] (analytic) = 1.9949531208374541611451649832706
y2[1] (numeric) = 1.9949531208132464214424718143393
absolute error = 2.42077397026931689313e-11
relative error = 1.2134490504985445153981084327539e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89965914423421365736064108997225
y1[1] (numeric) = 0.89965914423421674378312145635448
absolute error = 3.08642248036638223e-15
relative error = 3.4306575997663348002459121171859e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.5MB, time=30.06
NO POLE
NO POLE
x[1] = 0.10052
y2[1] (analytic) = 1.9949521173791488639637564063053
y2[1] (numeric) = 1.9949521173534889833804638840266
absolute error = 2.56598805832925222787e-11
relative error = 1.2862404245071791024515318022545e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89964919470802249143279728551105
y1[1] (numeric) = 0.89964919470802582714638241158569
absolute error = 3.33571358512607464e-15
relative error = 3.7077936652949119758552833646561e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.5MB, time=30.64
NO POLE
NO POLE
x[1] = 0.10053
y2[1] (analytic) = 1.9949511138213483550452620697082
y2[1] (numeric) = 1.9949511137941793899262220671494
absolute error = 2.71689651190400025588e-11
relative error = 1.3618862603102882231958739669895e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.8996392451918664060340676062355
y1[1] (numeric) = 0.89963924519187000584397182130116
absolute error = 3.59980990421506566e-15
relative error = 4.0013926954101839169996162687472e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.5MB, time=31.23
NO POLE
NO POLE
x[1] = 0.10054
y2[1] (analytic) = 1.9949501101640527347454620235347
y2[1] (numeric) = 1.994950110135316646128130763459
absolute error = 2.87360886173312600757e-11
relative error = 1.4404414662263497134746914831208e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89962929568574639611606765239419
y1[1] (numeric) = 0.89962929568575027540241836675405
absolute error = 3.87928635071435986e-15
relative error = 4.3120942918575775588166005447752e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.5MB, time=31.81
NO POLE
NO POLE
x[1] = 0.10055
y2[1] (analytic) = 1.9949491064072621034300858289785
y2[1] (numeric) = 1.994949106376899757035577980255
absolute error = 3.03623463945078487235e-11
relative error = 1.5219609511336315033055600981309e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89961934618966345662940941668769
y1[1] (numeric) = 0.89961934618966763135820024033558
absolute error = 4.17472879082364789e-15
relative error = 4.6405502599579545803074246997994e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.5MB, time=32.40
NO POLE
NO POLE
x[1] = 0.10056
y2[1] (analytic) = 1.9949481025509765614748125483346
y2[1] (numeric) = 1.9949481025189277276989554318799
absolute error = 3.20488337758571164547e-11
relative error = 1.6064996244702149180865374496386e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.8996093967036185825237011847734
y1[1] (numeric) = 0.89960939670362306925774513553843
absolute error = 4.48673404395076503e-15
relative error = 4.9874246093818259718387106933049e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.5MB, time=32.98
NO POLE
NO POLE
x[1] = 0.10057
y2[1] (analytic) = 1.994947098595196209265270734962
y2[1] (numeric) = 1.9949470985613995631696586392144
absolute error = 3.37966460956120957476e-11
relative error = 1.6941123962340179801861634031652e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89959944722761276874754743577066
y1[1] (numeric) = 0.8995994472276175846574302369192
absolute error = 4.81590988280114854e-15
relative error = 5.3533935549236145881807777838315e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.5MB, time=33.58
NO POLE
NO POLE
x[1] = 0.10058
y2[1] (analytic) = 1.994946094539921147197038423245
y2[1] (numeric) = 1.994946094504314268500087029172
absolute error = 3.56068786969513940730e-11
relative error = 1.7848541769828187109320512143851e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89958949776164701024854874276586
y1[1] (numeric) = 0.89958949776165217312358221005983
absolute error = 5.16287503346729397e-15
relative error = 5.7391455172759658680023471293426e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.5MB, time=34.18
NO POLE
NO POLE
x[1] = 0.10059
y2[1] (analytic) = 1.9949450903851514756756431185538
y2[1] (numeric) = 1.9949450903476708487436440341942
absolute error = 3.74806269319990843596e-11
relative error = 1.8787798778342784329680087386493e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89957954830572230197330167331767
y1[1] (numeric) = 0.89957954830572783023247719152804
absolute error = 5.52825917551821037e-15
relative error = 6.1453811238041066561990501242966e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=221.2MB, alloc=4.5MB, time=34.78
x[1] = 0.1006
y2[1] (analytic) = 1.9949440861308872951165617872037
y2[1] (numeric) = 1.9949440860914683089547371917446
absolute error = 3.94189861618245954591e-11
relative error = 1.9759444104659650730298315389114e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.8995695988598396388673986899624
y1[1] (numeric) = 0.89956959885984555157034077883679
absolute error = 5.91270294208887439e-15
relative error = 6.5728132093202521210095481940359e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.10061
y2[1] (analytic) = 1.9949430817771287059452208464137
y2[1] (numeric) = 1.9949430817357056541887782438038
absolute error = 4.14230517564426026099e-11
relative error = 2.0764026871153764650846437842255e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89955964942400001587542805071945
y1[1] (numeric) = 0.89955964942400633273334802040272
absolute error = 6.31685791996968327e-15
relative error = 7.0221668168580607689888479788503e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.5MB, time=35.40
NO POLE
NO POLE
x[1] = 0.10062
y2[1] (analytic) = 1.994942077323875808596996154264
y2[1] (numeric) = 1.9949420772803818895021832363638
absolute error = 4.34939190948129179002e-11
relative error = 2.1802096205799636538739034697374e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.8995496999982044279409737095968
y1[1] (numeric) = 0.89954969999821116932762340550362
absolute error = 6.74138664969590682e-15
relative error = 7.4941791984471376720753369397881e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.5MB, time=36.01
NO POLE
NO POLE
x[1] = 0.10063
y2[1] (analytic) = 1.9949410727711287035172129996523
y2[1] (numeric) = 1.9949410727254960199523726189223
absolute error = 4.56326835648403807300e-11
relative error = 2.2874201242171541988350238188840e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89953975058245387000661521709673
y1[1] (numeric) = 0.89953975058246105696924085423488
absolute error = 7.18696262563713815e-15
relative error = 7.9895998158875856430270427960125e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.5MB, time=36.61
NO POLE
NO POLE
x[1] = 0.10064
y2[1] (analytic) = 1.9949400681188874911611460922496
y2[1] (numeric) = 1.9949400680710470505977713439771
absolute error = 4.78404405633747482725e-11
relative error = 2.3980891119443754784266894470695e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89952980117674933701392762072148
y1[1] (numeric) = 0.89952980117675699128422370746496
absolute error = 7.65427029608674348e-15
relative error = 8.5091903415246047291436092946221e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.5MB, time=37.20
NO POLE
NO POLE
x[1] = 0.10065
y2[1] (analytic) = 1.9949390633671522719940195524542
y2[1] (numeric) = 1.9949390633170339864978089665201
absolute error = 5.01182854962105859341e-11
relative error = 2.5122714982390779948177810697035e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89951985178109182390348136547915
y1[1] (numeric) = 0.89951985178109996790854471678988
absolute error = 8.14400506335131073e-15
relative error = 9.0537246590231396938495033832677e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.5MB, time=37.81
NO POLE
NO POLE
x[1] = 0.10066
y2[1] (analytic) = 1.9949380585159231464910069013455
y2[1] (numeric) = 1.9949380584634558327129197435315
absolute error = 5.24673137780871578140e-11
relative error = 2.6300221981387586789900507416269e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89950990239548232561484219438962
y1[1] (numeric) = 0.89950990239549098248812603448667
absolute error = 8.65687328384009705e-15
relative error = 9.6239888641425756670742581905300e-13 %
Correct digits = 14
h = 1e-05
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.5MB, time=38.41
NO POLE
NO POLE
x[1] = 0.10067
y2[1] (analytic) = 1.9949370535652002151372310506365
y2[1] (numeric) = 1.9949370535103115943045427334735
absolute error = 5.48886208326883171630e-11
relative error = 2.7513961272409841962345121644388e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89949995301992183708657104899061
y1[1] (numeric) = 0.89949995301993103067883920346586
absolute error = 9.19359226815447525e-15
relative error = 1.0220781265511481923035745594799e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.5MB, time=39.04
NO POLE
NO POLE
x[1] = 0.10068
y2[1] (analytic) = 1.994936048514983578427764292625
y2[1] (numeric) = 1.9949360484576002763351218957844
absolute error = 5.73833020926423968406e-11
relative error = 2.8764482017034142519964470577438e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89949000365441135325622396984378
y1[1] (numeric) = 0.89949000365442110814650514722299
absolute error = 9.75489028117737921e-15
relative error = 1.0844912385402403877437678343066e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.5MB, time=39.65
NO POLE
NO POLE
x[1] = 0.10069
y2[1] (analytic) = 1.9949350433652733368676282901446
y2[1] (numeric) = 1.9949350433053208838681061903723
absolute error = 5.99524529995220997723e-11
relative error = 3.0052333382438248981642838559840e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89948005429895186906035199704105
y1[1] (numeric) = 0.89948005429896221056689415978908
absolute error = 1.034150654216274803e-14
relative error = 1.1497204960506703040339536711178e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.5MB, time=40.25
NO POLE
NO POLE
x[1] = 0.1007
y2[1] (analytic) = 1.9949340381160695909717940665135
y2[1] (numeric) = 1.9949340380534724219679496771088
absolute error = 6.25971690038443894047e-11
relative error = 3.1378064541401318396820594029190e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89947010495354437943450107071087
y1[1] (numeric) = 0.89947010495355533362572589568013
absolute error = 1.095419122482496926e-14
relative error = 1.2178493942709445305757812869713e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.5MB, time=40.86
NO POLE
NO POLE
x[1] = 0.10071
y2[1] (analytic) = 1.9949330327673724412651819954836
y2[1] (numeric) = 1.9949330327020538957001116153224
absolute error = 6.53185455650703801612e-11
relative error = 3.2742224672304137416258342100234e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.8994601556181898793132119315247
y1[1] (numeric) = 0.89946015561820147301866935984563
absolute error = 1.159370545742832093e-14
relative error = 1.2889626499864337269788773482823e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.5MB, time=41.47
NO POLE
NO POLE
x[1] = 0.10072
y2[1] (analytic) = 1.9949320273191819882826617911879
y2[1] (numeric) = 1.9949320272510643101310565632921
absolute error = 6.81176781516052278958e-11
relative error = 3.4145362959129355366187591989706e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89945020629288936363002002120355
y1[1] (numeric) = 0.89945020629290162445134289761607
absolute error = 1.226082132287641252e-14
relative error = 1.3631462016568710735967523785410e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.5MB, time=42.07
NO POLE
NO POLE
x[1] = 0.10073
y2[1] (analytic) = 1.9949310217714983325690524980867
y2[1] (numeric) = 1.9949310217005026703282544777407
absolute error = 7.09956622407980203460e-11
relative error = 3.5588028591461717326349360060863e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89944025697764382731745538302465
y1[1] (numeric) = 0.89944025697765678363931418464944
absolute error = 1.295632185880162479e-14
relative error = 1.4404872094938555321995571495560e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.5MB, time=42.67
NO POLE
NO POLE
x[1] = 0.10074
y2[1] (analytic) = 1.9949300161243215746791224809134
y2[1] (numeric) = 1.994930016050367981360180813328
absolute error = 7.39535933189416675854e-11
relative error = 3.7070770764488297212221623004065e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89943030767245426530704256232815
y1[1] (numeric) = 0.89943030767246794630810021687675
absolute error = 1.368100105765454860e-14
relative error = 1.5210740555383599315442552876135e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.5MB, time=43.26
NO POLE
NO POLE
x[1] = 0.10075
y2[1] (analytic) = 1.9949290103776518151775894146189
y2[1] (numeric) = 1.9949290103006592482963166221441
absolute error = 7.69925668812727924748e-11
relative error = 3.8594138678998730860834249140517e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89942035837732167252930050702401
y1[1] (numeric) = 0.89942035837733610819316730044657
absolute error = 1.443566386679342256e-14
relative error = 1.6049963437382438603610901564144e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.5MB, time=43.88
NO POLE
NO POLE
x[1] = 0.10076
y2[1] (analytic) = 1.9949280045314891546391202743153
y2[1] (numeric) = 1.9949280044513754762071486532023
absolute error = 8.01136784319716211130e-11
relative error = 4.0158681541385449120773084348371e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89941040909224704391374246809891
y1[1] (numeric) = 0.89941040909226226503993104166855
absolute error = 1.522112618857356964e-14
relative error = 1.6923449000257713825170157224016e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.5MB, time=44.48
NO POLE
NO POLE
x[1] = 0.10077
y2[1] (analytic) = 1.9949269985858336936483313252183
y2[1] (numeric) = 1.9949269985025156701641694519321
absolute error = 8.33180234841618732862e-11
relative error = 4.1764948563643910945821947146612e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89940045981723137438887590012336
y1[1] (numeric) = 0.89940045981724741260375633695595
absolute error = 1.603821488043683259e-14
relative error = 1.7832117723951335579862113995126e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.5MB, time=45.10
NO POLE
NO POLE
x[1] = 0.10078
y2[1] (analytic) = 1.9949259925406855327997881125885
y2[1] (numeric) = 1.994925992454078835239877459672
absolute error = 8.66066975599106529165e-11
relative error = 4.3413488963372836492493320016761e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89939051055227565888220236175876
y1[1] (numeric) = 0.89939051055229254664995736276717
absolute error = 1.688776775500100841e-14
relative error = 1.8776902309799757966190449637680e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.5MB, time=45.69
NO POLE
NO POLE
x[1] = 0.10079
y2[1] (analytic) = 1.9949249863960447726980054516726
y2[1] (numeric) = 1.9949249863060639765077771131625
absolute error = 8.99807961902283385101e-11
relative error = 4.5104851963774440221748652255013e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89938056129738089232021741626474
y1[1] (numeric) = 0.8993805612973986629537975655463
absolute error = 1.777063358014928156e-14
relative error = 1.9758747681309300105500293857913e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.5MB, time=46.29
NO POLE
NO POLE
x[1] = 0.1008
y2[1] (analytic) = 1.9949239801519115139574474176422
y2[1] (numeric) = 1.9949239800584700990423789440384
absolute error = 9.34414149150684736038e-11
relative error = 4.6839586793654664004206646396923e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89937061205254806962841053200644
y1[1] (numeric) = 0.89937061205256675730048965166268
absolute error = 1.868767207911965624e-14
relative error = 2.0778610984931516022431654407208e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.5MB, time=46.90
NO POLE
NO POLE
x[1] = 0.10081
y2[1] (analytic) = 1.9949229738082858572025273355328
y2[1] (numeric) = 1.9949229737112962079191996783215
absolute error = 9.69896492833276572113e-11
relative error = 4.8618242687423410229591587640182e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89936066281777818573126498296202
y1[1] (numeric) = 0.89936066281779782548519557734945
absolute error = 1.963975393059438743e-14
relative error = 2.1837461590838612540146675695765e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.5MB, time=47.51
NO POLE
NO POLE
x[1] = 0.10082
y2[1] (analytic) = 1.9949219673651679030676077701814
y2[1] (numeric) = 1.9949219672645413082147623359132
absolute error = 1.006265948528454342682e-10
relative error = 5.0441368885094774919870469605709e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89935071359307223555225774923015
y1[1] (numeric) = 0.89935071359309286331302653864109
absolute error = 2.062776076878941094e-14
relative error = 2.2936281093698915471371846026213e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.5MB, time=48.11
NO POLE
NO POLE
x[1] = 0.10083
y2[1] (analytic) = 1.9949209608225577521970005161627
y2[1] (numeric) = 1.9949209607182044050065963300866
absolute error = 1.043533471904041860761e-10
relative error = 5.2309514632287280846279577044552e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89934076437843121401385941753771
y1[1] (numeric) = 0.89934076437845286659904296131001
absolute error = 2.165258518354377230e-14
relative error = 2.4076063313452383919312337106622e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=308.9MB, alloc=4.5MB, time=48.70
x[1] = 0.10084
y2[1] (analytic) = 1.9949199541804555052449665877249
y2[1] (numeric) = 1.9949199540722845033732375669789
absolute error = 1.081710018717290207460e-10
relative error = 5.4223229180224110650340932261642e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89933081517385611603753408174754
y1[1] (numeric) = 0.89933081517387883116825449080209
absolute error = 2.271513072040905455e-14
relative error = 2.5257814296086172758224853149724e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.10085
y2[1] (analytic) = 1.9949189474388612628757162087245
memory used=312.8MB, alloc=4.5MB, time=49.29
y2[1] (numeric) = 1.9949189473267806083942285450834
absolute error = 1.120806544814876636411e-10
relative error = 5.6183061785733339968918885086026e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89932086597934793654373924336626
y1[1] (numeric) = 0.89932086597937175285561998217129
absolute error = 2.381631188073880503e-14
relative error = 2.6482552314410243407919488338961e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.10086
y2[1] (analytic) = 1.9949179405977751257634088025593
y2[1] (numeric) = 1.9949179404816917251501184547417
absolute error = 1.160834006132903478176e-10
relative error = 5.8189561711248170562615215796033e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89931091679490767045192571205226
y1[1] (numeric) = 0.89931091679493262750604749001319
absolute error = 2.495705412177796093e-14
relative error = 2.7751307868833022638403898553863e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.5MB, time=49.88
NO POLE
NO POLE
x[1] = 0.10087
y2[1] (analytic) = 1.9949169336571971945921529821017
y2[1] (numeric) = 1.9949169335370168587224632776357
absolute error = 1.201803358696897044660e-10
relative error = 6.0243278224807163448756086195383e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89930096762053631268053750612372
y1[1] (numeric) = 0.8993009676205624509743942583976
absolute error = 2.613829385675227388e-14
relative error = 2.9065123688137109719086572487447e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.5MB, time=50.49
NO POLE
NO POLE
x[1] = 0.10088
y2[1] (analytic) = 1.9949159266171275700560065396295
y2[1] (numeric) = 1.9949159264927550141938258862792
absolute error = 1.243725558621806533503e-10
relative error = 6.2344760600054472037667680386508e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89929101845623485814701175306682
y1[1] (numeric) = 0.89929101845626221912546671080014
absolute error = 2.736097845495773332e-14
relative error = 3.0425054730255031626510726151881e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.5MB, time=51.09
NO POLE
NO POLE
x[1] = 0.10089
y2[1] (analytic) = 1.9949149194775663528589764367573
y2[1] (numeric) = 1.9949149193489051966477761435098
absolute error = 1.286611562112002932475e-10
relative error = 6.4494558116240075273443744081064e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89928106930200430176777859004392
y1[1] (numeric) = 0.89928106930203292783402044003284
absolute error = 2.862606624184998892e-14
relative error = 3.1832168183045046613924643219894e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.5MB, time=51.69
NO POLE
NO POLE
x[1] = 0.1009
y2[1] (analytic) = 1.9949139122385136437150187943654
y2[1] (numeric) = 1.9949139121054664111688910019806
absolute error = 1.330472325461277923848e-10
relative error = 6.6693220058220010777901862331335e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89927112015784563845826106440201
y1[1] (numeric) = 0.89927112015787557298476019817374
absolute error = 2.993452649913377173e-14
relative error = 3.3287543465066995789934168281936e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.5MB, time=52.30
NO POLE
NO POLE
x[1] = 0.10091
y2[1] (analytic) = 1.9949129048999695433480388825288
y2[1] (numeric) = 1.9949129047624376628427546036515
absolute error = 1.375318805052842788773e-10
relative error = 6.8941295716456607999132195396560e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89926117102375986313287503418106
y1[1] (numeric) = 0.89926117102379115047233988649548
absolute error = 3.128733946485231442e-14
relative error = 3.4792272226358203109628092397503e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=335.6MB, alloc=4.5MB, time=52.90
NO POLE
NO POLE
x[1] = 0.10092
y2[1] (analytic) = 1.9949118974619341524918911104449
y2[1] (numeric) = 1.994911897319817956755958379281
absolute error = 1.421161957359327311639e-10
relative error = 7.1239334387018721363485894254431e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89925122189974797070502906862268
y1[1] (numeric) = 0.89925122189978065620136254539292
absolute error = 3.268549633347677024e-14
relative error = 3.6347458349209423369816314668526e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.5MB, time=53.51
NO POLE
NO POLE
x[1] = 0.10093
y2[1] (analytic) = 1.9949108899244075718903790163596
y2[1] (numeric) = 1.9949108897776062979961011479172
absolute error = 1.468012738942778684424e-10
relative error = 7.3587885371581963431504621840650e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89924127278581095608712434867872
y1[1] (numeric) = 0.89924127278584508608638034430976
absolute error = 3.412999925599563104e-14
relative error = 3.7954217948940838589538964045793e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.5MB, time=54.11
NO POLE
NO POLE
x[1] = 0.10094
y2[1] (analytic) = 1.9949098822873899022972552574936
y2[1] (numeric) = 1.9949098821358016916517892163892
absolute error = 1.515882106454660411044e-10
relative error = 7.5987497977428938058092097817352e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89923132368194981419055456752003
y1[1] (numeric) = 0.89923132368198543605189457166415
absolute error = 3.562186134000414412e-14
relative error = 3.9613679374678102523163624420740e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.5MB, time=54.72
NO POLE
NO POLE
x[1] = 0.10095
y2[1] (analytic) = 1.9949088745508812444762215999664
y2[1] (numeric) = 1.9949088743944031428126364787983
absolute error = 1.564781016635851211681e-10
relative error = 7.8438721517449473555975395816491e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89922137458816553992570583104535
y1[1] (numeric) = 0.89922137458820270203235562477332
absolute error = 3.716210664979372797e-14
relative error = 4.1326983210128433375866608779173e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=350.9MB, alloc=4.5MB, time=55.31
NO POLE
NO POLE
x[1] = 0.10096
y2[1] (analytic) = 1.9949078667148816992009289087204
y2[1] (numeric) = 1.994907866553409656569264516009
absolute error = 1.614720426316643927114e-10
relative error = 8.0942105310140855863659206275030e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89921142550445912820195655839026
y1[1] (numeric) = 0.8992114255044978799721629997772
absolute error = 3.875177020644138694e-14
relative error = 4.3095282274356754769058633610338e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=354.7MB, alloc=4.5MB, time=55.90
NO POLE
NO POLE
x[1] = 0.10097
y2[1] (analytic) = 1.9949068587793913672549771374432
y2[1] (numeric) = 1.9949068586128202380133026951398
absolute error = 1.665711292416744423034e-10
relative error = 8.3498198679608061716920793739253e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89920147643083157392767738243623
y1[1] (numeric) = 0.89920147643087196582566528156108
absolute error = 4.039189798789912485e-14
relative error = 4.4919741622561884969956457767668e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.5MB, time=56.50
NO POLE
NO POLE
x[1] = 0.10098
y2[1] (analytic) = 1.9949058507444103494319153184895
y2[1] (numeric) = 1.9949058505726338922373882690541
absolute error = 1.717764571945270494354e-10
relative error = 8.6107550955563991824397204037897e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89919152736728387201023105031979
y1[1] (numeric) = 0.89919152736732595555716013367722
absolute error = 4.208354692908335743e-14
relative error = 4.6801538546852774266050030026258e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=362.4MB, alloc=4.5MB, time=57.09
NO POLE
NO POLE
x[1] = 0.10099
y2[1] (analytic) = 1.9949048426099387465352415528016
y2[1] (numeric) = 1.9949048424328496243351664758511
absolute error = 1.770891222000750769505e-10
relative error = 8.8770711473329704046813724870816e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.8991815783138170173559723239418
y1[1] (numeric) = 0.89918157831386084514089428826551
absolute error = 4.382778492196432371e-14
relative error = 4.8741862577024790620992230089344e-12 %
Correct digits = 13
h = 1e-05
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.5MB, time=57.68
NO POLE
NO POLE
x[1] = 0.101
y2[1] (analytic) = 1.994903834375976659378402999829
y2[1] (numeric) = 1.9949038341934664394012906383562
absolute error = 1.825102199771123614728e-10
relative error = 9.1488229573834646580355028402080e-09 %
Correct digits = 10
h = 1e-05
y1[1] (analytic) = 0.89917162927043200487024788047681
y1[1] (numeric) = 0.89917162927047763056106353597311
absolute error = 4.562569081565549630e-14
relative error = 5.0741915481336053548266058606399e-12 %
Correct digits = 13
h = 1e-05
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y2 , x , 3 ) = m1 * cos(x) ;
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
Iterations = 100
Total Elapsed Time = 57 Seconds
Elapsed Time(since restart) = 57 Seconds
Expected Time Remaining = 3 Days 5 Hours 52 Minutes 4 Seconds
Optimized Time Remaining = 3 Days 5 Hours 48 Minutes 16 Seconds
Time to Timeout = 2 Seconds
Percent Done = 0.02061 %
> quit
memory used=367.8MB, alloc=4.5MB, time=57.91