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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
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> min_in_hour,
> glob_display_flag,
> djd_debug,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmax,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_normmax,
> glob_start,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_not_yet_start_msg,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_reached_optimal_h,
> glob_max_hours,
> glob_relerr,
> glob_look_poles,
> glob_h,
> glob_html_log,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_order,
> glob_abserr,
> glob_log10_abserr,
> glob_large_float,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_relerr,
> glob_last_good_h,
> glob_disp_incr,
> glob_optimal_done,
> years_in_century,
> djd_debug2,
> glob_log10relerr,
> glob_current_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin,
> glob_clock_sec,
> glob_almost_1,
> days_in_year,
> sec_in_min,
> glob_dump,
> glob_max_minutes,
> glob_small_float,
> glob_initial_pass,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> #END CONST
> array_type_pole,
> array_norms,
> array_x1_init,
> array_last_rel_error,
> array_1st_rel_error,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2,
> array_x1,
> array_pole,
> array_x2_init,
> array_m1,
> array_x2_higher_work,
> array_complex_pole,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_poles,
> array_x1_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_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_x2(ind_var);
> omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x2[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_x1(ind_var);
> omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_orig_start_sec, glob_max_rel_trunc_err, glob_not_yet_finished,
min_in_hour, glob_display_flag, djd_debug, glob_optimal_clock_start_sec,
glob_no_eqs, glob_max_trunc_err, glob_hmax, centuries_in_millinium,
glob_max_opt_iter, glob_log10normmin, glob_log10abserr, glob_normmax,
glob_start, glob_max_sec, glob_unchanged_h_cnt, glob_not_yet_start_msg,
glob_hmin_init, glob_clock_start_sec, glob_optimal_expect_sec,
glob_reached_optimal_h, glob_max_hours, glob_relerr, glob_look_poles,
glob_h, glob_html_log, glob_percent_done, MAX_UNCHANGED, glob_optimal_start,
glob_max_order, glob_abserr, glob_log10_abserr, glob_large_float, glob_iter,
glob_curr_iter_when_opt, glob_warned, glob_smallish_float, glob_max_iter,
glob_log10_relerr, glob_last_good_h, glob_disp_incr, glob_optimal_done,
years_in_century, djd_debug2, glob_log10relerr, glob_current_iter,
glob_warned2, glob_dump_analytic, glob_hmin, glob_clock_sec, glob_almost_1,
days_in_year, sec_in_min, glob_dump, glob_max_minutes, glob_small_float,
glob_initial_pass, hours_in_day, array_const_3D0, array_const_0D0,
array_const_4D0, array_const_1, array_const_2, array_const_2D0,
array_type_pole, array_norms, array_x1_init, array_last_rel_error,
array_1st_rel_error, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_pole,
array_x2_init, array_m1, array_x2_higher_work, array_complex_pole,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x1_higher_work2, array_x1_higher_work, array_poles, array_x1_higher,
glob_last;
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_x2(ind_var);
omniout_float(ALWAYS, "x2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x2[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x2[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_x1(ind_var);
omniout_float(ALWAYS, "x1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x1[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> min_in_hour,
> glob_display_flag,
> djd_debug,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmax,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_normmax,
> glob_start,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_not_yet_start_msg,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_reached_optimal_h,
> glob_max_hours,
> glob_relerr,
> glob_look_poles,
> glob_h,
> glob_html_log,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_order,
> glob_abserr,
> glob_log10_abserr,
> glob_large_float,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_relerr,
> glob_last_good_h,
> glob_disp_incr,
> glob_optimal_done,
> years_in_century,
> djd_debug2,
> glob_log10relerr,
> glob_current_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin,
> glob_clock_sec,
> glob_almost_1,
> days_in_year,
> sec_in_min,
> glob_dump,
> glob_max_minutes,
> glob_small_float,
> glob_initial_pass,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> #END CONST
> array_type_pole,
> array_norms,
> array_x1_init,
> array_last_rel_error,
> array_1st_rel_error,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2,
> array_x1,
> array_pole,
> array_x2_init,
> array_m1,
> array_x2_higher_work,
> array_complex_pole,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_poles,
> array_x1_higher,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_t[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_orig_start_sec, glob_max_rel_trunc_err, glob_not_yet_finished,
min_in_hour, glob_display_flag, djd_debug, glob_optimal_clock_start_sec,
glob_no_eqs, glob_max_trunc_err, glob_hmax, centuries_in_millinium,
glob_max_opt_iter, glob_log10normmin, glob_log10abserr, glob_normmax,
glob_start, glob_max_sec, glob_unchanged_h_cnt, glob_not_yet_start_msg,
glob_hmin_init, glob_clock_start_sec, glob_optimal_expect_sec,
glob_reached_optimal_h, glob_max_hours, glob_relerr, glob_look_poles,
glob_h, glob_html_log, glob_percent_done, MAX_UNCHANGED, glob_optimal_start,
glob_max_order, glob_abserr, glob_log10_abserr, glob_large_float, glob_iter,
glob_curr_iter_when_opt, glob_warned, glob_smallish_float, glob_max_iter,
glob_log10_relerr, glob_last_good_h, glob_disp_incr, glob_optimal_done,
years_in_century, djd_debug2, glob_log10relerr, glob_current_iter,
glob_warned2, glob_dump_analytic, glob_hmin, glob_clock_sec, glob_almost_1,
days_in_year, sec_in_min, glob_dump, glob_max_minutes, glob_small_float,
glob_initial_pass, hours_in_day, array_const_3D0, array_const_0D0,
array_const_4D0, array_const_1, array_const_2, array_const_2D0,
array_type_pole, array_norms, array_x1_init, array_last_rel_error,
array_1st_rel_error, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_pole,
array_x2_init, array_m1, array_x2_higher_work, array_complex_pole,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x1_higher_work2, array_x1_higher_work, array_poles, array_x1_higher,
glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_t[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(t_start,t_end)
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> min_in_hour,
> glob_display_flag,
> djd_debug,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmax,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_normmax,
> glob_start,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_not_yet_start_msg,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_reached_optimal_h,
> glob_max_hours,
> glob_relerr,
> glob_look_poles,
> glob_h,
> glob_html_log,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_order,
> glob_abserr,
> glob_log10_abserr,
> glob_large_float,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_relerr,
> glob_last_good_h,
> glob_disp_incr,
> glob_optimal_done,
> years_in_century,
> djd_debug2,
> glob_log10relerr,
> glob_current_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin,
> glob_clock_sec,
> glob_almost_1,
> days_in_year,
> sec_in_min,
> glob_dump,
> glob_max_minutes,
> glob_small_float,
> glob_initial_pass,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> #END CONST
> array_type_pole,
> array_norms,
> array_x1_init,
> array_last_rel_error,
> array_1st_rel_error,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2,
> array_x1,
> array_pole,
> array_x2_init,
> array_m1,
> array_x2_higher_work,
> array_complex_pole,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_poles,
> array_x1_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(t_end),convfloat(t_start),convfloat(array_t[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(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[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(t_start, t_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_orig_start_sec, glob_max_rel_trunc_err, glob_not_yet_finished,
min_in_hour, glob_display_flag, djd_debug, glob_optimal_clock_start_sec,
glob_no_eqs, glob_max_trunc_err, glob_hmax, centuries_in_millinium,
glob_max_opt_iter, glob_log10normmin, glob_log10abserr, glob_normmax,
glob_start, glob_max_sec, glob_unchanged_h_cnt, glob_not_yet_start_msg,
glob_hmin_init, glob_clock_start_sec, glob_optimal_expect_sec,
glob_reached_optimal_h, glob_max_hours, glob_relerr, glob_look_poles,
glob_h, glob_html_log, glob_percent_done, MAX_UNCHANGED, glob_optimal_start,
glob_max_order, glob_abserr, glob_log10_abserr, glob_large_float, glob_iter,
glob_curr_iter_when_opt, glob_warned, glob_smallish_float, glob_max_iter,
glob_log10_relerr, glob_last_good_h, glob_disp_incr, glob_optimal_done,
years_in_century, djd_debug2, glob_log10relerr, glob_current_iter,
glob_warned2, glob_dump_analytic, glob_hmin, glob_clock_sec, glob_almost_1,
days_in_year, sec_in_min, glob_dump, glob_max_minutes, glob_small_float,
glob_initial_pass, hours_in_day, array_const_3D0, array_const_0D0,
array_const_4D0, array_const_1, array_const_2, array_const_2D0,
array_type_pole, array_norms, array_x1_init, array_last_rel_error,
array_1st_rel_error, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_pole,
array_x2_init, array_m1, array_x2_higher_work, array_complex_pole,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x1_higher_work2, array_x1_higher_work, array_poles, array_x1_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(t_end), convfloat(t_start),
convfloat(array_t[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(t_end),
convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(t_end), convfloat(t_start),
convfloat(array_t[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
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> min_in_hour,
> glob_display_flag,
> djd_debug,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmax,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_normmax,
> glob_start,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_not_yet_start_msg,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_reached_optimal_h,
> glob_max_hours,
> glob_relerr,
> glob_look_poles,
> glob_h,
> glob_html_log,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_order,
> glob_abserr,
> glob_log10_abserr,
> glob_large_float,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_relerr,
> glob_last_good_h,
> glob_disp_incr,
> glob_optimal_done,
> years_in_century,
> djd_debug2,
> glob_log10relerr,
> glob_current_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin,
> glob_clock_sec,
> glob_almost_1,
> days_in_year,
> sec_in_min,
> glob_dump,
> glob_max_minutes,
> glob_small_float,
> glob_initial_pass,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> #END CONST
> array_type_pole,
> array_norms,
> array_x1_init,
> array_last_rel_error,
> array_1st_rel_error,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2,
> array_x1,
> array_pole,
> array_x2_init,
> array_m1,
> array_x2_higher_work,
> array_complex_pole,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_poles,
> array_x1_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 - 2 - 1;
> while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_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_x2_higher[1,m]/array_x2_higher[1,m-1];
> rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_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_x1_higher[1,m]/array_x1_higher[1,m-1];
> rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_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_x2_higher[1,m])/(array_x2_higher[1,m-1]);
> rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]);
> rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]);
> rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]);
> rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_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_x1_higher[1,m])/(array_x1_higher[1,m-1]);
> rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]);
> rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]);
> rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]);
> rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4
> ;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3
> ;
> #BOTTOM RADII COMPLEX EQ = 2
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 2
> if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 2
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if array_pole[1] > array_poles[2,1] then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 2
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_orig_start_sec, glob_max_rel_trunc_err, glob_not_yet_finished,
min_in_hour, glob_display_flag, djd_debug, glob_optimal_clock_start_sec,
glob_no_eqs, glob_max_trunc_err, glob_hmax, centuries_in_millinium,
glob_max_opt_iter, glob_log10normmin, glob_log10abserr, glob_normmax,
glob_start, glob_max_sec, glob_unchanged_h_cnt, glob_not_yet_start_msg,
glob_hmin_init, glob_clock_start_sec, glob_optimal_expect_sec,
glob_reached_optimal_h, glob_max_hours, glob_relerr, glob_look_poles,
glob_h, glob_html_log, glob_percent_done, MAX_UNCHANGED, glob_optimal_start,
glob_max_order, glob_abserr, glob_log10_abserr, glob_large_float, glob_iter,
glob_curr_iter_when_opt, glob_warned, glob_smallish_float, glob_max_iter,
glob_log10_relerr, glob_last_good_h, glob_disp_incr, glob_optimal_done,
years_in_century, djd_debug2, glob_log10relerr, glob_current_iter,
glob_warned2, glob_dump_analytic, glob_hmin, glob_clock_sec, glob_almost_1,
days_in_year, sec_in_min, glob_dump, glob_max_minutes, glob_small_float,
glob_initial_pass, hours_in_day, array_const_3D0, array_const_0D0,
array_const_4D0, array_const_1, array_const_2, array_const_2D0,
array_type_pole, array_norms, array_x1_init, array_last_rel_error,
array_1st_rel_error, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_pole,
array_x2_init, array_m1, array_x2_higher_work, array_complex_pole,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x1_higher_work2, array_x1_higher_work, array_poles, array_x1_higher,
glob_last;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or
abs(array_x2_higher[1, m - 1]) < glob_small_float or
abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or
abs(array_x1_higher[1, m - 1]) < glob_small_float or
abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_x2_higher[1, m]) or
glob_large_float <= abs(array_x2_higher[1, m - 1]) or
glob_large_float <= abs(array_x2_higher[1, m - 2]) or
glob_large_float <= abs(array_x2_higher[1, m - 3]) or
glob_large_float <= abs(array_x2_higher[1, m - 4]) or
glob_large_float <= abs(array_x2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3];
rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4];
rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= abs(array_x1_higher[1, m]) or
glob_large_float <= abs(array_x1_higher[1, m - 1]) or
glob_large_float <= abs(array_x1_higher[1, m - 2]) or
glob_large_float <= abs(array_x1_higher[1, m - 3]) or
glob_large_float <= abs(array_x1_higher[1, m - 4]) or
glob_large_float <= abs(array_x1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3];
rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4];
rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[2, 1] := rad_c;
array_complex_pole[2, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> min_in_hour,
> glob_display_flag,
> djd_debug,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmax,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_normmax,
> glob_start,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_not_yet_start_msg,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_reached_optimal_h,
> glob_max_hours,
> glob_relerr,
> glob_look_poles,
> glob_h,
> glob_html_log,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_order,
> glob_abserr,
> glob_log10_abserr,
> glob_large_float,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_relerr,
> glob_last_good_h,
> glob_disp_incr,
> glob_optimal_done,
> years_in_century,
> djd_debug2,
> glob_log10relerr,
> glob_current_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin,
> glob_clock_sec,
> glob_almost_1,
> days_in_year,
> sec_in_min,
> glob_dump,
> glob_max_minutes,
> glob_small_float,
> glob_initial_pass,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> #END CONST
> array_type_pole,
> array_norms,
> array_x1_init,
> array_last_rel_error,
> array_1st_rel_error,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2,
> array_x1,
> array_pole,
> array_x2_init,
> array_m1,
> array_x2_higher_work,
> array_complex_pole,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_poles,
> array_x1_higher,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 3
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_orig_start_sec, glob_max_rel_trunc_err, glob_not_yet_finished,
min_in_hour, glob_display_flag, djd_debug, glob_optimal_clock_start_sec,
glob_no_eqs, glob_max_trunc_err, glob_hmax, centuries_in_millinium,
glob_max_opt_iter, glob_log10normmin, glob_log10abserr, glob_normmax,
glob_start, glob_max_sec, glob_unchanged_h_cnt, glob_not_yet_start_msg,
glob_hmin_init, glob_clock_start_sec, glob_optimal_expect_sec,
glob_reached_optimal_h, glob_max_hours, glob_relerr, glob_look_poles,
glob_h, glob_html_log, glob_percent_done, MAX_UNCHANGED, glob_optimal_start,
glob_max_order, glob_abserr, glob_log10_abserr, glob_large_float, glob_iter,
glob_curr_iter_when_opt, glob_warned, glob_smallish_float, glob_max_iter,
glob_log10_relerr, glob_last_good_h, glob_disp_incr, glob_optimal_done,
years_in_century, djd_debug2, glob_log10relerr, glob_current_iter,
glob_warned2, glob_dump_analytic, glob_hmin, glob_clock_sec, glob_almost_1,
days_in_year, sec_in_min, glob_dump, glob_max_minutes, glob_small_float,
glob_initial_pass, hours_in_day, array_const_3D0, array_const_0D0,
array_const_4D0, array_const_1, array_const_2, array_const_2D0,
array_type_pole, array_norms, array_x1_init, array_last_rel_error,
array_1st_rel_error, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_pole,
array_x2_init, array_m1, array_x2_higher_work, array_complex_pole,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x1_higher_work2, array_x1_higher_work, array_poles, array_x1_higher,
glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x2[iii]) then
array_norms[iii] := abs(array_x2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x1[iii]) then
array_norms[iii] := abs(array_x1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> min_in_hour,
> glob_display_flag,
> djd_debug,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmax,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_normmax,
> glob_start,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_not_yet_start_msg,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_reached_optimal_h,
> glob_max_hours,
> glob_relerr,
> glob_look_poles,
> glob_h,
> glob_html_log,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_order,
> glob_abserr,
> glob_log10_abserr,
> glob_large_float,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_relerr,
> glob_last_good_h,
> glob_disp_incr,
> glob_optimal_done,
> years_in_century,
> djd_debug2,
> glob_log10relerr,
> glob_current_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin,
> glob_clock_sec,
> glob_almost_1,
> days_in_year,
> sec_in_min,
> glob_dump,
> glob_max_minutes,
> glob_small_float,
> glob_initial_pass,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> #END CONST
> array_type_pole,
> array_norms,
> array_x1_init,
> array_last_rel_error,
> array_1st_rel_error,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2,
> array_x1,
> array_pole,
> array_x2_init,
> array_m1,
> array_x2_higher_work,
> array_complex_pole,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_poles,
> array_x1_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1
> array_tmp1[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp4[1] := (array_const_2D0[1] * (array_x2[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp6[1] := array_x1_higher[3,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp8[1] := array_x1_higher[2,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp10[1] := array_tmp9[1] + array_x1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2);
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> # emit pre mult $eq_no = 2 i = 1
> array_tmp12[1] := (array_const_4D0[1] * (array_x2[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1]));
> # emit pre mult $eq_no = 2 i = 1
> array_tmp16[1] := (array_const_2D0[1] * (array_x1[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2
> array_tmp1[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp4[2] := ats(2,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp6[2] := array_x1_higher[3,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp8[2] := array_x1_higher[2,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2]));
> #emit pre add $eq_no = 1 i = 2
> array_tmp10[2] := array_tmp9[2] + array_x1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> # emit pre mult $eq_no = 2 i = 2
> array_tmp12[2] := ats(2,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2]));
> # emit pre mult $eq_no = 2 i = 2
> array_tmp16[2] := ats(2,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2]));
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3
> array_tmp1[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp4[3] := ats(3,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp6[3] := array_x1_higher[3,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp8[3] := array_x1_higher[2,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3]));
> #emit pre add $eq_no = 1 i = 3
> array_tmp10[3] := array_tmp9[3] + array_x1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> # emit pre mult $eq_no = 2 i = 3
> array_tmp12[3] := ats(3,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3]));
> # emit pre mult $eq_no = 2 i = 3
> array_tmp16[3] := ats(3,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3]));
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4
> array_tmp1[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp4[4] := ats(4,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp6[4] := array_x1_higher[3,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp8[4] := array_x1_higher[2,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4]));
> #emit pre add $eq_no = 1 i = 4
> array_tmp10[4] := array_tmp9[4] + array_x1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> # emit pre mult $eq_no = 2 i = 4
> array_tmp12[4] := ats(4,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4]));
> # emit pre mult $eq_no = 2 i = 4
> array_tmp16[4] := ats(4,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4]));
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5
> array_tmp1[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp4[5] := ats(5,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp6[5] := array_x1_higher[3,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp8[5] := array_x1_higher[2,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5]));
> #emit pre add $eq_no = 1 i = 5
> array_tmp10[5] := array_tmp9[5] + array_x1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> # emit pre mult $eq_no = 2 i = 5
> array_tmp12[5] := ats(5,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5]));
> # emit pre mult $eq_no = 2 i = 5
> array_tmp16[5] := ats(5,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5]));
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,5] := temporary
> ;
> 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 diff $eq_no = 1
> array_tmp1[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1);
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
> #emit mult $eq_no = 1
> array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1);
> #emit sub $eq_no = 1
> array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk]));
> #emit diff $eq_no = 1
> array_tmp6[kkk] := array_x1_higher[3,kkk];
> #emit sub $eq_no = 1
> array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk]));
> #emit diff $eq_no = 1
> array_tmp8[kkk] := array_x1_higher[2,kkk];
> #emit sub $eq_no = 1
> array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk]));
> #emit add $eq_no = 1
> array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x2[kkk + order_d] := temporary;
> array_x2_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_x2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> #emit mult $eq_no = 2
> array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1);
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 2
> array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1);
> #emit sub $eq_no = 2
> array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk]));
> #emit mult $eq_no = 2
> array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1);
> #emit sub $eq_no = 2
> array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk]));
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x1[kkk + order_d] := temporary;
> array_x1_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_x1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_orig_start_sec, glob_max_rel_trunc_err, glob_not_yet_finished,
min_in_hour, glob_display_flag, djd_debug, glob_optimal_clock_start_sec,
glob_no_eqs, glob_max_trunc_err, glob_hmax, centuries_in_millinium,
glob_max_opt_iter, glob_log10normmin, glob_log10abserr, glob_normmax,
glob_start, glob_max_sec, glob_unchanged_h_cnt, glob_not_yet_start_msg,
glob_hmin_init, glob_clock_start_sec, glob_optimal_expect_sec,
glob_reached_optimal_h, glob_max_hours, glob_relerr, glob_look_poles,
glob_h, glob_html_log, glob_percent_done, MAX_UNCHANGED, glob_optimal_start,
glob_max_order, glob_abserr, glob_log10_abserr, glob_large_float, glob_iter,
glob_curr_iter_when_opt, glob_warned, glob_smallish_float, glob_max_iter,
glob_log10_relerr, glob_last_good_h, glob_disp_incr, glob_optimal_done,
years_in_century, djd_debug2, glob_log10relerr, glob_current_iter,
glob_warned2, glob_dump_analytic, glob_hmin, glob_clock_sec, glob_almost_1,
days_in_year, sec_in_min, glob_dump, glob_max_minutes, glob_small_float,
glob_initial_pass, hours_in_day, array_const_3D0, array_const_0D0,
array_const_4D0, array_const_1, array_const_2, array_const_2D0,
array_type_pole, array_norms, array_x1_init, array_last_rel_error,
array_1st_rel_error, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_pole,
array_x2_init, array_m1, array_x2_higher_work, array_complex_pole,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x1_higher_work2, array_x1_higher_work, array_poles, array_x1_higher,
glob_last;
array_tmp1[1] := array_x2_higher[2, 1];
array_tmp2[1] := array_const_3D0[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_const_2D0[1]*array_x2[1];
array_tmp5[1] := array_tmp3[1] - array_tmp4[1];
array_tmp6[1] := array_x1_higher[3, 1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
array_tmp8[1] := array_x1_higher[2, 1];
array_tmp9[1] := array_tmp7[1] - array_tmp8[1];
array_tmp10[1] := array_tmp9[1] + array_x1[1];
if 1 <= glob_max_terms then
temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2);
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 1] := temporary
end if;
kkk := 2;
array_tmp12[1] := array_const_4D0[1]*array_x2[1];
array_tmp13[1] := array_x2_higher[2, 1];
array_tmp14[1] := array_const_2D0[1]*array_tmp13[1];
array_tmp15[1] := array_tmp12[1] - array_tmp14[1];
array_tmp16[1] := array_const_2D0[1]*array_x1[1];
array_tmp17[1] := array_tmp15[1] - array_tmp16[1];
if 1 <= glob_max_terms then
temporary := array_tmp17[1]*glob_h*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 1] := temporary
end if;
kkk := 2;
array_tmp1[2] := array_x2_higher[2, 2];
array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1);
array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1);
array_tmp5[2] := array_tmp3[2] - array_tmp4[2];
array_tmp6[2] := array_x1_higher[3, 2];
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
array_tmp8[2] := array_x1_higher[2, 2];
array_tmp9[2] := array_tmp7[2] - array_tmp8[2];
array_tmp10[2] := array_tmp9[2] + array_x1[2];
if 2 <= glob_max_terms then
temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 2] := temporary
end if;
kkk := 3;
array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1);
array_tmp13[2] := array_x2_higher[2, 2];
array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1);
array_tmp15[2] := array_tmp12[2] - array_tmp14[2];
array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1);
array_tmp17[2] := array_tmp15[2] - array_tmp16[2];
if 2 <= glob_max_terms then
temporary := array_tmp17[2]*glob_h*factorial_3(1, 2);
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 2] := temporary
end if;
kkk := 3;
array_tmp1[3] := array_x2_higher[2, 3];
array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1);
array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1);
array_tmp5[3] := array_tmp3[3] - array_tmp4[3];
array_tmp6[3] := array_x1_higher[3, 3];
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
array_tmp8[3] := array_x1_higher[2, 3];
array_tmp9[3] := array_tmp7[3] - array_tmp8[3];
array_tmp10[3] := array_tmp9[3] + array_x1[3];
if 3 <= glob_max_terms then
temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if;
kkk := 4;
array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1);
array_tmp13[3] := array_x2_higher[2, 3];
array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1);
array_tmp15[3] := array_tmp12[3] - array_tmp14[3];
array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1);
array_tmp17[3] := array_tmp15[3] - array_tmp16[3];
if 3 <= glob_max_terms then
temporary := array_tmp17[3]*glob_h*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 3] := temporary
end if;
kkk := 4;
array_tmp1[4] := array_x2_higher[2, 4];
array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1);
array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1);
array_tmp5[4] := array_tmp3[4] - array_tmp4[4];
array_tmp6[4] := array_x1_higher[3, 4];
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
array_tmp8[4] := array_x1_higher[2, 4];
array_tmp9[4] := array_tmp7[4] - array_tmp8[4];
array_tmp10[4] := array_tmp9[4] + array_x1[4];
if 4 <= glob_max_terms then
temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 4] := temporary
end if;
kkk := 5;
array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1);
array_tmp13[4] := array_x2_higher[2, 4];
array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1);
array_tmp15[4] := array_tmp12[4] - array_tmp14[4];
array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1);
array_tmp17[4] := array_tmp15[4] - array_tmp16[4];
if 4 <= glob_max_terms then
temporary := array_tmp17[4]*glob_h*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 4] := temporary
end if;
kkk := 5;
array_tmp1[5] := array_x2_higher[2, 5];
array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1);
array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1);
array_tmp5[5] := array_tmp3[5] - array_tmp4[5];
array_tmp6[5] := array_x1_higher[3, 5];
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
array_tmp8[5] := array_x1_higher[2, 5];
array_tmp9[5] := array_tmp7[5] - array_tmp8[5];
array_tmp10[5] := array_tmp9[5] + array_x1[5];
if 5 <= glob_max_terms then
temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 5] := temporary
end if;
kkk := 6;
array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1);
array_tmp13[5] := array_x2_higher[2, 5];
array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1);
array_tmp15[5] := array_tmp12[5] - array_tmp14[5];
array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1);
array_tmp17[5] := array_tmp15[5] - array_tmp16[5];
if 5 <= glob_max_terms then
temporary := array_tmp17[5]*glob_h*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 5] := temporary
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_x2_higher[2, kkk];
array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1);
array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1);
array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := array_x1_higher[3, kkk];
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
array_tmp8[kkk] := array_x1_higher[2, kkk];
array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk];
array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp10[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x2[kkk + order_d] := temporary;
array_x2_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_x2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1);
array_tmp13[kkk] := array_x2_higher[2, kkk];
array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1);
array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk];
array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1);
array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp17[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x1[kkk + order_d] := temporary;
array_x1_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_x1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_x1 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c1 + 6.0 * c3 * exp(-t);
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0*c2*exp(2.0*t) - c3*exp(-t)
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> t_start,t_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> min_in_hour,
> glob_display_flag,
> djd_debug,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmax,
> centuries_in_millinium,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_normmax,
> glob_start,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_not_yet_start_msg,
> glob_hmin_init,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_reached_optimal_h,
> glob_max_hours,
> glob_relerr,
> glob_look_poles,
> glob_h,
> glob_html_log,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_order,
> glob_abserr,
> glob_log10_abserr,
> glob_large_float,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_relerr,
> glob_last_good_h,
> glob_disp_incr,
> glob_optimal_done,
> years_in_century,
> djd_debug2,
> glob_log10relerr,
> glob_current_iter,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin,
> glob_clock_sec,
> glob_almost_1,
> days_in_year,
> sec_in_min,
> glob_dump,
> glob_max_minutes,
> glob_small_float,
> glob_initial_pass,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> #END CONST
> array_type_pole,
> array_norms,
> array_x1_init,
> array_last_rel_error,
> array_1st_rel_error,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2,
> array_x1,
> array_pole,
> array_x2_init,
> array_m1,
> array_x2_higher_work,
> array_complex_pole,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_poles,
> array_x1_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_max_terms := 30;
> ALWAYS := 1;
> INFO := 2;
> glob_iolevel := 5;
> glob_orig_start_sec := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_not_yet_finished := true;
> min_in_hour := 60.0;
> glob_display_flag := true;
> djd_debug := true;
> glob_optimal_clock_start_sec := 0.0;
> glob_no_eqs := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_hmax := 1.0;
> centuries_in_millinium := 10.0;
> glob_max_opt_iter := 10;
> glob_log10normmin := 0.1;
> glob_log10abserr := 0.0;
> glob_normmax := 0.0;
> glob_start := 0;
> glob_max_sec := 10000.0;
> glob_unchanged_h_cnt := 0;
> glob_not_yet_start_msg := true;
> glob_hmin_init := 0.001;
> glob_clock_start_sec := 0.0;
> glob_optimal_expect_sec := 0.1;
> glob_reached_optimal_h := false;
> glob_max_hours := 0.0;
> glob_relerr := 0.1e-10;
> glob_look_poles := false;
> glob_h := 0.1;
> glob_html_log := true;
> glob_percent_done := 0.0;
> MAX_UNCHANGED := 10;
> glob_optimal_start := 0.0;
> glob_max_order := 30;
> glob_abserr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_iter := 0;
> glob_curr_iter_when_opt := 0;
> glob_warned := false;
> glob_smallish_float := 0.1e-100;
> glob_max_iter := 1000;
> glob_log10_relerr := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_disp_incr := 0.1;
> glob_optimal_done := false;
> years_in_century := 100.0;
> djd_debug2 := true;
> glob_log10relerr := 0.0;
> glob_current_iter := 0;
> glob_warned2 := false;
> glob_dump_analytic := false;
> glob_hmin := 0.00000000001;
> glob_clock_sec := 0.0;
> glob_almost_1 := 0.9990;
> days_in_year := 365.0;
> sec_in_min := 60.0;
> glob_dump := false;
> glob_max_minutes := 0.0;
> glob_small_float := 0.1e-50;
> glob_initial_pass := true;
> hours_in_day := 24.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_max_order := 2;
> 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/complicatedrev3postode.ode#################");
> omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> 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
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_x1_init:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_t:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_tmp5:= Array(1..(max_terms + 1),[]);
> array_tmp6:= Array(1..(max_terms + 1),[]);
> array_tmp7:= Array(1..(max_terms + 1),[]);
> array_tmp8:= Array(1..(max_terms + 1),[]);
> array_tmp9:= Array(1..(max_terms + 1),[]);
> array_tmp10:= Array(1..(max_terms + 1),[]);
> array_tmp11:= Array(1..(max_terms + 1),[]);
> array_tmp12:= Array(1..(max_terms + 1),[]);
> array_tmp13:= Array(1..(max_terms + 1),[]);
> array_tmp14:= Array(1..(max_terms + 1),[]);
> array_tmp15:= Array(1..(max_terms + 1),[]);
> array_tmp16:= Array(1..(max_terms + 1),[]);
> array_tmp17:= Array(1..(max_terms + 1),[]);
> array_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1_init[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_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_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1[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_x2_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
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_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 <= 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 <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_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 <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_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_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp7[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_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_t := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0[1] := 3.0;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_4D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_4D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_4D0[1] := 4.0;
> 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_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 2;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0[1] := 2.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[1] := exact_soln_x1(t_start);
> array_x2_init[1] := exact_soln_x2(t_start);
> array_x2_init[2] := exact_soln_x2p(t_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> 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_t[1] := t_start;
> array_t[2] := glob_h;
> order_diff := 2;
> #Start Series array_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_x2();
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> start_array_x1();
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x1_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_t[1] <= t_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;
> sub_iter := 1;
> while sub_iter <= 3 + glob_max_terms do # do number 3
> atomall()
> ;
> sub_iter := sub_iter + 1;
> od;# end do number 3
> ;
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> order_diff := 2;
> #Jump Series array_x2
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x2
> order_diff := 2;
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x2_higher[ord,term_no] := array_x2_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
> order_diff := 1;
> #Jump Series array_x1
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x1
> order_diff := 1;
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x1_higher[ord,term_no] := array_x1_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 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 3
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 3
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if glob_html_log then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-02T01:51:37-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"complicatedrev3")
> ;
> logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;")
> ;
> logitem_float(html_log_file,t_start)
> ;
> logitem_float(html_log_file,t_end)
> ;
> logitem_float(html_log_file,array_t[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 4
> 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 4
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 4
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 4
> ;
> log_revs(html_log_file," 076 | ")
> ;
> logitem_str(html_log_file,"complicatedrev3 diffeq.mxt")
> ;
> logitem_str(html_log_file,"complicatedrev3 maple results")
> ;
> logitem_str(html_log_file,"sub iter tot order + max terms eqs reversed")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4
> 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 4
> ;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then # if number 4
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;# end if 4
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3
> ;
> if glob_html_log then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_orig_start_sec, glob_max_rel_trunc_err, glob_not_yet_finished,
min_in_hour, glob_display_flag, djd_debug, glob_optimal_clock_start_sec,
glob_no_eqs, glob_max_trunc_err, glob_hmax, centuries_in_millinium,
glob_max_opt_iter, glob_log10normmin, glob_log10abserr, glob_normmax,
glob_start, glob_max_sec, glob_unchanged_h_cnt, glob_not_yet_start_msg,
glob_hmin_init, glob_clock_start_sec, glob_optimal_expect_sec,
glob_reached_optimal_h, glob_max_hours, glob_relerr, glob_look_poles,
glob_h, glob_html_log, glob_percent_done, MAX_UNCHANGED, glob_optimal_start,
glob_max_order, glob_abserr, glob_log10_abserr, glob_large_float, glob_iter,
glob_curr_iter_when_opt, glob_warned, glob_smallish_float, glob_max_iter,
glob_log10_relerr, glob_last_good_h, glob_disp_incr, glob_optimal_done,
years_in_century, djd_debug2, glob_log10relerr, glob_current_iter,
glob_warned2, glob_dump_analytic, glob_hmin, glob_clock_sec, glob_almost_1,
days_in_year, sec_in_min, glob_dump, glob_max_minutes, glob_small_float,
glob_initial_pass, hours_in_day, array_const_3D0, array_const_0D0,
array_const_4D0, array_const_1, array_const_2, array_const_2D0,
array_type_pole, array_norms, array_x1_init, array_last_rel_error,
array_1st_rel_error, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_pole,
array_x2_init, array_m1, array_x2_higher_work, array_complex_pole,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x1_higher_work2, array_x1_higher_work, array_poles, array_x1_higher,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_max_terms := 30;
ALWAYS := 1;
INFO := 2;
glob_iolevel := 5;
glob_orig_start_sec := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_not_yet_finished := true;
min_in_hour := 60.0;
glob_display_flag := true;
djd_debug := true;
glob_optimal_clock_start_sec := 0.;
glob_no_eqs := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_hmax := 1.0;
centuries_in_millinium := 10.0;
glob_max_opt_iter := 10;
glob_log10normmin := 0.1;
glob_log10abserr := 0.;
glob_normmax := 0.;
glob_start := 0;
glob_max_sec := 10000.0;
glob_unchanged_h_cnt := 0;
glob_not_yet_start_msg := true;
glob_hmin_init := 0.001;
glob_clock_start_sec := 0.;
glob_optimal_expect_sec := 0.1;
glob_reached_optimal_h := false;
glob_max_hours := 0.;
glob_relerr := 0.1*10^(-10);
glob_look_poles := false;
glob_h := 0.1;
glob_html_log := true;
glob_percent_done := 0.;
MAX_UNCHANGED := 10;
glob_optimal_start := 0.;
glob_max_order := 30;
glob_abserr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_iter := 0;
glob_curr_iter_when_opt := 0;
glob_warned := false;
glob_smallish_float := 0.1*10^(-100);
glob_max_iter := 1000;
glob_log10_relerr := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_disp_incr := 0.1;
glob_optimal_done := false;
years_in_century := 100.0;
djd_debug2 := true;
glob_log10relerr := 0.;
glob_current_iter := 0;
glob_warned2 := false;
glob_dump_analytic := false;
glob_hmin := 0.1*10^(-10);
glob_clock_sec := 0.;
glob_almost_1 := 0.9990;
days_in_year := 365.0;
sec_in_min := 60.0;
glob_dump := false;
glob_max_minutes := 0.;
glob_small_float := 0.1*10^(-50);
glob_initial_pass := true;
hours_in_day := 24.0;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_max_order := 2;
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/complicatedrev3postode.ode#################");
omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
diff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_type_pole := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_x1_init := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_t := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_tmp5 := Array(1 .. max_terms + 1, []);
array_tmp6 := Array(1 .. max_terms + 1, []);
array_tmp7 := Array(1 .. max_terms + 1, []);
array_tmp8 := Array(1 .. max_terms + 1, []);
array_tmp9 := Array(1 .. max_terms + 1, []);
array_tmp10 := Array(1 .. max_terms + 1, []);
array_tmp11 := Array(1 .. max_terms + 1, []);
array_tmp12 := Array(1 .. max_terms + 1, []);
array_tmp13 := Array(1 .. max_terms + 1, []);
array_tmp14 := Array(1 .. max_terms + 1, []);
array_tmp15 := Array(1 .. max_terms + 1, []);
array_tmp16 := Array(1 .. max_terms + 1, []);
array_tmp17 := Array(1 .. max_terms + 1, []);
array_x2 := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1_init[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_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_t[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp10[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp15[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp16[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp17[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1[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_x2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_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 <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_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 <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp17 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp17[term] := 0.; term := term + 1
end do;
array_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[term] := 0.; term := term + 1
end do;
array_tmp15 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp15[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_tmp9 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[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_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1
end do;
array_x1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
end do;
array_x2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1
end do;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_4D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_4D0[term] := 0.; term := term + 1
end do;
array_const_4D0[1] := 4.0;
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_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x2_higher[r_order, term_no] := array_x2_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x1_higher[r_order, term_no] := array_x1_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_x2();
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_x1();
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_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_t[1] <= t_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;
sub_iter := 1;
while sub_iter <= 3 + glob_max_terms do
atomall(); sub_iter := sub_iter + 1
end do;
if glob_look_poles then check_for_pole() end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 2;
order_diff := 2;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
order_diff := 1;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x1[term_no] := array_x1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x1_higher[ord, term_no] :=
array_x1_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 (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
ff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-02T01:51:37-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"complicatedrev3");
logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \
2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
logitem_float(html_log_file, t_start);
logitem_float(html_log_file, t_end);
logitem_float(html_log_file, array_t[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 076 | ");
logitem_str(html_log_file, "complicatedrev3 diffeq.mxt");
logitem_str(html_log_file, "complicatedrev3 maple results");
logitem_str(html_log_file,
"sub iter tot order + max terms eqs reversed");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/complicatedrev3postode.ode#################
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
#END FIRST INPUT BLOCK
!
#BEGIN SECOND INPUT BLOCK
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.0001
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.0001
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.0001
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.1MB, time=0.21
NO POLE
NO POLE
t[1] = 0.5001
x2[1] (analytic) = 0.00082570611074256394598966051590164
x2[1] (numeric) = 0.00082570612166176475828375563625841
absolute error = 1.091920081229409512035677e-11
relative error = 1.3224076545193994820854843861428e-06 %
h = 0.0001
x1[1] (analytic) = 0.001291646017422585871235266471237
x1[1] (numeric) = 0.0012916459955874115883876516432992
absolute error = 2.18351742828476148279378e-11
relative error = 1.6904921308408164222799221557642e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.4MB, time=0.49
memory used=11.4MB, alloc=4.5MB, time=0.77
NO POLE
NO POLE
t[1] = 0.5002
x2[1] (analytic) = 0.0008257966814495432344339416603249
x2[1] (numeric) = 0.0008257967251348281213240397717433
absolute error = 4.368528488689009811141840e-11
relative error = 5.2900775539819482964456239418727e-06 %
h = 0.0001
x1[1] (analytic) = 0.0012915368582788917633066026400632
x1[1] (numeric) = 0.0012915367709374977626314682122386
absolute error = 8.73413940006751344278246e-11
relative error = 6.7625939934123673917117472616999e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.5MB, time=1.05
NO POLE
NO POLE
t[1] = 0.5003
x2[1] (analytic) = 0.00082588727573070556349803310856235
x2[1] (numeric) = 0.00082588737404206323699479131958051
absolute error = 9.831135767349675821101816e-11
relative error = 1.1903725915442342986011473240371e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012914277100505662472629969306448
x1[1] (numeric) = 0.0012914275135231744959666645494493
absolute error = 1.965273917512963323811955e-10
relative error = 1.5217839157532189099822908729479e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.5MB, time=1.33
memory used=22.8MB, alloc=4.6MB, time=1.61
NO POLE
NO POLE
t[1] = 0.5004
x2[1] (analytic) = 0.00082597789359022044558440876232671
x2[1] (numeric) = 0.00082597806840075009054192480428531
absolute error = 1.7481052964495751604195860e-10
relative error = 2.1164068796698758000087584996618e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012913185727365178408202846139762
x1[1] (numeric) = 0.0012913182233346146526429415648609
absolute error = 3.494019031881773430491153e-10
relative error = 2.7057761776610775813865188645998e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.6MB, time=1.91
NO POLE
NO POLE
t[1] = 0.5005
x2[1] (analytic) = 0.00082606853503225828165826201261726
x2[1] (numeric) = 0.00082606880822817458065566608468088
absolute error = 2.7319591629899740407206362e-10
relative error = 3.3071822096253672529814342595982e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012912094463356551708370721480129
x1[1] (numeric) = 0.0012912089003619881495276236442818
absolute error = 5.459736670213094485037311e-10
relative error = 4.2283896587864751662850114171515e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.6MB, time=2.21
NO POLE
NO POLE
t[1] = 0.5006
x2[1] (analytic) = 0.00082615920006099036141977864461309
x2[1] (numeric) = 0.00082615959354162852139029553969999
absolute error = 3.9348063815997051689508690e-10
relative error = 4.7627701553274745301124904918847e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012911003308468869733038234462486
x1[1] (numeric) = 0.0012910995445954619552216918628985
absolute error = 7.862514250180821315833501e-10
relative error = 6.0897778912530118781843214985023e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.6MB, time=2.49
memory used=38.1MB, alloc=4.6MB, time=2.79
NO POLE
NO POLE
t[1] = 0.5007
x2[1] (analytic) = 0.00082624988868058886347644474630742
x2[1] (numeric) = 0.00082625042435840964408449625907903
absolute error = 5.3567782078060805151277161e-10
relative error = 6.4832422747555737323251290410568e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012909912262691220933319472376107
x1[1] (numeric) = 0.0012909901560252000891755520871946
absolute error = 1.0702439220041563951504161e-09
relative error = 8.2900944656075581841330534863578e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.6MB, time=3.09
NO POLE
NO POLE
t[1] = 0.5008
x2[1] (analytic) = 0.00082634060089522685551538962782877
x2[1] (numeric) = 0.00082634130069582159928230742624309
absolute error = 6.9980059474376691779841432e-10
relative error = 8.4686701099477482590816082079472e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012908821326012694851428855175656
x1[1] (numeric) = 0.0012908807346413636208045378857785
absolute error = 1.3979599058643383476317871e-09
relative error = 0.00010829493030841594898848037042863 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.6MB, time=3.38
memory used=49.5MB, alloc=4.6MB, time=3.69
NO POLE
NO POLE
t[1] = 0.5009
x2[1] (analytic) = 0.00082643133670907829447576375839823
x2[1] (numeric) = 0.00082643222257117395865468308073796
absolute error = 8.8586209566417891932233973e-10
relative error = 0.0001071912518699689067375276751612 %
h = 0.0001
x1[1] (analytic) = 0.0012907730498422382120572030903234
x1[1] (numeric) = 0.0012907712804341106686041481695877
absolute error = 1.7694081275434530549207357e-09
relative error = 0.00013708127294412560922713204910065 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.6MB, time=3.98
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = 0.00082652319000178221692165644762245
absolute error = 1.09387546419020050471975059e-09
relative error = 0.00013234679016046809363947892540427 %
h = 0.0001
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = 0.0012906617933935963992650194819135
absolute error = 2.1845973410472186587201216e-09
relative error = 0.00016926151022265208626335304262806 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.6MB, time=4.28
NO POLE
NO POLE
t[1] = 0.5011
x2[1] (analytic) = 0.00082661287915112178821202023981947
x2[1] (numeric) = 0.00082661420300496779377511002129173
absolute error = 1.32385384600556308978147226e-09
relative error = 0.000160154030912883399966030674825 %
h = 0.0001
x1[1] (analytic) = 0.0012905549170462764699083942648711
x1[1] (numeric) = 0.0012905522735099730267876328586639
absolute error = 2.6435363034431207614062072e-09
relative error = 0.0002048371803885296688434147424405 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.6MB, time=4.58
memory used=64.8MB, alloc=4.6MB, time=4.88
NO POLE
NO POLE
t[1] = 0.5012
x2[1] (analytic) = 0.00082670368578766620467820114309252
x2[1] (numeric) = 0.00082670526159805803580215159125978
absolute error = 1.57581039183112395044816726e-09
relative error = 0.00019061368890955461767624335587272 %
h = 0.0001
x1[1] (analytic) = 0.0012904458670071646728838326718726
x1[1] (numeric) = 0.0012904427207733898115967551792614
absolute error = 3.1462337748612870774926112e-09
relative error = 0.0002438098222715931176110464258225 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.6MB, time=5.18
NO POLE
NO POLE
t[1] = 0.5013
x2[1] (analytic) = 0.00082679451604012879179140950883443
x2[1] (numeric) = 0.00082679636579838621840909639748647
absolute error = 1.84975825742661768688865204e-09
relative error = 0.0002237264787732141844588017234919 %
h = 0.0001
x1[1] (analytic) = 0.0012903368278725115550179667024679
x1[1] (numeric) = 0.0012903331351739930596556149285469
absolute error = 3.6926985184953623517739210e-09
relative error = 0.00028618097528719144851083630215737 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.6MB, time=5.48
memory used=76.2MB, alloc=4.6MB, time=5.78
NO POLE
NO POLE
t[1] = 0.5014
x2[1] (analytic) = 0.00082688536991268795533779675988916
x2[1] (numeric) = 0.00082688751562329154774605560289219
absolute error = 2.14571060359240825884300303e-09
relative error = 0.00025949311496694844211335937101064 %
h = 0.0001
x1[1] (analytic) = 0.0012902277996412267249633565185424
x1[1] (numeric) = 0.0012902235167019261215798122900374
absolute error = 4.2829393006033835442285050e-09
relative error = 0.00033195217943640179276465745734051 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.6MB, time=6.08
NO POLE
NO POLE
t[1] = 0.5015
x2[1] (analytic) = 0.00082697624740952299139053885956424
x2[1] (numeric) = 0.00082697871109011916263213127076052
absolute error = 2.46368059617124159241119628e-09
relative error = 0.0002979143117941589428712115909298 %
h = 0.0001
x1[1] (analytic) = 0.0012901187823122199004062452509559
x1[1] (numeric) = 0.0012901138653473293917509634908609
absolute error = 4.9169648905086552817600950e-09
relative error = 0.00038112497530624333344800612771511 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.6MB, time=6.37
NO POLE
NO POLE
t[1] = 0.5016
x2[1] (analytic) = 0.00082706714853481408648245956670656
x2[1] (numeric) = 0.00082706995221622013648121803478665
absolute error = 2.80368140604999875846808009e-09
relative error = 0.0003389907833985238036531867914599 %
h = 0.0001
x1[1] (analytic) = 0.001290009775884400908055656176395
x1[1] (numeric) = 0.0012900041811003403074300793186693
absolute error = 5.5947840606006255768577257e-09
relative error = 0.00043370090406989131869314839747387 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.6MB, time=6.67
memory used=91.5MB, alloc=4.6MB, time=6.97
NO POLE
NO POLE
t[1] = 0.5017
x2[1] (analytic) = 0.00082715807329274231777868876405026
x2[1] (numeric) = 0.00082716123901895147922841164958704
absolute error = 3.16572620916144972288553678e-09
relative error = 0.00038272324376395910826262853617108 %
h = 0.0001
x1[1] (analytic) = 0.0012899007803566796836324909844552
x1[1] (numeric) = 0.0012898944639510933478706777308042
absolute error = 6.3164055863357618132536510e-09
relative error = 0.00048968150748689115154598131080375 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.6MB, time=7.27
NO POLE
NO POLE
t[1] = 0.5018
x2[1] (analytic) = 0.00082724902168748965324935586679766
x2[1] (numeric) = 0.00082725257151567613925702460954306
absolute error = 3.54982818648600766874274540e-09
relative error = 0.00042911240671458035751132200353971 %
h = 0.0001
x1[1] (analytic) = 0.0012897917957279662718586291348401
x1[1] (numeric) = 0.0012897847138897200334316304759689
absolute error = 7.0818382462384269986588712e-09
relative error = 0.00054906832790337255650352287158302 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.6MB, time=7.57
memory used=102.9MB, alloc=4.6MB, time=7.87
NO POLE
NO POLE
t[1] = 0.5019
x2[1] (analytic) = 0.00082733999372323895184231831839524
x2[1] (numeric) = 0.00082734394972376300532620902390904
absolute error = 3.95600052405348389070551380e-09
relative error = 0.0004781589859146639672762005158482 %
h = 0.0001
x1[1] (analytic) = 0.0012896828219971708264460283045716
x1[1] (numeric) = 0.0012896749309063489246897436486337
absolute error = 7.8910908219017562846559379e-09
relative error = 0.00061186290825226382275895530587325 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.6MB, time=8.16
NO POLE
NO POLE
t[1] = 0.502
x2[1] (analytic) = 0.0008274309894041739636559251804687
x2[1] (numeric) = 0.00082743537366058690849918693617254
absolute error = 4.38425641294484326175570384e-09
relative error = 0.00052986369486860881448464949319478 %
h = 0.0001
x1[1] (analytic) = 0.0012895738591632036100858259251
x1[1] (numeric) = 0.0012895651149911056215520720963797
absolute error = 8.7441720979885337538287203e-09
relative error = 0.00067806679205350612418115464270507 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.6MB, time=8.45
NO POLE
NO POLE
t[1] = 0.5021
x2[1] (analytic) = 0.00082752200873447933011181582388164
x2[1] (numeric) = 0.00082752684334352862407208827571239
absolute error = 4.83460904929396027245183075e-09
relative error = 0.00058422724692089783102620712671228 %
h = 0.0001
x1[1] (analytic) = 0.0012894649072249749944374418092067
x1[1] (numeric) = 0.0012894552661341127623679676003605
absolute error = 9.6410908622320694742088462e-09
relative error = 0.00074768152341426791605564933591343 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.6MB, time=8.73
memory used=118.2MB, alloc=4.6MB, time=9.03
NO POLE
NO POLE
t[1] = 0.5022
x2[1] (analytic) = 0.0008276130517183405841277537278848
x2[1] (numeric) = 0.00082761835878997487350339662985745
absolute error = 5.30707163428937564290197265e-09
relative error = 0.00064125035525605964558844273983996 %
h = 0.0001
x1[1] (analytic) = 0.0012893559661813954601176818675888
x1[1] (numeric) = 0.0012893453843254900230408607490387
absolute error = 1.05818559054370768211185501e-08
relative error = 0.00082070864702915940861395950552609 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.6MB, time=9.32
NO POLE
NO POLE
t[1] = 0.5023
x2[1] (analytic) = 0.00082770411835994415029049539432325
x2[1] (numeric) = 0.0008277099200173183263440030245067
absolute error = 5.80165737417605350763018345e-09
relative error = 0.00070093373289863027341477575436999 %
h = 0.0001
x1[1] (analytic) = 0.0012892470360313755966898429150187
x1[1] (numeric) = 0.00128923546955535411613977642533
absolute error = 1.15664760214805500664896887e-08
relative error = 0.0008971497081804471173782779177523 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.6MB, time=9.61
memory used=129.7MB, alloc=4.6MB, time=9.91
NO POLE
NO POLE
t[1] = 0.5024
x2[1] (analytic) = 0.00082779520866347734502869438387111
x2[1] (numeric) = 0.0008278015270429576021678679015289
absolute error = 6.31837948025713917351765779e-09
relative error = 0.00076327809271311485398197991792102 %
h = 0.0001
x1[1] (analytic) = 0.0012891381167738261026528185659675
x1[1] (numeric) = 0.0012891255218138187900105828272625
absolute error = 1.25949600073126422357387050e-08
relative error = 0.00097700625273826849034846282291629 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.6MB, time=10.19
NO POLE
NO POLE
t[1] = 0.5025
x2[1] (analytic) = 0.00082788632263312837678584048126422
x2[1] (numeric) = 0.00082789317988429727250329148121763
absolute error = 6.85725116889571745099995341e-09
relative error = 0.00082828414740394943659509935133701 %
h = 0.0001
x1[1] (analytic) = 0.0012890292084076577854302062195851
x1[1] (numeric) = 0.0012890155410909948278869739422368
absolute error = 1.36673166629575432322773483e-08
relative error = 0.0010602798271608466120583221767139 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.6MB, time=10.48
NO POLE
NO POLE
t[1] = 0.5026
x2[1] (analytic) = 0.00082797746027308634619323399650282
x2[1] (numeric) = 0.00082798487855874786276479269813518
absolute error = 7.41828566151657155870163236e-09
relative error = 0.00089595260951546281389748479655479 %
h = 0.0001
x1[1] (analytic) = 0.001288920310931781561359415133927
x1[1] (numeric) = 0.0012889055273769900470011853949461
absolute error = 1.47835547915143582297389809e-08
relative error = 0.0011469719784947049845281779771324 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.6MB, time=10.76
memory used=144.9MB, alloc=4.6MB, time=11.06
NO POLE
NO POLE
t[1] = 0.5027
x2[1] (analytic) = 0.00082806862158754124624299520899781
x2[1] (numeric) = 0.00082807662308372585418559689873644
absolute error = 8.00149618460794260168973863e-09
relative error = 0.0009662841914318384032936402916902 %
h = 0.0001
x1[1] (analytic) = 0.0012888114243451084556807755893193
x1[1] (numeric) = 0.0012887954806619092976944435889943
absolute error = 1.59436831991579863320003250e-08
relative error = 0.001237084254374882385140708596751 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.6MB, time=11.35
NO POLE
NO POLE
t[1] = 0.5028
x2[1] (analytic) = 0.00082815980658068396246110896163522
x2[1] (numeric) = 0.00082816841347665368575073248922157
absolute error = 8.60689596972328962352758635e-09
relative error = 0.001039279605377076176282552400637 %
h = 0.0001
x1[1] (analytic) = 0.0012887025486465496025266491407532
x1[1] (numeric) = 0.0012886854009358544625271480622239
absolute error = 1.71477106951399995010785293e-08
relative error = 0.0013306182030251478014670763960316 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.6MB, time=11.65
memory used=156.4MB, alloc=4.6MB, time=11.96
NO POLE
NO POLE
t[1] = 0.5029
x2[1] (analytic) = 0.0008282510152567062730805044117353
x2[1] (numeric) = 0.00082826024975495975613073672212399
absolute error = 9.23449825348305023231038869e-09
relative error = 0.0011149395634149546356991559597817 %
h = 0.0001
x1[1] (analytic) = 0.0012885936838350162449105399591989
x1[1] (numeric) = 0.0012885752881889244553887869757424
absolute error = 1.83956460917895217529834565e-08
relative error = 0.0014275753732582154430703569780457 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.6MB, time=12.26
NO POLE
NO POLE
t[1] = 0.503
x2[1] (analytic) = 0.0008283422476198008492141699458837
x2[1] (numeric) = 0.00082835213193607842561597081019783
absolute error = 9.88431627757640180086431413e-09
relative error = 0.0011932647774489928408615722134331 %
h = 0.0001
x1[1] (analytic) = 0.0012884848299094197347162072617323
x1[1] (numeric) = 0.0012884651424112152206075856566119
absolute error = 1.96874982045141086216051204e-08
relative error = 0.0015279573144759598303132959724411 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.6MB, time=12.56
NO POLE
NO POLE
t[1] = 0.5031
x2[1] (analytic) = 0.00082843350367416125502830326561401
x2[1] (numeric) = 0.00082844406003745001805154455622685
absolute error = 1.055636328876302324129061284e-08
relative error = 0.001274255959222412480621737067848 %
h = 0.0001
x1[1] (analytic) = 0.0012883759868686715326867788303632
x1[1] (numeric) = 0.001288354963592819732059888114143
absolute error = 2.10232758518006268907162202e-08
relative error = 0.0016317655766696309601974280990352 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.6MB, time=12.83
memory used=171.6MB, alloc=4.6MB, time=13.12
NO POLE
NO POLE
t[1] = 0.5032
x2[1] (analytic) = 0.00082852478342398194791549665092172
x2[1] (numeric) = 0.00082853603407652082277285068743447
absolute error = 1.125065253887485735403651275e-08
relative error = 0.001357913820318099994317019151046 %
h = 0.0001
x1[1] (analytic) = 0.0012882671547116832084138656194575
x1[1] (numeric) = 0.0012882447517238279922792714497083
absolute error = 2.24029878552161345941697492e-08
relative error = 0.0017390017104200695492606029567982 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.6MB, time=13.40
NO POLE
NO POLE
t[1] = 0.5033
x2[1] (analytic) = 0.00082861608687345827866795740859187
x2[1] (numeric) = 0.00082862805407074309654170908323235
absolute error = 1.196719728481787375167464048e-08
relative error = 0.0014442390721585687406204091780652 %
h = 0.0001
x1[1] (analytic) = 0.0012881583334373664403266774516441
x1[1] (numeric) = 0.0012881345067943270315653930799699
absolute error = 2.38266430394087612843716742e-08
relative error = 0.0018496672668979223535599708670963 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.6MB, time=13.67
memory used=183.1MB, alloc=4.7MB, time=13.95
NO POLE
NO POLE
t[1] = 0.5034
x2[1] (analytic) = 0.00082870741402678649165076351232339
x2[1] (numeric) = 0.00082872012003757506548312108510276
absolute error = 1.270601078857383235757277937e-08
relative error = 0.0015332324260059212142868441185336 %
h = 0.0001
x1[1] (analytic) = 0.0012880495230446330156811398020981
x1[1] (numeric) = 0.0012880242287944009070925706933876
absolute error = 2.52942502321085885691087105e-08
relative error = 0.0019637637978638575657674917229598 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.7MB, time=14.23
NO POLE
NO POLE
t[1] = 0.5035
x2[1] (analytic) = 0.00082879876488816372497515444163463
x2[1] (numeric) = 0.00082881223199448092702263407746779
absolute error = 1.346710631720204747963583316e-08
relative error = 0.001624894592961811310793211574946 %
h = 0.0001
x1[1] (analytic) = 0.0012879407235323948305490116710912
x1[1] (numeric) = 0.0012879139177141307020180948598542
absolute error = 2.68058182641285309168112370e-08
relative error = 0.0020812928556687802894050387230391 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.7MB, time=14.52
NO POLE
NO POLE
t[1] = 0.5036
x2[1] (analytic) = 0.00082889013946178801067185722653652
x2[1] (numeric) = 0.00082890438995893085182431652845615
absolute error = 1.425049714284115245930191963e-08
relative error = 0.001719226283967406638869561631304 %
h = 0.0001
x1[1] (analytic) = 0.0012878319348995638898070045446997
x1[1] (numeric) = 0.0012878035735435945245902742132765
absolute error = 2.83613559693652167303314232e-08
relative error = 0.0022022559932540480902461783959746 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.7MB, time=14.80
memory used=198.3MB, alloc=4.7MB, time=15.08
NO POLE
NO POLE
t[1] = 0.5037
x2[1] (analytic) = 0.00082898153775185827486444770496057
x2[1] (numeric) = 0.00082899659394840098572934367953633
absolute error = 1.505619654271086489597457576e-08
relative error = 0.0018162282098033508809190354689488 %
h = 0.0001
x1[1] (analytic) = 0.0012877231571450523071259024435631
x1[1] (numeric) = 0.0012876931962728675072562131269
absolute error = 2.99608721847998696893166631e-08
relative error = 0.0023266547641516866249117175322965 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.7MB, time=15.36
NO POLE
NO POLE
t[1] = 0.5038
x2[1] (analytic) = 0.0008290729597625743379427469999303
x2[1] (numeric) = 0.00082908884398037345169519407304261
absolute error = 1.588421779911375244707311231e-08
relative error = 0.0019159010810897262013240019798466 %
h = 0.0001
x1[1] (analytic) = 0.0012876143902677723049596830595824
x1[1] (numeric) = 0.0012875827858920218057693218011492
absolute error = 3.16043757504991903612584332e-08
relative error = 0.0024544907224846053466861167771793 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.7MB, time=15.63
memory used=209.8MB, alloc=4.7MB, time=15.92
NO POLE
NO POLE
t[1] = 0.5039
x2[1] (analytic) = 0.00082916440549813691473625322346704
x2[1] (numeric) = 0.00082918114007233635173545710667825
absolute error = 1.673457419943699920388321121e-08
relative error = 0.0020182456082860157026358754446106 %
h = 0.0001
x1[1] (analytic) = 0.0012875056342666362145346399804511
x1[1] (numeric) = 0.001287472342391126598296558683731
absolute error = 3.32918755096162380812967201e-08
relative error = 0.0025857654229668132885818802497772 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.7MB, time=16.20
NO POLE
NO POLE
t[1] = 0.504
x2[1] (analytic) = 0.00082925587496274761468760841422102
x2[1] (numeric) = 0.00082927348224178376886025180413823
absolute error = 1.760727903615417264338991721e-08
relative error = 0.002123262501691065929646069495739 %
h = 0.0001
x1[1] (analytic) = 0.0012873968891405564758385060019091
x1[1] (numeric) = 0.0012873618657602480845254051417271
absolute error = 3.50233803083913131008601820e-08
relative error = 0.0027204804209036349236790394321334 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.7MB, time=16.48
NO POLE
NO POLE
t[1] = 0.5041
x2[1] (analytic) = 0.00082934736816060894202610071582133
x2[1] (numeric) = 0.00082936587050621576901725699105167
absolute error = 1.850234560682699115627523034e-08
relative error = 0.0022309524714430494213355243887596 %
h = 0.0001
x1[1] (analytic) = 0.0012872881548884456376095775276106
x1[1] (numeric) = 0.001287251355989449484770572305374
absolute error = 3.67988989961528390052222366e-08
relative error = 0.0028586372721919261027668591803511 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.7MB, time=16.76
memory used=225.0MB, alloc=4.7MB, time=17.04
NO POLE
NO POLE
t[1] = 0.5042
x2[1] (analytic) = 0.00082943888509592429594120180293885
x2[1] (numeric) = 0.00082945830488313840303335306550202
absolute error = 1.941978721410709215126256317e-08
relative error = 0.0023413162275194273107002266946118 %
h = 0.0001
x1[1] (analytic) = 0.0012871794315092163573258400564985
x1[1] (numeric) = 0.0012871408130687910390804400032077
absolute error = 3.86184404253182454000532908e-08
relative error = 0.0030002375333202900693149029114296 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.7MB, time=17.32
NO POLE
NO POLE
t[1] = 0.5043
x2[1] (analytic) = 0.00082953042577289797075613956205843
x2[1] (numeric) = 0.00082955078539006370855687555244108
absolute error = 2.035961716573780073599038265e-08
relative error = 0.0024543544797369119724501224243586 %
h = 0.0001
x1[1] (analytic) = 0.0012870707190017814011940947575749
x1[1] (numeric) = 0.001287030236988330006343227708225
absolute error = 4.04820134513948508670493499e-08
relative error = 0.0031452827613692935518006031757335 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.7MB, time=17.60
memory used=236.5MB, alloc=4.7MB, time=17.88
NO POLE
NO POLE
t[1] = 0.5044
x2[1] (analytic) = 0.00082962199019573515610150603395714
x2[1] (numeric) = 0.00082964331204450971200048063137085
absolute error = 2.132184877455589897459741371e-08
relative error = 0.0025700679377514297185788066953835 %
h = 0.0001
x1[1] (analytic) = 0.00128696201736505364413908613196
x1[1] (numeric) = 0.0012869196277381206633928974146887
absolute error = 4.23896269329807461887172713e-08
relative error = 0.0032937745140116829334204933725561 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.7MB, time=18.17
NO POLE
NO POLE
t[1] = 0.5045
x2[1] (analytic) = 0.00082971357836864193708890062488759
x2[1] (numeric) = 0.00082973588486400043048462282672515
absolute error = 2.230649535849339572220183756e-08
relative error = 0.0026884573110580835418013549546924 %
h = 0.0001
x1[1] (analytic) = 0.0012868533265979460697926307621308
x1[1] (numeric) = 0.0012868089853082143041147883651812
absolute error = 4.43412897317656778423969496e-08
relative error = 0.003445714349512600499212265496829 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.7MB, time=18.45
NO POLE
NO POLE
t[1] = 0.5046
x2[1] (analytic) = 0.00082980519029582529448460859346626
x2[1] (numeric) = 0.00082982850386606587378164505044103
absolute error = 2.331357024057929703645697477e-08
relative error = 0.002809523308991115906857642853963 %
h = 0.0001
x1[1] (analytic) = 0.0012867446466993717704827471482299
x1[1] (numeric) = 0.0012866983096886592385509835474863
absolute error = 4.63370107125319317636007436e-08
relative error = 0.0036011038267298007606148280701437 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.7MB, time=18.73
memory used=251.7MB, alloc=4.7MB, time=19.01
NO POLE
NO POLE
t[1] = 0.5047
x2[1] (analytic) = 0.00082989682598149310488331482026843
x2[1] (numeric) = 0.00082992116906824204626048118626785
absolute error = 2.434308674894137716636599942e-08
relative error = 0.0029332666407238715896784838440594 %
h = 0.0001
x1[1] (analytic) = 0.0012866359776682439472227866313365
x1[1] (numeric) = 0.0012865876008695007920054078808539
absolute error = 4.83767987431552173787504826e-08
relative error = 0.0037599445051138668574935479333402 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.7MB, time=19.30
NO POLE
NO POLE
t[1] = 0.5048
x2[1] (analytic) = 0.00082998848542985414088185286713247
x2[1] (numeric) = 0.00083001388048807094883197140542011
absolute error = 2.539505821680795011853828764e-08
relative error = 0.003059688015268760564411895634821 %
h = 0.0001
x1[1] (analytic) = 0.0012865273195034759097005654035915
x1[1] (numeric) = 0.0012864768588407813041486580111799
absolute error = 5.04606626946055519073924116e-08
relative error = 0.0039222379447084270376578687393878 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.7MB, time=19.58
memory used=263.2MB, alloc=4.7MB, time=19.86
NO POLE
NO POLE
t[1] = 0.5049
x2[1] (analytic) = 0.00083008016864511807125298933317795
x2[1] (numeric) = 0.00083010663814310058089479040323803
absolute error = 2.646949798250964180107006008e-08
relative error = 0.0031887881414772209383067886525879 %
h = 0.0001
x1[1] (analytic) = 0.001286418672203981076267497605066
x1[1] (numeric) = 0.0012863660835925401281225636346085
absolute error = 5.25886114409481449339704575e-08
relative error = 0.0040879857061503712138985081725013 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.7MB, time=20.14
NO POLE
NO POLE
t[1] = 0.505
x2[1] (analytic) = 0.00083017187563149546111924351454314
x2[1] (numeric) = 0.00083019944205088494228198874657799
absolute error = 2.756641938948116274523203485e-08
relative error = 0.0033205677280396819344513517147763 %
h = 0.0001
x1[1] (analytic) = 0.0012863100357686729739277295072664
x1[1] (numeric) = 0.0012862552751148136296444802690396
absolute error = 5.47606538593442832492382268e-08
relative error = 0.004257189350670067598571445567754 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.7MB, time=20.43
NO POLE
NO POLE
t[1] = 0.5051
x2[1] (analytic) = 0.00083026360639319777212674237484908
x2[1] (numeric) = 0.00083029229222898403520814752171301
absolute error = 2.868583578626308140514686393e-08
relative error = 0.0034550274834855269223633921687938 %
h = 0.0001
x1[1] (analytic) = 0.0012862014101964652383272747831672
x1[1] (numeric) = 0.0012861444333976351861113133930012
absolute error = 5.69767988300522159613901660e-08
relative error = 0.0044298504400915794157559206579034 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.7MB, time=20.71
memory used=278.4MB, alloc=4.7MB, time=20.99
NO POLE
NO POLE
t[1] = 0.5052
x2[1] (analytic) = 0.0008303553609344373626191108333988
x2[1] (numeric) = 0.00083038518869496386621714647258158
absolute error = 2.982776052650359803563918278e-08
relative error = 0.0035921681161830564964298698093072 %
h = 0.0001
x1[1] (analytic) = 0.0012860927954862716137431508636619
x1[1] (numeric) = 0.0012860335584310351857032738713206
absolute error = 5.92370552364280398769923413e-08
relative error = 0.0046059705368328816910136735943879 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.7MB, time=21.27
NO POLE
NO POLE
t[1] = 0.5053
x2[1] (analytic) = 0.00083044713925942748781139737812144
x2[1] (numeric) = 0.00083047813146639644813054581928114
absolute error = 3.099220696896031914844115970e-08
relative error = 0.0037319903343394516021928459716536 %
h = 0.0001
x1[1] (analytic) = 0.0012859841916370059530725163803239
x1[1] (numeric) = 0.0012859226502050410264873645870064
absolute error = 6.15414319649265851517933175e-08
relative error = 0.0047855512039060781187766656489903 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.7MB, time=21.55
memory used=289.9MB, alloc=4.7MB, time=21.84
NO POLE
NO POLE
t[1] = 0.5054
x2[1] (analytic) = 0.00083053894137238229996403501027281
x2[1] (numeric) = 0.00083057112056085980199658194676091
absolute error = 3.217918847750203254693648810e-08
relative error = 0.0038744948460007367104790512638851 %
h = 0.0001
x1[1] (analytic) = 0.0012858755986475822178218096943695
x1[1] (numeric) = 0.0012858117087096771155205981987264
absolute error = 6.38899379051023012114956431e-08
relative error = 0.0049685940049176180073905295602222 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.7MB, time=22.12
NO POLE
NO POLE
t[1] = 0.5055
x2[1] (analytic) = 0.0008306307672775168485568375279051
x2[1] (numeric) = 0.00083066415599593795903977715372656
absolute error = 3.338871842111048293962582146e-08
relative error = 0.0040196823590517430393702574720904 %
h = 0.0001
x1[1] (analytic) = 0.0012857670165169144780958885117126
x1[1] (numeric) = 0.0012857007339349648679529459432453
absolute error = 6.62825819496101429425684673e-08
relative error = 0.0051551005040685133018410073954478 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.7MB, time=22.40
NO POLE
NO POLE
t[1] = 0.5056
x2[1] (analytic) = 0.0008307226169790470804630311551197
x2[1] (numeric) = 0.00083075723778922096261116365182769
absolute error = 3.462081017388214813249670799e-08
relative error = 0.0041675535812160718240116213254719 %
h = 0.0001
x1[1] (analytic) = 0.001285658445243916912587170584005
x1[1] (numeric) = 0.0012855897258709227061300174021591
absolute error = 6.87193729942064571531818459e-08
relative error = 0.0053450722661545556841906436889724 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.7MB, time=22.68
memory used=305.1MB, alloc=4.7MB, time=22.96
NO POLE
NO POLE
t[1] = 0.5057
x2[1] (analytic) = 0.00083081449048118984012332152411889
x2[1] (numeric) = 0.00083085036595830487013912200525709
absolute error = 3.587547711503001580048113820e-08
relative error = 0.0043181092200560576342551498417088 %
h = 0.0001
x1[1] (analytic) = 0.0012855498848275038085647754955507
x1[1] (numeric) = 0.001285478684507566058695471152241
absolute error = 7.12003199377498693043433097e-08
relative error = 0.0055385108565665337517530103650443 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.7MB, time=23.24
NO POLE
NO POLE
t[1] = 0.5058
x2[1] (analytic) = 0.00083090638778816286971999601707344
x2[1] (numeric) = 0.0008309435405207917550808342009491
absolute error = 3.715273262888536083818387566e-08
relative error = 0.0044713499829727317401354191182138 %
h = 0.0001
x1[1] (analytic) = 0.0012854413352665895618636675359888
x1[1] (numeric) = 0.0012853676098349073596931562186884
absolute error = 7.37254316822021705113173004e-08
relative error = 0.0057354178412904502730317498568432 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.7MB, time=23.52
memory used=316.6MB, alloc=4.7MB, time=23.80
NO POLE
NO POLE
t[1] = 0.5059
x2[1] (analytic) = 0.0008309983089041848093510614748241
x2[1] (numeric) = 0.00083103676149428970887435153962236
absolute error = 3.845259010489952329006479826e-08
relative error = 0.0046272765772057855251746605813933 %
h = 0.0001
x1[1] (analytic) = 0.0012853327965600886768737996586336
x1[1] (numeric) = 0.0012852565018429560476689842505367
absolute error = 7.62947171326292048154080969e-08
relative error = 0.0059357947869077395214517316873615 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.7MB, time=24.09
NO POLE
NO POLE
t[1] = 0.506
x2[1] (analytic) = 0.00083109025383347519720441727943742
x2[1] (numeric) = 0.00083113002889641284289127753797086
absolute error = 3.977506293764568686025853344e-08
relative error = 0.0047858897098335339475143107540663 %
h = 0.0001
x1[1] (analytic) = 0.0012852242687069157665292585243653
x1[1] (numeric) = 0.0012851453605217185647725323374805
absolute error = 7.89081851972017567261868848e-08
relative error = 0.0061396432605954846869096275687349 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.7MB, time=24.37
NO POLE
NO POLE
t[1] = 0.5061
x2[1] (analytic) = 0.00083118222258025446973206381763632
x2[1] (numeric) = 0.00083122334274478129039006603236507
absolute error = 4.112016452682065800221472875e-08
relative error = 0.0049471900877728790488701028637606 %
h = 0.0001
x1[1] (analytic) = 0.0012851157517059855522974106309618
x1[1] (numeric) = 0.0012850341858611983558583763873211
absolute error = 8.15658447871964390342436407e-08
relative error = 0.006346964830126635365171219006401 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.7MB, time=24.64
memory used=331.8MB, alloc=4.7MB, time=24.93
NO POLE
NO POLE
t[1] = 0.5062
x2[1] (analytic) = 0.00083127421514874396182434633212867
x2[1] (numeric) = 0.00083131670305702120846993467448344
absolute error = 4.248790827724664558834235477e-08
relative error = 0.0051111784177792735113077606162416 %
h = 0.0001
x1[1] (analytic) = 0.001285007245556212864168049527763
x1[1] (numeric) = 0.0012849229778513958675871549832312
absolute error = 8.42677048169965808945445318e-08
relative error = 0.0065577610638702251251427611124898 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=335.6MB, alloc=4.7MB, time=25.21
NO POLE
NO POLE
t[1] = 0.5063
x2[1] (analytic) = 0.00083136623154316590698423416785765
x2[1] (numeric) = 0.00083141010985076478002539400935281
absolute error = 4.387830759887304115984149516e-08
relative error = 0.0052778554064466842618363367157099 %
h = 0.0001
x1[1] (analytic) = 0.0012848987502565126406425441155605
x1[1] (numeric) = 0.001284811736482308547526363640007
absolute error = 8.70137742040931161804755535e-08
relative error = 0.0067720335307915891540437355322451 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.7MB, time=25.49
memory used=343.3MB, alloc=4.7MB, time=25.77
NO POLE
NO POLE
t[1] = 0.5064
x2[1] (analytic) = 0.00083145827176774343750163542019918
x2[1] (numeric) = 0.00083150356314365021570139232633452
absolute error = 4.529137590677819975690613534e-08
relative error = 0.0054472217602075561248162208548929 %
h = 0.0001
x1[1] (analytic) = 0.0012847902658057999287229880316013
x1[1] (numeric) = 0.0012847004617439308432508793784516
absolute error = 8.98040618690854721086531497e-08
relative error = 0.006989783800452581980508334573569 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.7MB, time=26.06
NO POLE
NO POLE
t[1] = 0.5065
x2[1] (analytic) = 0.00083155033582670058462774699213345
x2[1] (numeric) = 0.0008315970629533217558490764736514
absolute error = 4.672712662117122132948151795e-08
relative error = 0.0056192781853327755221788240367555 %
h = 0.0001
x1[1] (analytic) = 0.0012846817922029898839013501196003
x1[1] (numeric) = 0.0012845891536262542014432155370099
absolute error = 9.26385767356824581345825904e-08
relative error = 0.0072110134430117952756430284333626 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=350.9MB, alloc=4.7MB, time=26.33
NO POLE
NO POLE
t[1] = 0.5066
x2[1] (analytic) = 0.00083164242372426227874944006741881
x2[1] (numeric) = 0.00083169060929742967248216882710911
absolute error = 4.818557316739373272875969030e-08
relative error = 0.0057940253879316342214549282837012 %
h = 0.0001
x1[1] (analytic) = 0.0012845733294469977701486259846507
x1[1] (numeric) = 0.0012844778121192670669935067397509
absolute error = 9.55173277307031551192448998e-08
relative error = 0.0074357240292247757320675763412034 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=354.7MB, alloc=4.7MB, time=26.61
memory used=358.5MB, alloc=4.7MB, time=26.90
NO POLE
NO POLE
t[1] = 0.5067
x2[1] (analytic) = 0.00083173453546465434956368100679754
x2[1] (numeric) = 0.00083178420219363027123396060372371
absolute error = 4.966672897592167027959692617e-08
relative error = 0.0059714640739517931316086730014033 %
h = 0.0001
x1[1] (analytic) = 0.001284464877536738959903990632925
x1[1] (numeric) = 0.0012843664372129548820992239397696
absolute error = 9.84403237840778047666931554e-08
relative error = 0.00766391713044424302096685204725 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=362.4MB, alloc=4.7MB, time=27.17
NO POLE
NO POLE
t[1] = 0.5068
x2[1] (analytic) = 0.00083182667105210352625198767426466
x2[1] (numeric) = 0.00083187784165958589331492171102574
absolute error = 5.117060748236706293403676108e-08
relative error = 0.0061515949491792461466741314350985 %
h = 0.0001
x1[1] (analytic) = 0.0012843564364711289340639521960578
x1[1] (numeric) = 0.0012842550288973000853646194570552
absolute error = 1.014075738288486993327390026e-07
relative error = 0.0078955943186203078271808634334365 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.7MB, time=27.45
memory used=370.0MB, alloc=4.7MB, time=27.75
NO POLE
NO POLE
t[1] = 0.5069
x2[1] (analytic) = 0.00083191883049083743765492120043225
x2[1] (numeric) = 0.00083197152771296491747092732286938
absolute error = 5.269722212747981600612243713e-08
relative error = 0.0063344187192382840371914128596691 %
h = 0.0001
x1[1] (analytic) = 0.0012842480062490832819715067401017
x1[1] (numeric) = 0.0012841435871622821108999019298492
absolute error = 1.044190868011710716048102525e-07
relative error = 0.0081307571663006899623603553194228 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=373.8MB, alloc=4.7MB, time=28.03
NO POLE
NO POLE
t[1] = 0.507
x2[1] (analytic) = 0.00083201101378508461244661319002326
x2[1] (numeric) = 0.00083206526037144176194210137263379
absolute error = 5.424658635714949548818261053e-08
relative error = 0.0065199360895914583894392083594845 %
h = 0.0001
x1[1] (analytic) = 0.001284139586869517701405294158948
x1[1] (numeric) = 0.0012840321119978773874201410984924
absolute error = 1.074748716403139851530604556e-07
relative error = 0.0083694072466309365562153939698314 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.7MB, time=28.31
NO POLE
NO POLE
t[1] = 0.5071
x2[1] (analytic) = 0.00083210322093907447930932838052986
x2[1] (numeric) = 0.00083215903965269688642227715476213
absolute error = 5.581871362240711294877423227e-08
relative error = 0.006708147765539545592460680312226 %
h = 0.0001
x1[1] (analytic) = 0.0012840311783313479985687551521049
x1[1] (numeric) = 0.0012839206033940593373439023407348
absolute error = 1.105749372886612248528113701e-07
relative error = 0.0086115461333546403258843413248285 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=381.4MB, alloc=4.7MB, time=28.59
memory used=385.2MB, alloc=4.7MB, time=28.88
NO POLE
NO POLE
t[1] = 0.5072
x2[1] (analytic) = 0.00083219545195703736710806275907346
x2[1] (numeric) = 0.00083225286557441679401907522564216
absolute error = 5.741361737942691101246656870e-08
relative error = 0.0068990544522215108728795778341167 %
h = 0.0001
x1[1] (analytic) = 0.0012839227806334900880792892867217
x1[1] (numeric) = 0.0012838090613407983758916108774593
absolute error = 1.137192926917121876784092624e-07
relative error = 0.008857175400813657923450635941339 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=389.1MB, alloc=4.7MB, time=29.17
NO POLE
NO POLE
t[1] = 0.5073
x2[1] (analytic) = 0.00083228770684320450506517714450406
x2[1] (numeric) = 0.0008323467381542940332145987948909
absolute error = 5.903131108952814942165038684e-08
relative error = 0.007092656854614472377503442801497 %
h = 0.0001
x1[1] (analytic) = 0.0012838143937748599929574141437547
x1[1] (numeric) = 0.0012836974858280619101836455677445
absolute error = 1.169079467980827737685760102e-07
relative error = 0.0091062966239483283616348076822788 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=392.9MB, alloc=4.7MB, time=29.45
memory used=396.7MB, alloc=4.7MB, time=29.74
NO POLE
NO POLE
t[1] = 0.5074
x2[1] (analytic) = 0.00083237998560180802293506624177892
x2[1] (numeric) = 0.00083244065741002719982674679816419
absolute error = 6.067180821917689168055638527e-08
relative error = 0.0072889556775336653037107531847721 %
h = 0.0001
x1[1] (analytic) = 0.0012837060177543738446159255481629
x1[1] (numeric) = 0.0012835858768458143383381622121691
absolute error = 1.201409085595062777633359938e-07
relative error = 0.0093589113782976915176891618734141 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=400.5MB, alloc=4.7MB, time=30.02
NO POLE
NO POLE
t[1] = 0.5075
x2[1] (analytic) = 0.0008324722882370809511788631756612
x2[1] (numeric) = 0.00083253462335932093897114484267055
absolute error = 6.233512223998779228166700935e-08
relative error = 0.0074879516256324060776188327829862 %
h = 0.0001
x1[1] (analytic) = 0.0012835976525709478828490588830272
x1[1] (numeric) = 0.0012834742343840170485686462832344
absolute error = 1.234181869308342804125997928e-07
relative error = 0.0096150212399997067155225786092621 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=404.3MB, alloc=4.7MB, time=30.31
NO POLE
NO POLE
t[1] = 0.5076
x2[1] (analytic) = 0.00083256461475325722113917951078113
x2[1] (numeric) = 0.00083262863601988594702369421662734
absolute error = 6.402126662872588451470584621e-08
relative error = 0.0076896454034020565800293386604544 %
h = 0.0001
x1[1] (analytic) = 0.0012834892982234984558216514874832
x1[1] (numeric) = 0.0012833625584326284182811950017585
absolute error = 1.267397908700375404564857247e-07
relative error = 0.0098746277857914713860828818959854 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=408.1MB, alloc=4.7MB, time=30.60
memory used=411.9MB, alloc=4.7MB, time=30.89
NO POLE
NO POLE
t[1] = 0.5077
x2[1] (analytic) = 0.00083265696515457166521488076510333
x2[1] (numeric) = 0.00083272269540943897358373915395561
absolute error = 6.573025486730836885838885228e-08
relative error = 0.0078940377151719884201481198833739 %
h = 0.0001
x1[1] (analytic) = 0.0012833809547109420200583061383613
x1[1] (numeric) = 0.0012832508489816038131715286780704
absolute error = 1.301057293382068867774602909e-07
relative error = 0.010137732593009439806024243083787 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=415.8MB, alloc=4.7MB, time=31.17
NO POLE
NO POLE
t[1] = 0.5078
x2[1] (analytic) = 0.00083274933944526001703589742384568
x2[1] (numeric) = 0.00083281680154570282343785254556867
absolute error = 6.746210044280640195512172299e-08
relative error = 0.0081011292651095472570762234007533 %
h = 0.0001
x1[1] (analytic) = 0.001283272622032195140432555615423
x1[1] (numeric) = 0.0012831391060208955863217312368084
absolute error = 1.335160112995541108243786146e-07
relative error = 0.010404337239589641914687092029512 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=419.6MB, alloc=4.7MB, time=31.46
memory used=423.4MB, alloc=4.7MB, time=31.76
NO POLE
NO POLE
t[1] = 0.5079
x2[1] (analytic) = 0.00083284173762955891163807146089618
x2[1] (numeric) = 0.00083291095444640635852424028866808
absolute error = 6.921681684744688616882777190e-08
relative error = 0.0083109207572200171690688052593214 %
h = 0.0001
x1[1] (analytic) = 0.0012831643001861744901560283500877
x1[1] (numeric) = 0.0012830273295404530772967198441035
absolute error = 1.369706457214128593085059842e-07
relative error = 0.010674443304067902209418019207636 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=427.2MB, alloc=4.7MB, time=32.06
NO POLE
NO POLE
t[1] = 0.508
x2[1] (analytic) = 0.00083293415971170588563803837477598
x2[1] (numeric) = 0.0008330051541292844998977644655191
absolute error = 7.099441757861425972609074312e-08
relative error = 0.0085234128953465850705586875700924 %
h = 0.0001
x1[1] (analytic) = 0.0012830559891717968507676151575396
x1[1] (numeric) = 0.0012829155195302226112404435559021
absolute error = 1.404696415742395271716016375e-07
relative error = 0.010948052365580058719257161191475 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=431.0MB, alloc=4.7MB, time=32.35
NO POLE
NO POLE
t[1] = 0.5081
x2[1] (analytic) = 0.00083302660569593937740814474619785
x2[1] (numeric) = 0.00083309940061207822969558554323655
absolute error = 7.279491613885228744079703870e-08
relative error = 0.0087386063831703051769412840252295 %
h = 0.0001
x1[1] (analytic) = 0.0012829476889879791121226370521077
x1[1] (numeric) = 0.0012828036759801474979718109061603
absolute error = 1.440130078316141508261459474e-07
relative error = 0.011225166003862182057020571420827 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=434.8MB, alloc=4.7MB, time=32.64
memory used=438.6MB, alloc=4.7MB, time=32.92
NO POLE
NO POLE
t[1] = 0.5082
x2[1] (analytic) = 0.0008331190755864987272514013242712
x2[1] (numeric) = 0.00083319369391253459310342378617042
absolute error = 7.461832603586585202246189922e-08
relative error = 0.0089565019242100635171175989987235 %
h = 0.0001
x1[1] (analytic) = 0.0012828393996336382723820141458102
x1[1] (numeric) = 0.0012826917988801680310803463536164
absolute error = 1.476007534702413016677921938e-07
relative error = 0.011505785799250794549805087560192 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=442.5MB, alloc=4.7MB, time=33.20
NO POLE
NO POLE
t[1] = 0.5083
x2[1] (analytic) = 0.00083321156938762417757647164840573
x2[1] (numeric) = 0.00083328803404840670032244007253938
absolute error = 7.646466078252274596842413365e-08
relative error = 0.0091771002218225424937919876606247 %
h = 0.0001
x1[1] (analytic) = 0.0012827311211076914380014356299545
x1[1] (numeric) = 0.0012825798882202214870215755058236
absolute error = 1.512328874699509798601241309e-07
relative error = 0.011789913332683089447943216181099 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=446.3MB, alloc=4.7MB, time=33.48
memory used=450.1MB, alloc=4.7MB, time=33.77
NO POLE
NO POLE
t[1] = 0.5084
x2[1] (analytic) = 0.00083330408710355687307269621296731
x2[1] (numeric) = 0.00083338242103745372853673630701888
absolute error = 7.833393389685546404009405157e-08
relative error = 0.0094004019792021854915213468387485 %
h = 0.0001
x1[1] (analytic) = 0.0012826228534090558237205308396847
x1[1] (numeric) = 0.001282467943990242124212139039102
absolute error = 1.549094188136995083918005827e-07
relative error = 0.012077550185697150212435564863948 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=453.9MB, alloc=4.7MB, time=34.05
NO POLE
NO POLE
t[1] = 0.5085
x2[1] (analytic) = 0.00083339662873853886088515218174166
x2[1] (numeric) = 0.00083347685489744092388147562104932
absolute error = 8.022615890206299632343930766e-08
relative error = 0.0096264078993811615325123886484336 %
h = 0.0001
x1[1] (analytic) = 0.0012825145965366487525520414013697
x1[1] (numeric) = 0.0012823559661801611821246352330422
absolute error = 1.586303564875704274061683275e-07
relative error = 0.012368697940432169880888361522097 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=457.7MB, alloc=4.7MB, time=34.32
NO POLE
NO POLE
t[1] = 0.5086
x2[1] (analytic) = 0.00083348919429681309078974865926187
x2[1] (numeric) = 0.00083357133564613960341162255268841
absolute error = 8.214134932651262187389342654e-08
relative error = 0.0098551186852293299801636313660853 %
h = 0.0001
x1[1] (analytic) = 0.0012824063504893876557709944627208
x1[1] (numeric) = 0.0012822439547799068803821910381717
absolute error = 1.623957094807753888034245491e-07
relative error = 0.012663358179628670511983609595686 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=461.5MB, alloc=4.7MB, time=34.60
memory used=465.4MB, alloc=4.7MB, time=34.89
NO POLE
NO POLE
t[1] = 0.5087
x2[1] (analytic) = 0.00083358178378262341536835752605775
x2[1] (numeric) = 0.00083366586330132715707130339789054
absolute error = 8.407951870374170294587183279e-08
relative error = 0.010086535039454205290348724313386 %
h = 0.0001
x1[1] (analytic) = 0.0012822981152661900729038770055334
x1[1] (numeric) = 0.0012821319097794044178527615953667
absolute error = 1.662054867856550511154101667e-07
relative error = 0.012961532486628722708509437966238 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=469.2MB, alloc=4.7MB, time=35.16
NO POLE
NO POLE
t[1] = 0.5088
x2[1] (analytic) = 0.00083367439720021459018397984488692
x2[1] (numeric) = 0.0008337604378807870496637869251548
absolute error = 8.604068057245947980708026788e-08
relative error = 0.010320657664600921810437705834736 %
h = 0.0001
x1[1] (analytic) = 0.0012821898908659736517178112409428
x1[1] (numeric) = 0.001282019831168575971743158125572
absolute error = 1.700596973976799746531153708e-07
relative error = 0.013263222445376165218978213168196 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=473.0MB, alloc=4.7MB, time=35.44
memory used=476.8MB, alloc=4.7MB, time=35.73
NO POLE
NO POLE
t[1] = 0.5089
x2[1] (analytic) = 0.0008337670345538322739559478450075
x2[1] (numeric) = 0.00083385505940230882282208564554199
absolute error = 8.802484847654886613780053449e-08
relative error = 0.010557487263052198626052775994591 %
h = 0.0001
x1[1] (analytic) = 0.0012820816772876561482097310870861
x1[1] (numeric) = 0.0012819077189373406966928041083634
absolute error = 1.739583503154515169269787227e-07
relative error = 0.013568429640416824617859991370502 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=480.6MB, alloc=4.7MB, time=36.01
NO POLE
NO POLE
t[1] = 0.509
x2[1] (analytic) = 0.00083385969584772302873516249155556
x2[1] (numeric) = 0.00083394972788368809698017783011963
absolute error = 9.003203596506824501533856407e-08
relative error = 0.010797024537028304455555147766439 %
h = 0.0001
x1[1] (analytic) = 0.001281973474530155426595559729063
x1[1] (numeric) = 0.0012817955730756147238672196678652
absolute error = 1.779014545407027283400611978e-07
relative error = 0.013877155656898735064458896900587 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=484.4MB, alloc=4.7MB, time=36.29
NO POLE
NO POLE
t[1] = 0.5091
x2[1] (analytic) = 0.00083395238108613432007936664709021
x2[1] (numeric) = 0.00083404444334272657334485046695307
absolute error = 9.206225659225326548381986286e-08
relative error = 0.011039270188587022592259523116584 %
h = 0.0001
x1[1] (analytic) = 0.0012818652825923894592993882610856
x1[1] (numeric) = 0.0012816833935733111600512340845095
absolute error = 1.818890190782992481541765761e-07
relative error = 0.014189402080572358140460023431754 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=488.2MB, alloc=4.7MB, time=36.56
memory used=492.1MB, alloc=4.7MB, time=36.85
NO POLE
NO POLE
t[1] = 0.5092
x2[1] (analytic) = 0.00083404509027331451722845383237174
x2[1] (numeric) = 0.00083413920579723203586816334981919
absolute error = 9.411552391751863970951744745e-08
relative error = 0.011284224919623615894372722602807 %
h = 0.0001
x1[1] (analytic) = 0.0012817571014732763269426554107106
x1[1] (numeric) = 0.0012815711804203400867419263511001
absolute error = 1.859210529362402007290596105e-07
relative error = 0.01450517049779080276617446361798 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=495.9MB, alloc=4.7MB, time=37.12
NO POLE
NO POLE
t[1] = 0.5093
x2[1] (analytic) = 0.00083413782341351289327981259343914
x2[1] (numeric) = 0.00083423401526501835322053449087842
absolute error = 9.619185150545994072189743928e-08
relative error = 0.0115318894318707918226529796264 %
h = 0.0001
x1[1] (analytic) = 0.0012816489311717342183333283450442
x1[1] (numeric) = 0.0012814589336066085592412936916197
absolute error = 1.899975651256590920346534245e-07
relative error = 0.014824462495510045195510082142304 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=499.7MB, alloc=4.7MB, time=37.40
memory used=503.5MB, alloc=4.7MB, time=37.68
NO POLE
NO POLE
t[1] = 0.5094
x2[1] (analytic) = 0.00083423058051097962536370648205495
x2[1] (numeric) = 0.00083432887176390548076444704959934
absolute error = 9.829125292585540074056754439e-08
relative error = 0.011782264426898667525786392831974 %
h = 0.0001
x1[1] (analytic) = 0.0012815407716866814304550845588136
x1[1] (numeric) = 0.0012813466531220206057486479611935
absolute error = 1.941185646608247064365976201e-07
relative error = 0.015147279661289149089695656969247 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=507.3MB, alloc=4.7MB, time=37.97
NO POLE
NO POLE
t[1] = 0.5095
x2[1] (analytic) = 0.00083432336156996579481868965658664
x2[1] (numeric) = 0.00083442377531171946252877797028917
absolute error = 1.0041374175366771008831370253e-07
relative error = 0.01203535060611473497347701261852 %
h = 0.0001
x1[1] (analytic) = 0.0012814326230170363684564948441937
x1[1] (numeric) = 0.0012812343389564772264527398455992
absolute error = 1.982840605591420037549985945e-07
relative error = 0.015473623583290485669786022529305 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=511.1MB, alloc=4.7MB, time=38.24
NO POLE
NO POLE
t[1] = 0.5096
x2[1] (analytic) = 0.0008344161665947233873670581103952
x2[1] (numeric) = 0.0008345187259262924331837485206422
absolute error = 1.0255933156904581669041024700e-07
relative error = 0.012291148670763826137247020136113 %
h = 0.0001
x1[1] (analytic) = 0.0012813244851617175456402073422847
x1[1] (numeric) = 0.0012811219910998763926236107786878
absolute error = 2.024940618411530165965635969e-07
relative error = 0.015803495850279953947975858666047 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=514.9MB, alloc=4.7MB, time=38.52
memory used=518.8MB, alloc=4.7MB, time=38.81
NO POLE
NO POLE
t[1] = 0.5097
x2[1] (analytic) = 0.00083450899558950529329033653480331
x2[1] (numeric) = 0.0008346137236254626200164969237773
absolute error = 1.0472803595732672616038897399e-07
relative error = 0.012549659321928078218943439576855 %
h = 0.0001
x1[1] (analytic) = 0.0012812163581196435834521326761291
x1[1] (numeric) = 0.0012810096095421130457041724960561
absolute error = 2.067485775305377479601800730e-07
relative error = 0.016136898051627201037749778002036 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=522.6MB, alloc=4.7MB, time=39.09
NO POLE
NO POLE
t[1] = 0.5098
x2[1] (analytic) = 0.00083460184855856530760480082371625
x2[1] (numeric) = 0.00083470876842707434490727327629432
absolute error = 1.0691986850903730247245257807e-07
relative error = 0.012810883260526898926947807066936 %
h = 0.0001
x1[1] (analytic) = 0.0012811082418897332114706301651619
x1[1] (numeric) = 0.0012808971942730790964015141432863
absolute error = 2.110476166541150691160218756e-07
relative error = 0.016473831777305842542896374339259 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=526.4MB, alloc=4.7MB, time=39.39
memory used=530.2MB, alloc=4.7MB, time=39.70
NO POLE
NO POLE
t[1] = 0.5099
x2[1] (analytic) = 0.00083469472550615813023703622697089
x2[1] (numeric) = 0.00083480386034897802630625694493831
absolute error = 1.0913484281989606922071796742e-07
relative error = 0.013074821187316931800085201858884 %
h = 0.0001
x1[1] (analytic) = 0.0012810001364709052673956951209852
x1[1] (numeric) = 0.0012807847452826634237779368570444
absolute error = 2.153911882418436177582639408e-07
relative error = 0.016814298617893683025413903915007 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=534.0MB, alloc=4.7MB, time=39.98
NO POLE
NO POLE
t[1] = 0.51
x2[1] (analytic) = 0.00083478762643653936619953115948893
x2[1] (numeric) = 0.00083489899940903018121099663451941
absolute error = 1.1137297249081501146547503048e-07
relative error = 0.013341473802892021579229028059602 %
h = 0.0001
x1[1] (analytic) = 0.0012808920418620786970381472243591
x1[1] (numeric) = 0.0012806722625607518743417157373043
absolute error = 2.197793013268226964314870548e-07
relative error = 0.017158300164572936552335280885316 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
Iterations = 100
Total Elapsed Time = 40 Seconds
Elapsed Time(since restart) = 40 Seconds
Expected Time Remaining = 4 Hours 57 Minutes 2 Seconds
Optimized Time Remaining = 4 Hours 56 Minutes 56 Seconds
Time to Timeout = 14 Minutes 19 Seconds
Percent Done = 0.2244 %
> quit
memory used=536.3MB, alloc=4.7MB, time=40.13