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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,
> INFO,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_h,
> min_in_hour,
> djd_debug2,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> sec_in_min,
> djd_debug,
> glob_large_float,
> glob_look_poles,
> glob_not_yet_finished,
> glob_clock_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_start,
> glob_log10_abserr,
> glob_hmax,
> glob_disp_incr,
> glob_almost_1,
> glob_warned2,
> glob_warned,
> glob_abserr,
> glob_dump_analytic,
> glob_initial_pass,
> hours_in_day,
> glob_orig_start_sec,
> glob_max_iter,
> glob_relerr,
> glob_hmin_init,
> glob_log10normmin,
> glob_percent_done,
> glob_log10abserr,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> years_in_century,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> array_const_2,
> array_const_1,
> #END CONST
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_norms,
> array_type_pole,
> array_pole,
> array_1st_rel_error,
> array_x2_set_initial,
> array_x1_higher_work2,
> array_complex_pole,
> array_poles,
> array_x1_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_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_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[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_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[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, INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_current_iter, glob_max_trunc_err, glob_last_good_h, glob_max_opt_iter,
glob_html_log, glob_log10relerr, glob_max_hours, glob_h, min_in_hour,
djd_debug2, glob_curr_iter_when_opt, glob_small_float, glob_no_eqs,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, sec_in_min, djd_debug,
glob_large_float, glob_look_poles, glob_not_yet_finished, glob_clock_sec,
centuries_in_millinium, glob_display_flag, glob_dump, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_reached_optimal_h, glob_clock_start_sec,
glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_sec,
glob_unchanged_h_cnt, glob_smallish_float, glob_optimal_clock_start_sec,
glob_start, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_almost_1,
glob_warned2, glob_warned, glob_abserr, glob_dump_analytic,
glob_initial_pass, hours_in_day, glob_orig_start_sec, glob_max_iter,
glob_relerr, glob_hmin_init, glob_log10normmin, glob_percent_done,
glob_log10abserr, glob_optimal_start, glob_max_rel_trunc_err,
glob_log10_relerr, years_in_century, days_in_year, array_const_4D0,
array_const_0D0, array_const_2D0, array_const_3D0, array_const_2,
array_const_1, array_x1_init, array_m1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error,
array_x2_init, array_x1, array_x2, array_norms, array_type_pole, array_pole,
array_1st_rel_error, array_x2_set_initial, array_x1_higher_work2,
array_complex_pole, array_poles, array_x1_higher, array_x2_higher_work,
array_x1_set_initial, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_x2_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_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[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_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[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,
> INFO,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_h,
> min_in_hour,
> djd_debug2,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> sec_in_min,
> djd_debug,
> glob_large_float,
> glob_look_poles,
> glob_not_yet_finished,
> glob_clock_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_start,
> glob_log10_abserr,
> glob_hmax,
> glob_disp_incr,
> glob_almost_1,
> glob_warned2,
> glob_warned,
> glob_abserr,
> glob_dump_analytic,
> glob_initial_pass,
> hours_in_day,
> glob_orig_start_sec,
> glob_max_iter,
> glob_relerr,
> glob_hmin_init,
> glob_log10normmin,
> glob_percent_done,
> glob_log10abserr,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> years_in_century,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> array_const_2,
> array_const_1,
> #END CONST
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_norms,
> array_type_pole,
> array_pole,
> array_1st_rel_error,
> array_x2_set_initial,
> array_x1_higher_work2,
> array_complex_pole,
> array_poles,
> array_x1_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> 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 (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 (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, INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_current_iter, glob_max_trunc_err, glob_last_good_h, glob_max_opt_iter,
glob_html_log, glob_log10relerr, glob_max_hours, glob_h, min_in_hour,
djd_debug2, glob_curr_iter_when_opt, glob_small_float, glob_no_eqs,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, sec_in_min, djd_debug,
glob_large_float, glob_look_poles, glob_not_yet_finished, glob_clock_sec,
centuries_in_millinium, glob_display_flag, glob_dump, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_reached_optimal_h, glob_clock_start_sec,
glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_sec,
glob_unchanged_h_cnt, glob_smallish_float, glob_optimal_clock_start_sec,
glob_start, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_almost_1,
glob_warned2, glob_warned, glob_abserr, glob_dump_analytic,
glob_initial_pass, hours_in_day, glob_orig_start_sec, glob_max_iter,
glob_relerr, glob_hmin_init, glob_log10normmin, glob_percent_done,
glob_log10abserr, glob_optimal_start, glob_max_rel_trunc_err,
glob_log10_relerr, years_in_century, days_in_year, array_const_4D0,
array_const_0D0, array_const_2D0, array_const_3D0, array_const_2,
array_const_1, array_x1_init, array_m1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error,
array_x2_init, array_x1, array_x2, array_norms, array_type_pole, array_pole,
array_1st_rel_error, array_x2_set_initial, array_x1_higher_work2,
array_complex_pole, array_poles, array_x1_higher, array_x2_higher_work,
array_x1_set_initial, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
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_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_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,
> INFO,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_h,
> min_in_hour,
> djd_debug2,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> sec_in_min,
> djd_debug,
> glob_large_float,
> glob_look_poles,
> glob_not_yet_finished,
> glob_clock_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_start,
> glob_log10_abserr,
> glob_hmax,
> glob_disp_incr,
> glob_almost_1,
> glob_warned2,
> glob_warned,
> glob_abserr,
> glob_dump_analytic,
> glob_initial_pass,
> hours_in_day,
> glob_orig_start_sec,
> glob_max_iter,
> glob_relerr,
> glob_hmin_init,
> glob_log10normmin,
> glob_percent_done,
> glob_log10abserr,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> years_in_century,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> array_const_2,
> array_const_1,
> #END CONST
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_norms,
> array_type_pole,
> array_pole,
> array_1st_rel_error,
> array_x2_set_initial,
> array_x1_higher_work2,
> array_complex_pole,
> array_poles,
> array_x1_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_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, INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_current_iter, glob_max_trunc_err, glob_last_good_h, glob_max_opt_iter,
glob_html_log, glob_log10relerr, glob_max_hours, glob_h, min_in_hour,
djd_debug2, glob_curr_iter_when_opt, glob_small_float, glob_no_eqs,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, sec_in_min, djd_debug,
glob_large_float, glob_look_poles, glob_not_yet_finished, glob_clock_sec,
centuries_in_millinium, glob_display_flag, glob_dump, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_reached_optimal_h, glob_clock_start_sec,
glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_sec,
glob_unchanged_h_cnt, glob_smallish_float, glob_optimal_clock_start_sec,
glob_start, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_almost_1,
glob_warned2, glob_warned, glob_abserr, glob_dump_analytic,
glob_initial_pass, hours_in_day, glob_orig_start_sec, glob_max_iter,
glob_relerr, glob_hmin_init, glob_log10normmin, glob_percent_done,
glob_log10abserr, glob_optimal_start, glob_max_rel_trunc_err,
glob_log10_relerr, years_in_century, days_in_year, array_const_4D0,
array_const_0D0, array_const_2D0, array_const_3D0, array_const_2,
array_const_1, array_x1_init, array_m1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error,
array_x2_init, array_x1, array_x2, array_norms, array_type_pole, array_pole,
array_1st_rel_error, array_x2_set_initial, array_x1_higher_work2,
array_complex_pole, array_poles, array_x1_higher, array_x2_higher_work,
array_x1_set_initial, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_x2_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,
> INFO,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_h,
> min_in_hour,
> djd_debug2,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> sec_in_min,
> djd_debug,
> glob_large_float,
> glob_look_poles,
> glob_not_yet_finished,
> glob_clock_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_start,
> glob_log10_abserr,
> glob_hmax,
> glob_disp_incr,
> glob_almost_1,
> glob_warned2,
> glob_warned,
> glob_abserr,
> glob_dump_analytic,
> glob_initial_pass,
> hours_in_day,
> glob_orig_start_sec,
> glob_max_iter,
> glob_relerr,
> glob_hmin_init,
> glob_log10normmin,
> glob_percent_done,
> glob_log10abserr,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> years_in_century,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> array_const_2,
> array_const_1,
> #END CONST
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_norms,
> array_type_pole,
> array_pole,
> array_1st_rel_error,
> array_x2_set_initial,
> array_x1_higher_work2,
> array_complex_pole,
> array_poles,
> array_x1_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_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[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 - 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[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x1_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_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 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := 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 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 - 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 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_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 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := 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 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, INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_current_iter, glob_max_trunc_err, glob_last_good_h, glob_max_opt_iter,
glob_html_log, glob_log10relerr, glob_max_hours, glob_h, min_in_hour,
djd_debug2, glob_curr_iter_when_opt, glob_small_float, glob_no_eqs,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, sec_in_min, djd_debug,
glob_large_float, glob_look_poles, glob_not_yet_finished, glob_clock_sec,
centuries_in_millinium, glob_display_flag, glob_dump, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_reached_optimal_h, glob_clock_start_sec,
glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_sec,
glob_unchanged_h_cnt, glob_smallish_float, glob_optimal_clock_start_sec,
glob_start, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_almost_1,
glob_warned2, glob_warned, glob_abserr, glob_dump_analytic,
glob_initial_pass, hours_in_day, glob_orig_start_sec, glob_max_iter,
glob_relerr, glob_hmin_init, glob_log10normmin, glob_percent_done,
glob_log10abserr, glob_optimal_start, glob_max_rel_trunc_err,
glob_log10_relerr, years_in_century, days_in_year, array_const_4D0,
array_const_0D0, array_const_2D0, array_const_3D0, array_const_2,
array_const_1, array_x1_init, array_m1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error,
array_x2_init, array_x1, array_x2, array_norms, array_type_pole, array_pole,
array_1st_rel_error, array_x2_set_initial, array_x1_higher_work2,
array_complex_pole, array_poles, array_x1_higher, array_x2_higher_work,
array_x1_set_initial, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
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[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 - 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[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_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[1, 1] := glob_large_float;
array_complex_pole[1, 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[1, 1] := glob_large_float;
array_complex_pole[1, 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[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 - 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[2, 1] := glob_large_float;
array_complex_pole[2, 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[2, 1] := glob_large_float;
array_complex_pole[2, 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[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,
> INFO,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_h,
> min_in_hour,
> djd_debug2,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> sec_in_min,
> djd_debug,
> glob_large_float,
> glob_look_poles,
> glob_not_yet_finished,
> glob_clock_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_start,
> glob_log10_abserr,
> glob_hmax,
> glob_disp_incr,
> glob_almost_1,
> glob_warned2,
> glob_warned,
> glob_abserr,
> glob_dump_analytic,
> glob_initial_pass,
> hours_in_day,
> glob_orig_start_sec,
> glob_max_iter,
> glob_relerr,
> glob_hmin_init,
> glob_log10normmin,
> glob_percent_done,
> glob_log10abserr,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> years_in_century,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> array_const_2,
> array_const_1,
> #END CONST
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_norms,
> array_type_pole,
> array_pole,
> array_1st_rel_error,
> array_x2_set_initial,
> array_x1_higher_work2,
> array_complex_pole,
> array_poles,
> array_x1_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_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_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
> ;
> 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
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGL, INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_current_iter, glob_max_trunc_err, glob_last_good_h, glob_max_opt_iter,
glob_html_log, glob_log10relerr, glob_max_hours, glob_h, min_in_hour,
djd_debug2, glob_curr_iter_when_opt, glob_small_float, glob_no_eqs,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, sec_in_min, djd_debug,
glob_large_float, glob_look_poles, glob_not_yet_finished, glob_clock_sec,
centuries_in_millinium, glob_display_flag, glob_dump, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_reached_optimal_h, glob_clock_start_sec,
glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_sec,
glob_unchanged_h_cnt, glob_smallish_float, glob_optimal_clock_start_sec,
glob_start, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_almost_1,
glob_warned2, glob_warned, glob_abserr, glob_dump_analytic,
glob_initial_pass, hours_in_day, glob_orig_start_sec, glob_max_iter,
glob_relerr, glob_hmin_init, glob_log10normmin, glob_percent_done,
glob_log10abserr, glob_optimal_start, glob_max_rel_trunc_err,
glob_log10_relerr, years_in_century, days_in_year, array_const_4D0,
array_const_0D0, array_const_2D0, array_const_3D0, array_const_2,
array_const_1, array_x1_init, array_m1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error,
array_x2_init, array_x1, array_x2, array_norms, array_type_pole, array_pole,
array_1st_rel_error, array_x2_set_initial, array_x1_higher_work2,
array_complex_pole, array_poles, array_x1_higher, array_x2_higher_work,
array_x1_set_initial, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_x2_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_x1[iii]) then
array_norms[iii] := abs(array_x1[iii])
end if;
iii := iii + 1
end do;
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
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGL,
> INFO,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_h,
> min_in_hour,
> djd_debug2,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> sec_in_min,
> djd_debug,
> glob_large_float,
> glob_look_poles,
> glob_not_yet_finished,
> glob_clock_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_start,
> glob_log10_abserr,
> glob_hmax,
> glob_disp_incr,
> glob_almost_1,
> glob_warned2,
> glob_warned,
> glob_abserr,
> glob_dump_analytic,
> glob_initial_pass,
> hours_in_day,
> glob_orig_start_sec,
> glob_max_iter,
> glob_relerr,
> glob_hmin_init,
> glob_log10normmin,
> glob_percent_done,
> glob_log10abserr,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> years_in_century,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> array_const_2,
> array_const_1,
> #END CONST
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_norms,
> array_type_pole,
> array_pole,
> array_1st_rel_error,
> array_x2_set_initial,
> array_x1_higher_work2,
> array_complex_pole,
> array_poles,
> array_x1_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult $eq_no = 1 i = 1
> array_tmp1[1] := (array_const_4D0[1] * (array_x2[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre diff $eq_no = 1 i = 1
> array_tmp3[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp4[1] := (array_const_2D0[1] * (array_tmp3[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp2[1] - (array_tmp4[1]));
> # emit pre mult $eq_no = 1 i = 1
> array_tmp6[1] := (array_const_2D0[1] * (array_x1[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1]));
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_x1_set_initial[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[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 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1
> array_tmp9[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp10[1] := (array_const_3D0[1] * (array_tmp9[1]));
> # emit pre mult $eq_no = 2 i = 1
> array_tmp11[1] := (array_const_2D0[1] * (array_x2[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp12[1] := (array_tmp10[1] - (array_tmp11[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x1_higher[3,1];
> #emit pre sub $eq_no = 2 i = 1
> array_tmp14[1] := (array_tmp12[1] - (array_tmp13[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp15[1] := array_x1_higher[2,1];
> #emit pre sub $eq_no = 2 i = 1
> array_tmp16[1] := (array_tmp14[1] - (array_tmp15[1]));
> #emit pre add $eq_no = 2 i = 1
> array_tmp17[1] := array_tmp16[1] + array_x1[1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if not array_x2_set_initial[2,3] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[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 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> # emit pre mult $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_const_4D0,array_x2,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre diff $eq_no = 1 i = 2
> array_tmp3[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp4[2] := ats(2,array_const_2D0,array_tmp3,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp2[2] - (array_tmp4[2]));
> # emit pre mult $eq_no = 1 i = 2
> array_tmp6[2] := ats(2,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2]));
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_x1_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[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 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2
> array_tmp9[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp10[2] := ats(2,array_const_3D0,array_tmp9,1);
> # emit pre mult $eq_no = 2 i = 2
> array_tmp11[2] := ats(2,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp12[2] := (array_tmp10[2] - (array_tmp11[2]));
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x1_higher[3,2];
> #emit pre sub $eq_no = 2 i = 2
> array_tmp14[2] := (array_tmp12[2] - (array_tmp13[2]));
> #emit pre diff $eq_no = 2 i = 2
> array_tmp15[2] := array_x1_higher[2,2];
> #emit pre sub $eq_no = 2 i = 2
> array_tmp16[2] := (array_tmp14[2] - (array_tmp15[2]));
> #emit pre add $eq_no = 2 i = 2
> array_tmp17[2] := array_tmp16[2] + array_x1[2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if not array_x2_set_initial[2,4] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[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 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> # emit pre mult $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_const_4D0,array_x2,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre diff $eq_no = 1 i = 3
> array_tmp3[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp4[3] := ats(3,array_const_2D0,array_tmp3,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp2[3] - (array_tmp4[3]));
> # emit pre mult $eq_no = 1 i = 3
> array_tmp6[3] := ats(3,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3]));
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_x1_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[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 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3
> array_tmp9[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp10[3] := ats(3,array_const_3D0,array_tmp9,1);
> # emit pre mult $eq_no = 2 i = 3
> array_tmp11[3] := ats(3,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp12[3] := (array_tmp10[3] - (array_tmp11[3]));
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x1_higher[3,3];
> #emit pre sub $eq_no = 2 i = 3
> array_tmp14[3] := (array_tmp12[3] - (array_tmp13[3]));
> #emit pre diff $eq_no = 2 i = 3
> array_tmp15[3] := array_x1_higher[2,3];
> #emit pre sub $eq_no = 2 i = 3
> array_tmp16[3] := (array_tmp14[3] - (array_tmp15[3]));
> #emit pre add $eq_no = 2 i = 3
> array_tmp17[3] := array_tmp16[3] + array_x1[3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if not array_x2_set_initial[2,5] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[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 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> # emit pre mult $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_const_4D0,array_x2,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre diff $eq_no = 1 i = 4
> array_tmp3[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp4[4] := ats(4,array_const_2D0,array_tmp3,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp2[4] - (array_tmp4[4]));
> # emit pre mult $eq_no = 1 i = 4
> array_tmp6[4] := ats(4,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4]));
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_x1_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[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 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4
> array_tmp9[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp10[4] := ats(4,array_const_3D0,array_tmp9,1);
> # emit pre mult $eq_no = 2 i = 4
> array_tmp11[4] := ats(4,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp12[4] := (array_tmp10[4] - (array_tmp11[4]));
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x1_higher[3,4];
> #emit pre sub $eq_no = 2 i = 4
> array_tmp14[4] := (array_tmp12[4] - (array_tmp13[4]));
> #emit pre diff $eq_no = 2 i = 4
> array_tmp15[4] := array_x1_higher[2,4];
> #emit pre sub $eq_no = 2 i = 4
> array_tmp16[4] := (array_tmp14[4] - (array_tmp15[4]));
> #emit pre add $eq_no = 2 i = 4
> array_tmp17[4] := array_tmp16[4] + array_x1[4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if not array_x2_set_initial[2,6] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[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 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> # emit pre mult $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_const_4D0,array_x2,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre diff $eq_no = 1 i = 5
> array_tmp3[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp4[5] := ats(5,array_const_2D0,array_tmp3,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp2[5] - (array_tmp4[5]));
> # emit pre mult $eq_no = 1 i = 5
> array_tmp6[5] := ats(5,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5]));
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_x1_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[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 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5
> array_tmp9[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp10[5] := ats(5,array_const_3D0,array_tmp9,1);
> # emit pre mult $eq_no = 2 i = 5
> array_tmp11[5] := ats(5,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp12[5] := (array_tmp10[5] - (array_tmp11[5]));
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x1_higher[3,5];
> #emit pre sub $eq_no = 2 i = 5
> array_tmp14[5] := (array_tmp12[5] - (array_tmp13[5]));
> #emit pre diff $eq_no = 2 i = 5
> array_tmp15[5] := array_x1_higher[2,5];
> #emit pre sub $eq_no = 2 i = 5
> array_tmp16[5] := (array_tmp14[5] - (array_tmp15[5]));
> #emit pre add $eq_no = 2 i = 5
> array_tmp17[5] := array_tmp16[5] + array_x1[5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if not array_x2_set_initial[2,7] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[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 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_const_4D0,array_x2,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit diff $eq_no = 1
> array_tmp3[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp4[kkk] := ats(kkk,array_const_2D0,array_tmp3,1);
> #emit sub $eq_no = 1
> array_tmp5[kkk] := (array_tmp2[kkk] - (array_tmp4[kkk]));
> #emit mult $eq_no = 1
> array_tmp6[kkk] := ats(kkk,array_const_2D0,array_x1,1);
> #emit sub $eq_no = 1
> array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk]));
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_x1_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp7[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 2
> fi;# end if 1
> ;
> #emit diff $eq_no = 2
> array_tmp9[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 2
> array_tmp10[kkk] := ats(kkk,array_const_3D0,array_tmp9,1);
> #emit mult $eq_no = 2
> array_tmp11[kkk] := ats(kkk,array_const_2D0,array_x2,1);
> #emit sub $eq_no = 2
> array_tmp12[kkk] := (array_tmp10[kkk] - (array_tmp11[kkk]));
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x1_higher[3,kkk];
> #emit sub $eq_no = 2
> array_tmp14[kkk] := (array_tmp12[kkk] - (array_tmp13[kkk]));
> #emit diff $eq_no = 2
> array_tmp15[kkk] := array_x1_higher[2,kkk];
> #emit sub $eq_no = 2
> array_tmp16[kkk] := (array_tmp14[kkk] - (array_tmp15[kkk]));
> #emit add $eq_no = 2
> array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk];
> #emit assign $eq_no = 2
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_x2_set_initial[2,kkk + order_d] then # if number 2
> temporary := array_tmp17[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 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, INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_current_iter, glob_max_trunc_err, glob_last_good_h, glob_max_opt_iter,
glob_html_log, glob_log10relerr, glob_max_hours, glob_h, min_in_hour,
djd_debug2, glob_curr_iter_when_opt, glob_small_float, glob_no_eqs,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, sec_in_min, djd_debug,
glob_large_float, glob_look_poles, glob_not_yet_finished, glob_clock_sec,
centuries_in_millinium, glob_display_flag, glob_dump, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_reached_optimal_h, glob_clock_start_sec,
glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_sec,
glob_unchanged_h_cnt, glob_smallish_float, glob_optimal_clock_start_sec,
glob_start, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_almost_1,
glob_warned2, glob_warned, glob_abserr, glob_dump_analytic,
glob_initial_pass, hours_in_day, glob_orig_start_sec, glob_max_iter,
glob_relerr, glob_hmin_init, glob_log10normmin, glob_percent_done,
glob_log10abserr, glob_optimal_start, glob_max_rel_trunc_err,
glob_log10_relerr, years_in_century, days_in_year, array_const_4D0,
array_const_0D0, array_const_2D0, array_const_3D0, array_const_2,
array_const_1, array_x1_init, array_m1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error,
array_x2_init, array_x1, array_x2, array_norms, array_type_pole, array_pole,
array_1st_rel_error, array_x2_set_initial, array_x1_higher_work2,
array_complex_pole, array_poles, array_x1_higher, array_x2_higher_work,
array_x1_set_initial, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
array_tmp1[1] := array_const_4D0[1]*array_x2[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_x2_higher[2, 1];
array_tmp4[1] := array_const_2D0[1]*array_tmp3[1];
array_tmp5[1] := array_tmp2[1] - array_tmp4[1];
array_tmp6[1] := array_const_2D0[1]*array_x1[1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
if not array_x1_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp7[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
end if;
kkk := 2;
array_tmp9[1] := array_x2_higher[2, 1];
array_tmp10[1] := array_const_3D0[1]*array_tmp9[1];
array_tmp11[1] := array_const_2D0[1]*array_x2[1];
array_tmp12[1] := array_tmp10[1] - array_tmp11[1];
array_tmp13[1] := array_x1_higher[3, 1];
array_tmp14[1] := array_tmp12[1] - array_tmp13[1];
array_tmp15[1] := array_x1_higher[2, 1];
array_tmp16[1] := array_tmp14[1] - array_tmp15[1];
array_tmp17[1] := array_tmp16[1] + array_x1[1];
if not array_x2_set_initial[2, 3] then
if 1 <= glob_max_terms then
temporary := array_tmp17[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
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_const_4D0, array_x2, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
array_tmp3[2] := array_x2_higher[2, 2];
array_tmp4[2] := ats(2, array_const_2D0, array_tmp3, 1);
array_tmp5[2] := array_tmp2[2] - array_tmp4[2];
array_tmp6[2] := ats(2, array_const_2D0, array_x1, 1);
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
if not array_x1_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp7[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
end if;
kkk := 3;
array_tmp9[2] := array_x2_higher[2, 2];
array_tmp10[2] := ats(2, array_const_3D0, array_tmp9, 1);
array_tmp11[2] := ats(2, array_const_2D0, array_x2, 1);
array_tmp12[2] := array_tmp10[2] - array_tmp11[2];
array_tmp13[2] := array_x1_higher[3, 2];
array_tmp14[2] := array_tmp12[2] - array_tmp13[2];
array_tmp15[2] := array_x1_higher[2, 2];
array_tmp16[2] := array_tmp14[2] - array_tmp15[2];
array_tmp17[2] := array_tmp16[2] + array_x1[2];
if not array_x2_set_initial[2, 4] then
if 2 <= glob_max_terms then
temporary := array_tmp17[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
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_const_4D0, array_x2, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
array_tmp3[3] := array_x2_higher[2, 3];
array_tmp4[3] := ats(3, array_const_2D0, array_tmp3, 1);
array_tmp5[3] := array_tmp2[3] - array_tmp4[3];
array_tmp6[3] := ats(3, array_const_2D0, array_x1, 1);
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
if not array_x1_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp7[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
end if;
kkk := 4;
array_tmp9[3] := array_x2_higher[2, 3];
array_tmp10[3] := ats(3, array_const_3D0, array_tmp9, 1);
array_tmp11[3] := ats(3, array_const_2D0, array_x2, 1);
array_tmp12[3] := array_tmp10[3] - array_tmp11[3];
array_tmp13[3] := array_x1_higher[3, 3];
array_tmp14[3] := array_tmp12[3] - array_tmp13[3];
array_tmp15[3] := array_x1_higher[2, 3];
array_tmp16[3] := array_tmp14[3] - array_tmp15[3];
array_tmp17[3] := array_tmp16[3] + array_x1[3];
if not array_x2_set_initial[2, 5] then
if 3 <= glob_max_terms then
temporary := array_tmp17[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
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_const_4D0, array_x2, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
array_tmp3[4] := array_x2_higher[2, 4];
array_tmp4[4] := ats(4, array_const_2D0, array_tmp3, 1);
array_tmp5[4] := array_tmp2[4] - array_tmp4[4];
array_tmp6[4] := ats(4, array_const_2D0, array_x1, 1);
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
if not array_x1_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp7[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
end if;
kkk := 5;
array_tmp9[4] := array_x2_higher[2, 4];
array_tmp10[4] := ats(4, array_const_3D0, array_tmp9, 1);
array_tmp11[4] := ats(4, array_const_2D0, array_x2, 1);
array_tmp12[4] := array_tmp10[4] - array_tmp11[4];
array_tmp13[4] := array_x1_higher[3, 4];
array_tmp14[4] := array_tmp12[4] - array_tmp13[4];
array_tmp15[4] := array_x1_higher[2, 4];
array_tmp16[4] := array_tmp14[4] - array_tmp15[4];
array_tmp17[4] := array_tmp16[4] + array_x1[4];
if not array_x2_set_initial[2, 6] then
if 4 <= glob_max_terms then
temporary := array_tmp17[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
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_const_4D0, array_x2, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
array_tmp3[5] := array_x2_higher[2, 5];
array_tmp4[5] := ats(5, array_const_2D0, array_tmp3, 1);
array_tmp5[5] := array_tmp2[5] - array_tmp4[5];
array_tmp6[5] := ats(5, array_const_2D0, array_x1, 1);
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
if not array_x1_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp7[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
end if;
kkk := 6;
array_tmp9[5] := array_x2_higher[2, 5];
array_tmp10[5] := ats(5, array_const_3D0, array_tmp9, 1);
array_tmp11[5] := ats(5, array_const_2D0, array_x2, 1);
array_tmp12[5] := array_tmp10[5] - array_tmp11[5];
array_tmp13[5] := array_x1_higher[3, 5];
array_tmp14[5] := array_tmp12[5] - array_tmp13[5];
array_tmp15[5] := array_x1_higher[2, 5];
array_tmp16[5] := array_tmp14[5] - array_tmp15[5];
array_tmp17[5] := array_tmp16[5] + array_x1[5];
if not array_x2_set_initial[2, 7] then
if 5 <= glob_max_terms then
temporary := array_tmp17[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
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_const_4D0, array_x2, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
array_tmp3[kkk] := array_x2_higher[2, kkk];
array_tmp4[kkk] := ats(kkk, array_const_2D0, array_tmp3, 1);
array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := ats(kkk, array_const_2D0, array_x1, 1);
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_x1_set_initial[1, kkk + order_d] then
temporary := array_tmp7[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
end if;
array_tmp9[kkk] := array_x2_higher[2, kkk];
array_tmp10[kkk] := ats(kkk, array_const_3D0, array_tmp9, 1);
array_tmp11[kkk] := ats(kkk, array_const_2D0, array_x2, 1);
array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk];
array_tmp13[kkk] := array_x1_higher[3, kkk];
array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk];
array_tmp15[kkk] := array_x1_higher[2, kkk];
array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk];
array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
if not array_x2_set_initial[2, kkk + order_d] then
temporary := array_tmp17[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
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 := 1.0;
> 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 := 1.0; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x1p := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> - 6.0 * c3 * exp(-t);
> end;
exact_soln_x1p := proc(t)
local c1, c2, c3;
c1 := 1.0; c2 := 0.0002; c3 := 0.0003; -6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> 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 := 1.0; 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 := 1.0;
> 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 := 1.0; 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,
> INFO,
> ALWAYS,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_h,
> min_in_hour,
> djd_debug2,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_no_eqs,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> sec_in_min,
> djd_debug,
> glob_large_float,
> glob_look_poles,
> glob_not_yet_finished,
> glob_clock_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_start,
> glob_log10_abserr,
> glob_hmax,
> glob_disp_incr,
> glob_almost_1,
> glob_warned2,
> glob_warned,
> glob_abserr,
> glob_dump_analytic,
> glob_initial_pass,
> hours_in_day,
> glob_orig_start_sec,
> glob_max_iter,
> glob_relerr,
> glob_hmin_init,
> glob_log10normmin,
> glob_percent_done,
> glob_log10abserr,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> years_in_century,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> array_const_2,
> array_const_1,
> #END CONST
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_norms,
> array_type_pole,
> array_pole,
> array_1st_rel_error,
> array_x2_set_initial,
> array_x1_higher_work2,
> array_complex_pole,
> array_poles,
> array_x1_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> INFO := 2;
> ALWAYS := 1;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_current_iter := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_max_opt_iter := 10;
> glob_html_log := true;
> glob_log10relerr := 0.0;
> glob_max_hours := 0.0;
> glob_h := 0.1;
> min_in_hour := 60.0;
> djd_debug2 := true;
> glob_curr_iter_when_opt := 0;
> glob_small_float := 0.1e-50;
> glob_no_eqs := 0;
> glob_hmin := 0.00000000001;
> glob_optimal_done := false;
> glob_not_yet_start_msg := true;
> sec_in_min := 60.0;
> djd_debug := true;
> glob_large_float := 9.0e100;
> glob_look_poles := false;
> glob_not_yet_finished := true;
> glob_clock_sec := 0.0;
> centuries_in_millinium := 10.0;
> glob_display_flag := true;
> glob_dump := false;
> glob_subiter_method := 3;
> glob_normmax := 0.0;
> MAX_UNCHANGED := 10;
> glob_reached_optimal_h := false;
> glob_clock_start_sec := 0.0;
> glob_optimal_expect_sec := 0.1;
> glob_max_minutes := 0.0;
> glob_iter := 0;
> glob_max_sec := 10000.0;
> glob_unchanged_h_cnt := 0;
> glob_smallish_float := 0.1e-100;
> glob_optimal_clock_start_sec := 0.0;
> glob_start := 0;
> glob_log10_abserr := 0.1e-10;
> glob_hmax := 1.0;
> glob_disp_incr := 0.1;
> glob_almost_1 := 0.9990;
> glob_warned2 := false;
> glob_warned := false;
> glob_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_initial_pass := true;
> hours_in_day := 24.0;
> glob_orig_start_sec := 0.0;
> glob_max_iter := 1000;
> glob_relerr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_log10normmin := 0.1;
> glob_percent_done := 0.0;
> glob_log10abserr := 0.0;
> glob_optimal_start := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> years_in_century := 100.0;
> days_in_year := 365.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest6postode.ode#################");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> 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,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#");
> omniout_str(ALWAYS,"# was complicated.ode");
> omniout_str(ALWAYS,"#");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x1_init[1 + 1] := exact_soln_x1p(t_start);");
> omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1 + 1] := 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 := 1.0;");
> 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_x1p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"- 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 := 1.0;");
> 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 := 1.0;");
> 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
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_x1_init:= Array(1..(max_terms + 1),[]);
> array_m1:= 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_t:= 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_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_x2:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_x2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> 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_m1[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_t[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_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_x2_init[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_x2[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_type_pole[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_1st_rel_error[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_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 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 <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_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 <=3 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
> ;
> 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 <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 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 <=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 <=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
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> 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_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_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_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_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_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_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0[1] := 2.0;
> array_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_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_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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #
> # was complicated.ode
> #
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[0 + 1] := exact_soln_x1(t_start);
> array_x1_init[1 + 1] := exact_soln_x1p(t_start);
> array_x2_init[0 + 1] := exact_soln_x2(t_start);
> array_x2_init[1 + 1] := 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
> array_x1_set_initial[1,1] := true;
> array_x1_set_initial[1,2] := true;
> array_x1_set_initial[1,3] := false;
> array_x1_set_initial[1,4] := false;
> array_x1_set_initial[1,5] := false;
> array_x1_set_initial[1,6] := false;
> array_x1_set_initial[1,7] := false;
> array_x1_set_initial[1,8] := false;
> array_x1_set_initial[1,9] := false;
> array_x1_set_initial[1,10] := false;
> array_x1_set_initial[1,11] := false;
> array_x1_set_initial[1,12] := false;
> array_x1_set_initial[1,13] := false;
> array_x1_set_initial[1,14] := false;
> array_x1_set_initial[1,15] := false;
> array_x1_set_initial[1,16] := false;
> array_x1_set_initial[1,17] := false;
> array_x1_set_initial[1,18] := false;
> array_x1_set_initial[1,19] := false;
> array_x1_set_initial[1,20] := false;
> array_x1_set_initial[1,21] := false;
> array_x1_set_initial[1,22] := false;
> array_x1_set_initial[1,23] := false;
> array_x1_set_initial[1,24] := false;
> array_x1_set_initial[1,25] := false;
> array_x1_set_initial[1,26] := false;
> array_x1_set_initial[1,27] := false;
> array_x1_set_initial[1,28] := false;
> array_x1_set_initial[1,29] := false;
> array_x1_set_initial[1,30] := false;
> array_x2_set_initial[2,1] := true;
> array_x2_set_initial[2,2] := true;
> array_x2_set_initial[2,3] := false;
> array_x2_set_initial[2,4] := false;
> array_x2_set_initial[2,5] := false;
> array_x2_set_initial[2,6] := false;
> array_x2_set_initial[2,7] := false;
> array_x2_set_initial[2,8] := false;
> array_x2_set_initial[2,9] := false;
> array_x2_set_initial[2,10] := false;
> array_x2_set_initial[2,11] := false;
> array_x2_set_initial[2,12] := false;
> array_x2_set_initial[2,13] := false;
> array_x2_set_initial[2,14] := false;
> array_x2_set_initial[2,15] := false;
> array_x2_set_initial[2,16] := false;
> array_x2_set_initial[2,17] := false;
> array_x2_set_initial[2,18] := false;
> array_x2_set_initial[2,19] := false;
> array_x2_set_initial[2,20] := false;
> array_x2_set_initial[2,21] := false;
> array_x2_set_initial[2,22] := false;
> array_x2_set_initial[2,23] := false;
> array_x2_set_initial[2,24] := false;
> array_x2_set_initial[2,25] := false;
> array_x2_set_initial[2,26] := false;
> array_x2_set_initial[2,27] := false;
> array_x2_set_initial[2,28] := false;
> array_x2_set_initial[2,29] := false;
> array_x2_set_initial[2,30] := false;
> if glob_html_log then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_t[1] := t_start;
> array_t[2] := glob_h;
> order_diff := 2;
> #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
> ;
> 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
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> 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)
> ;
> 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)
> ;
> 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;
> if glob_subiter_method = 1 then # if number 3
> atomall();
> elif glob_subiter_method = 2 then # if number 4
> subiter := 1;
> while subiter <= 3 do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while subiter <= 3 + glob_max_terms do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> fi;# end if 4
> ;
> if (glob_look_poles) then # if number 4
> #left paren 0004C
> check_for_pole();
> fi;# end if 4
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> #Jump Series array_x1
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[3,iii] := array_x1_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_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 =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #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 =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> 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 =1
> #BEFORE ADJUST SUBSERIES EQ =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 =1
> #BEFORE SUM SUBSERIES EQ =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 =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #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 =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #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 =1
> #BEFORE ADJUST SUBSERIES EQ =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 =1
> #BEFORE SUM SUBSERIES EQ =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 =1
> #BEFORE ADJUST SUBSERIES EQ =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 =1
> #BEFORE SUM SUBSERIES EQ =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 =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_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
> #Jump Series array_x2
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x2
> #BEFORE ADJUST SUBSERIES EQ =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 =2
> #BEFORE SUM SUBSERIES EQ =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 =2
> #BEFORE ADJUST SUBSERIES EQ =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 =2
> #BEFORE SUM SUBSERIES EQ =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 =2
> #BEFORE ADJUST SUBSERIES EQ =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 =2
> #BEFORE SUM SUBSERIES EQ =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 =2
> #BEFORE ADJUST SUBSERIES EQ =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 =2
> #BEFORE SUM SUBSERIES EQ =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 =2
> #BEFORE ADJUST SUBSERIES EQ =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 =2
> #BEFORE SUM SUBSERIES EQ =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 =2
> #BEFORE ADJUST SUBSERIES EQ =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 =2
> #BEFORE SUM SUBSERIES EQ =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 =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_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
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 4
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 4
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 4
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> 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_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if glob_html_log then # if number 4
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-13T02:43:31-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest6")
> ;
> logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * 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 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 5
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 5
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"mtest6 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest6 maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + 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 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then # if number 5
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;# end if 5
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 4
> ;
> if glob_html_log then # if number 4
> fclose(html_log_file);
> fi;# end if 4
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
Warning, `subiter` is implicitly declared local to procedure `mainprog`
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp,
subiter;
global DEBUGL, INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_current_iter, glob_max_trunc_err, glob_last_good_h, glob_max_opt_iter,
glob_html_log, glob_log10relerr, glob_max_hours, glob_h, min_in_hour,
djd_debug2, glob_curr_iter_when_opt, glob_small_float, glob_no_eqs,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, sec_in_min, djd_debug,
glob_large_float, glob_look_poles, glob_not_yet_finished, glob_clock_sec,
centuries_in_millinium, glob_display_flag, glob_dump, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_reached_optimal_h, glob_clock_start_sec,
glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_sec,
glob_unchanged_h_cnt, glob_smallish_float, glob_optimal_clock_start_sec,
glob_start, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_almost_1,
glob_warned2, glob_warned, glob_abserr, glob_dump_analytic,
glob_initial_pass, hours_in_day, glob_orig_start_sec, glob_max_iter,
glob_relerr, glob_hmin_init, glob_log10normmin, glob_percent_done,
glob_log10abserr, glob_optimal_start, glob_max_rel_trunc_err,
glob_log10_relerr, years_in_century, days_in_year, array_const_4D0,
array_const_0D0, array_const_2D0, array_const_3D0, array_const_2,
array_const_1, array_x1_init, array_m1, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error,
array_x2_init, array_x1, array_x2, array_norms, array_type_pole, array_pole,
array_1st_rel_error, array_x2_set_initial, array_x1_higher_work2,
array_complex_pole, array_poles, array_x1_higher, array_x2_higher_work,
array_x1_set_initial, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
INFO := 2;
ALWAYS := 1;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_current_iter := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_max_opt_iter := 10;
glob_html_log := true;
glob_log10relerr := 0.;
glob_max_hours := 0.;
glob_h := 0.1;
min_in_hour := 60.0;
djd_debug2 := true;
glob_curr_iter_when_opt := 0;
glob_small_float := 0.1*10^(-50);
glob_no_eqs := 0;
glob_hmin := 0.1*10^(-10);
glob_optimal_done := false;
glob_not_yet_start_msg := true;
sec_in_min := 60.0;
djd_debug := true;
glob_large_float := 0.90*10^101;
glob_look_poles := false;
glob_not_yet_finished := true;
glob_clock_sec := 0.;
centuries_in_millinium := 10.0;
glob_display_flag := true;
glob_dump := false;
glob_subiter_method := 3;
glob_normmax := 0.;
MAX_UNCHANGED := 10;
glob_reached_optimal_h := false;
glob_clock_start_sec := 0.;
glob_optimal_expect_sec := 0.1;
glob_max_minutes := 0.;
glob_iter := 0;
glob_max_sec := 10000.0;
glob_unchanged_h_cnt := 0;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_clock_start_sec := 0.;
glob_start := 0;
glob_log10_abserr := 0.1*10^(-10);
glob_hmax := 1.0;
glob_disp_incr := 0.1;
glob_almost_1 := 0.9990;
glob_warned2 := false;
glob_warned := false;
glob_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_initial_pass := true;
hours_in_day := 24.0;
glob_orig_start_sec := 0.;
glob_max_iter := 1000;
glob_relerr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_log10normmin := 0.1;
glob_percent_done := 0.;
glob_log10abserr := 0.;
glob_optimal_start := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
years_in_century := 100.0;
days_in_year := 365.0;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest6postode.ode#################");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
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, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#");
omniout_str(ALWAYS, "# was complicated.ode");
omniout_str(ALWAYS, "#");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x1_init[1 + 1] := exact_soln_x1p(t_start);")
;
omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[1 + 1] := 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 := 1.0;");
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_x1p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "- 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 := 1.0;");
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 := 1.0;");
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_x1_init := Array(1 .. max_terms + 1, []);
array_m1 := 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_t := 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_last_rel_error := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_x2 := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_x2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x1_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_x1_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
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_m1[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_t[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_last_rel_error[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_x1[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_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_set_initial[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_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 <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[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_x1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 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 <= 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 <= 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;
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_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_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[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_x1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
end do;
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_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_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_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_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_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_x1_init[2] := exact_soln_x1p(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();
array_x1_set_initial[1, 1] := true;
array_x1_set_initial[1, 2] := true;
array_x1_set_initial[1, 3] := false;
array_x1_set_initial[1, 4] := false;
array_x1_set_initial[1, 5] := false;
array_x1_set_initial[1, 6] := false;
array_x1_set_initial[1, 7] := false;
array_x1_set_initial[1, 8] := false;
array_x1_set_initial[1, 9] := false;
array_x1_set_initial[1, 10] := false;
array_x1_set_initial[1, 11] := false;
array_x1_set_initial[1, 12] := false;
array_x1_set_initial[1, 13] := false;
array_x1_set_initial[1, 14] := false;
array_x1_set_initial[1, 15] := false;
array_x1_set_initial[1, 16] := false;
array_x1_set_initial[1, 17] := false;
array_x1_set_initial[1, 18] := false;
array_x1_set_initial[1, 19] := false;
array_x1_set_initial[1, 20] := false;
array_x1_set_initial[1, 21] := false;
array_x1_set_initial[1, 22] := false;
array_x1_set_initial[1, 23] := false;
array_x1_set_initial[1, 24] := false;
array_x1_set_initial[1, 25] := false;
array_x1_set_initial[1, 26] := false;
array_x1_set_initial[1, 27] := false;
array_x1_set_initial[1, 28] := false;
array_x1_set_initial[1, 29] := false;
array_x1_set_initial[1, 30] := false;
array_x2_set_initial[2, 1] := true;
array_x2_set_initial[2, 2] := true;
array_x2_set_initial[2, 3] := false;
array_x2_set_initial[2, 4] := false;
array_x2_set_initial[2, 5] := false;
array_x2_set_initial[2, 6] := false;
array_x2_set_initial[2, 7] := false;
array_x2_set_initial[2, 8] := false;
array_x2_set_initial[2, 9] := false;
array_x2_set_initial[2, 10] := false;
array_x2_set_initial[2, 11] := false;
array_x2_set_initial[2, 12] := false;
array_x2_set_initial[2, 13] := false;
array_x2_set_initial[2, 14] := false;
array_x2_set_initial[2, 15] := false;
array_x2_set_initial[2, 16] := false;
array_x2_set_initial[2, 17] := false;
array_x2_set_initial[2, 18] := false;
array_x2_set_initial[2, 19] := false;
array_x2_set_initial[2, 20] := false;
array_x2_set_initial[2, 21] := false;
array_x2_set_initial[2, 22] := false;
array_x2_set_initial[2, 23] := false;
array_x2_set_initial[2, 24] := false;
array_x2_set_initial[2, 25] := false;
array_x2_set_initial[2, 26] := false;
array_x2_set_initial[2, 27] := false;
array_x2_set_initial[2, 28] := false;
array_x2_set_initial[2, 29] := false;
array_x2_set_initial[2, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
order_diff := 2;
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;
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;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
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);
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);
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;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 3 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
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;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[3, iii] := array_x1_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_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)!;
ord := 2;
calc_term := 2;
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;
temp_sum := 0.;
ord := 2;
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)!;
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;
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)!;
ord := 1;
calc_term := 3;
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;
temp_sum := 0.;
ord := 1;
calc_term := 3;
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)!;
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;
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)!;
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;
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;
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;
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)!;
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;
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)!;
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;
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)!;
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;
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)!;
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;
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)!;
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;
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;
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 (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
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_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, "2012-06-13T02:43:31-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest6")
;
logitem_str(html_log_file,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * 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, " 090 | ");
logitem_str(html_log_file,
"mtest6 diffeq.mxt");
logitem_str(html_log_file,
"mtest6 maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \
2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + 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/mtest6postode.ode#################
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
#
# was complicated.ode
#
t_start := 0.5;
t_end := 5.0;
array_x1_init[0 + 1] := exact_soln_x1(t_start);
array_x1_init[1 + 1] := exact_soln_x1p(t_start);
array_x2_init[0 + 1] := exact_soln_x2(t_start);
array_x2_init[1 + 1] := 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 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x1p := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
- 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 1.0;
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 := 1.0;
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
x1[1] (analytic) = 2.001091755187482740162486839163
x1[1] (numeric) = 2.001091755187482740162486839163
absolute error = 0
relative error = 0 %
h = 0.0001
x2[1] (analytic) = 1.0007256155636055990741531973548
x2[1] (numeric) = 1.0007256155636055990741531973548
absolute error = 0
relative error = 0 %
h = 0.0001
t[1] = 0.5
x1[1] (analytic) = 2.001091755187482740162486839163
x1[1] (numeric) = 2.001091755187482740162486839163
absolute error = 0
relative error = 0 %
h = 0.0001
x2[1] (analytic) = 1.0007256155636055990741531973548
x2[1] (numeric) = 1.0007256155636055990741531973548
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
x1[1] (analytic) = 2.0010916460174225858712352664712
x1[1] (numeric) = 2.001091646006505255470640983898
absolute error = 1.09173304005942825732e-11
relative error = 5.4556873606073863903748488926446e-10 %
h = 0.0001
x2[1] (analytic) = 1.0007257061107425639459896605159
x2[1] (numeric) = 1.0007257061162020742151580693388
absolute error = 5.4595102691684088229e-12
relative error = 5.4555511423669245702936044230717e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.4MB, time=0.48
memory used=11.4MB, alloc=4.4MB, time=0.76
NO POLE
NO POLE
t[1] = 0.5002
x1[1] (analytic) = 2.0010915368582788917633066026401
x1[1] (numeric) = 2.0010915368145916675299795643453
absolute error = 4.36872242333270382948e-11
relative error = 2.1831697065650550796183674704255e-09 %
h = 0.0001
x2[1] (analytic) = 1.0007257966814495432344339416603
x2[1] (numeric) = 1.0007257967032906645626797694799
absolute error = 2.18411213282458278196e-11
relative error = 2.1825280612005928860442019527042e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.4MB, time=1.03
NO POLE
NO POLE
t[1] = 0.5003
x1[1] (analytic) = 2.0010914277100505662472629969306
x1[1] (numeric) = 2.0010914276117408853032277932713
absolute error = 9.83096809440352036593e-11
relative error = 4.9128030625035413584519207841583e-09 %
h = 0.0001
x2[1] (analytic) = 1.0007258872757307055634980331085
x2[1] (numeric) = 1.0007258873248799067876632386685
absolute error = 4.91492012241652055600e-11
relative error = 4.9113550322919838364022401174740e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.4MB, time=1.30
memory used=22.8MB, alloc=4.5MB, time=1.58
NO POLE
NO POLE
t[1] = 0.5004
x1[1] (analytic) = 2.001091318572736517840820284614
x1[1] (numeric) = 2.0010913183979518176445775430023
absolute error = 1.747847001962427416117e-10
relative error = 8.7344689657095023289491022221377e-09 %
h = 0.0001
x2[1] (analytic) = 1.0007259778935902204455844087623
x2[1] (numeric) = 1.0007259779809783394315848171717
absolute error = 8.73881189860004084094e-11
relative error = 8.7324723167416977908507146443463e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.5MB, time=1.84
NO POLE
NO POLE
t[1] = 0.5005
x1[1] (analytic) = 2.001091209446335655170837072148
x1[1] (numeric) = 2.0010912091732233732996766117045
absolute error = 2.731122818711604604435e-10
relative error = 1.3648167588858955514853423353676e-08 %
h = 0.0001
x2[1] (analytic) = 1.0007260685350322582816582620126
x2[1] (numeric) = 1.0007260686715945029068425367838
absolute error = 1.365622446251842747712e-10
relative error = 1.3646316301632714187506947314974e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.5MB, time=2.11
NO POLE
NO POLE
t[1] = 0.5006
x1[1] (analytic) = 2.0010911003308468869733038234462
x1[1] (numeric) = 2.0010910999375544609056179886155
absolute error = 3.932924260676858348307e-10
relative error = 1.9653899115470631069134819564991e-08 %
h = 0.0001
x2[1] (analytic) = 1.0007261592000609903614197786446
x2[1] (numeric) = 1.0007261593967369394971464926269
absolute error = 1.966759491357267139823e-10
relative error = 1.9653323471921760806638407772079e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.5MB, time=2.38
memory used=38.1MB, alloc=4.5MB, time=2.67
NO POLE
NO POLE
t[1] = 0.5007
x1[1] (analytic) = 2.0010909912262691220933319472376
x1[1] (numeric) = 2.0010909906909439889909291182261
absolute error = 5.353251331024028290115e-10
relative error = 2.6751663739905971838031954100662e-08 %
h = 0.0001
x2[1] (analytic) = 1.0007262498886805888634764447463
x2[1] (numeric) = 1.0007262501564141933579092946166
absolute error = 2.677336044944328498703e-10
relative error = 2.6753930410460919523106383485470e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.5MB, time=2.94
NO POLE
NO POLE
t[1] = 0.5008
x1[1] (analytic) = 2.0010908821326012694851428855176
x1[1] (numeric) = 2.001090881433390865975561163414
absolute error = 6.992104035095817221036e-10
relative error = 3.4941461667369133530238331006972e-08 %
h = 0.0001
x2[1] (analytic) = 1.0007263406008952268555153896278
x2[1] (numeric) = 1.0007263409506348105166365986095
absolute error = 3.497395836611212089817e-10
relative error = 3.4948573798019236425347323071455e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.5MB, time=3.21
memory used=49.5MB, alloc=4.5MB, time=3.49
NO POLE
NO POLE
t[1] = 0.5009
x1[1] (analytic) = 2.0010907730498422382120572030903
x1[1] (numeric) = 2.0010907721648940001708782675271
absolute error = 8.849482380411789355632e-10
relative error = 4.4223293113906984991337531440920e-08 %
h = 0.0001
x2[1] (analytic) = 1.0007264313367090782944757637584
x2[1] (numeric) = 1.0007264317794073388733177172481
absolute error = 4.426982605788419534897e-10
relative error = 4.4237690413304336301705945767196e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.5MB, time=3.77
NO POLE
NO POLE
t[1] = 0.501
x1[1] (analytic) = 2.001090663977990937446483678202
x1[1] (numeric) = 2.0010906628854522997796468154187
absolute error = 1.0925386376668368627833e-09
relative error = 5.4597158306409108583368010413427e-08 %
h = 0.0001
x2[1] (analytic) = 1.0007265220961263180267211517279
x2[1] (numeric) = 1.00072652264274032820081631052
absolute error = 5.466140101740951587921e-10
relative error = 5.4621717132984041495124052030636e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.5MB, time=4.04
NO POLE
NO POLE
t[1] = 0.5011
x1[1] (analytic) = 2.0010905549170462764699083942649
x1[1] (numeric) = 2.0010905535950646728960246934323
absolute error = 1.3219816035738837008326e-09
relative error = 6.6063057482607800669582790087733e-08 %
h = 0.0001
x2[1] (analytic) = 1.0007266128791511217882120202398
x2[1] (numeric) = 1.0007266135406423301452611560463
absolute error = 6.614912083570491358065e-10
relative error = 6.6101090931707995126859189806599e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.5MB, time=4.31
memory used=64.8MB, alloc=4.5MB, time=4.59
NO POLE
NO POLE
t[1] = 0.5012
x1[1] (analytic) = 2.0010904458670071646728838326719
x1[1] (numeric) = 2.0010904442937300275055505483374
absolute error = 1.5732771371673332843345e-09
relative error = 7.8620990891078072204379434751757e-08 %
h = 0.0001
x2[1] (analytic) = 1.000726703685787666204678201143
x2[1] (numeric) = 1.0007267044731218982264369991164
absolute error = 7.873342320217587979734e-10
relative error = 7.8676248882129288690247064292639e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.5MB, time=4.86
NO POLE
NO POLE
t[1] = 0.5013
x1[1] (analytic) = 2.0010903368278725115550179667025
x1[1] (numeric) = 2.0010903349814472714851330452158
absolute error = 1.8464252400698849214867e-09
relative error = 9.2270958791237649428425665254899e-08 %
h = 0.0001
x2[1] (analytic) = 1.0007267945160401287917914095088
x2[1] (numeric) = 1.0007267954401875878381754824849
absolute error = 9.241474590463840729761e-10
relative error = 9.2347628154926094015351682441506e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.5MB, time=5.14
memory used=76.2MB, alloc=4.6MB, time=5.43
NO POLE
NO POLE
t[1] = 0.5014
x1[1] (analytic) = 2.0010902277996412267249633565185
x1[1] (numeric) = 2.0010902256582153126030401242979
absolute error = 2.1414259141219232322206e-09
relative error = 1.0701296145334697466894100604997e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007268853699126879553377967599
x2[1] (numeric) = 1.0007268864418479562487461559465
absolute error = 1.0719352682934083591866e-09
relative error = 1.0711566601882329960537718169916e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.6MB, time=5.73
NO POLE
NO POLE
t[1] = 0.5015
x1[1] (analytic) = 2.001090118782312219900406245251
x1[1] (numeric) = 2.0010901163240330585188882567491
absolute error = 2.4582791613815179885019e-09
relative error = 1.2284699915850920724520479796573e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007269762474095229913905388596
x2[1] (numeric) = 1.0007269774781115626012475657053
absolute error = 1.2307020396098570268457e-09
relative error = 1.2298079984061415134561534514462e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.6MB, time=6.02
NO POLE
NO POLE
t[1] = 0.5016
x1[1] (analytic) = 2.0010900097758844009080556561764
x1[1] (numeric) = 2.0010900069788994167836316994067
absolute error = 2.7969849841244239567697e-09
relative error = 1.3977307219867022447915602145759e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007270671485348140864824595667
x2[1] (numeric) = 1.0007270685489869679139984235543
absolute error = 1.4004521538275159639876e-09
relative error = 1.3994346708518189758591263271196e-07 %
h = 0.0001
memory used=87.7MB, alloc=4.6MB, time=6.30
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.6MB, time=6.59
NO POLE
NO POLE
t[1] = 0.5017
x1[1] (analytic) = 2.0010899007803566796836324909845
x1[1] (numeric) = 2.0010898976228132948395517484667
absolute error = 3.1575433848440807425178e-09
relative error = 1.5779118087661862281127020066184e-07 %
h = 0.0001
x2[1] (analytic) = 1.000727158073292742317778688764
x2[1] (numeric) = 1.0007271596544827350809288558817
absolute error = 1.5811899927631501671177e-09
relative error = 1.5800410531552143859748065436125e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.6MB, time=6.87
NO POLE
NO POLE
t[1] = 0.5018
x1[1] (analytic) = 2.0010897917957279662718586291348
x1[1] (numeric) = 2.0010897882557736000202459921201
absolute error = 3.5399543662516126370147e-09
relative error = 1.7690132550598571902153885464191e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007272490216874896532493558668
x2[1] (numeric) = 1.0007272507946074288719717325198
absolute error = 1.7729199392187223766530e-09
relative error = 1.7716315219276098040494394022900e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.6MB, time=7.14
memory used=102.9MB, alloc=4.6MB, time=7.43
NO POLE
NO POLE
t[1] = 0.5019
x1[1] (analytic) = 2.0010896828219971708264460283046
x1[1] (numeric) = 2.0010896788777792395506175621395
absolute error = 3.9442179312758284661651e-09
relative error = 1.9710350641124555155569179053298e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007273399937232389518423183184
x2[1] (numeric) = 1.0007273419693696159334540754524
absolute error = 1.9756463769816117571340e-09
relative error = 1.9742104547618369299446887910379e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.6MB, time=7.71
NO POLE
NO POLE
t[1] = 0.502
x1[1] (analytic) = 2.0010895738591632036100858259251
x1[1] (numeric) = 2.0010895694888291205468643844151
absolute error = 4.3703340830632214415100e-09
relative error = 2.1839772392771488195651768845875e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007274309894041739636559251805
x2[1] (numeric) = 1.0007274331787778647884885473975
absolute error = 2.1893736908248326222170e-09
relative error = 2.1877822302324937289881767657499e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.6MB, time=8.01
NO POLE
NO POLE
memory used=114.4MB, alloc=4.6MB, time=8.30
t[1] = 0.5021
x1[1] (analytic) = 2.0010894649072249749944374418092
x1[1] (numeric) = 2.0010894600889221500164684284404
absolute error = 4.8183028249779690133688e-09
relative error = 2.4078397840155319640045325645955e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007275220087344793301118158238
x2[1] (numeric) = 1.0007275244228407458373650202804
absolute error = 2.4141062665072532044566e-09
relative error = 2.4123512278961611016026109876809e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.6MB, time=8.59
NO POLE
NO POLE
t[1] = 0.5022
x1[1] (analytic) = 2.0010893559661813954601176818676
x1[1] (numeric) = 2.0010893506780572348581849557472
absolute error = 5.2881241606019327261204e-09
relative error = 2.6426227018976270733929140787377e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007276130517183405841277537279
x2[1] (numeric) = 1.0007276157015668313579422236147
absolute error = 2.6498484907738144698868e-09
relative error = 2.6479218282916195967214384929129e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.6MB, time=8.88
NO POLE
NO POLE
t[1] = 0.5023
x1[1] (analytic) = 2.001089247036031375596689842915
x1[1] (numeric) = 2.0010892412562332818620317672906
absolute error = 5.7797980937346580756244e-09
relative error = 2.8883259966018835524706380188824e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007277041183599441502904953943
x2[1] (numeric) = 1.0007277070149646955060394728059
absolute error = 2.8966047513557489774116e-09
relative error = 2.8944984129400661690014622523950e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.6MB, time=9.17
memory used=129.7MB, alloc=4.6MB, time=9.47
NO POLE
NO POLE
t[1] = 0.5024
x1[1] (analytic) = 2.001089138116773826102652818566
x1[1] (numeric) = 2.0010891318234491977092784497824
absolute error = 6.2933246283933743687836e-09
relative error = 3.1449496719151781047215808520220e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007277952086634773450286943839
x2[1] (numeric) = 1.000727798363042914315828477395
absolute error = 3.1543794369707997830111e-09
relative error = 3.1520853643453309798379603428368e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.6MB, time=9.77
NO POLE
NO POLE
t[1] = 0.5025
x1[1] (analytic) = 2.0010890292084076577854302062196
x1[1] (numeric) = 2.0010890223797038889724356209744
absolute error = 6.8287037688129945852452e-09
relative error = 3.4124937317328147519454027610353e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007278863226331283767858404813
x2[1] (numeric) = 1.0007278897458100657002252292572
absolute error = 3.4231769373234393887759e-09
relative error = 3.4206870659940942421946424044487e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.6MB, time=10.05
memory used=141.1MB, alloc=4.6MB, time=10.34
NO POLE
NO POLE
t[1] = 0.5026
x1[1] (analytic) = 2.0010889203109317815613594151339
x1[1] (numeric) = 2.0010889129249962621152441738905
absolute error = 7.3859355194461152412434e-09
relative error = 3.6909581800585248548821758792195e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007279774602730863461932339965
x2[1] (numeric) = 1.0007279811632747294512819707725
absolute error = 3.7030016431050887367760e-09
relative error = 3.7003079023561031092541826593401e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.6MB, time=10.62
NO POLE
NO POLE
t[1] = 0.5027
x1[1] (analytic) = 2.0010888114243451084556807755893
x1[1] (numeric) = 2.0010888034593252234926645200078
absolute error = 7.9650198849630162555815e-09
relative error = 3.9803430210044671348884711395453e-07 %
h = 0.0001
x2[1] (analytic) = 1.000728068621587541246242995209
x2[1] (numeric) = 1.0007280726154454872405792429842
absolute error = 3.9938579459943362477752e-09
relative error = 3.9909522588843886068998650736205e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.6MB, time=10.90
NO POLE
NO POLE
t[1] = 0.5028
x1[1] (analytic) = 2.0010887025486465496025266491408
x1[1] (numeric) = 2.0010886939826896793508658313869
absolute error = 8.5659568702516608177539e-09
relative error = 4.2806482587912276966651073327741e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007281598065806839624611089617
x2[1] (numeric) = 1.0007281641023309226196180137612
absolute error = 4.2957502386571569047995e-09
relative error = 4.2926245220154826100363778631386e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.6MB, time=11.18
memory used=156.4MB, alloc=4.6MB, time=11.66
NO POLE
NO POLE
t[1] = 0.5029
x1[1] (analytic) = 2.0010885936838350162449105399592
x1[1] (numeric) = 2.0010885844950885358272152817503
absolute error = 9.1887464804176952582089e-09
relative error = 4.5918738977478200520370158319263e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007282510152567062730805044118
x2[1] (numeric) = 1.0007282556239396210202118859809
absolute error = 4.6086829147471313815691e-09
relative error = 4.6053290791696348627588935418688e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.6MB, time=12.36
NO POLE
NO POLE
t[1] = 0.503
x1[1] (analytic) = 2.0010884848299094197347162072617
x1[1] (numeric) = 2.0010884749965206989502672865103
absolute error = 9.8333887207844489207514e-09
relative error = 4.9140199423116851447847749296013e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007283422476198008492141699459
x2[1] (numeric) = 1.0007283471802801697548793857478
absolute error = 4.9326603689056652158019e-09
relative error = 4.9290703187510300423778717479047e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.6MB, time=13.06
memory used=167.8MB, alloc=4.6MB, time=13.78
NO POLE
NO POLE
t[1] = 0.5031
x1[1] (analytic) = 2.0010883759868686715326867788304
x1[1] (numeric) = 2.0010883654869850746397527417449
absolute error = 1.04998835968929340370855e-08
relative error = 5.2470863970286913765278174889696e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007284335036741612550283032656
x2[1] (numeric) = 1.0007284387713611580172363306651
absolute error = 5.2676869967622080273995e-09
relative error = 5.2638526301480048673101196253578e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.6MB, time=14.49
NO POLE
NO POLE
t[1] = 0.5032
x1[1] (analytic) = 2.0010882671547116832084138656195
x1[1] (numeric) = 2.0010882559664805687065682621227
absolute error = 1.11882311145018456034968e-08
relative error = 5.5910732665531346336592156629025e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007285247834239819479154966509
x2[1] (numeric) = 1.0007285303971911768823882781747
absolute error = 5.6137671949344727815238e-09
relative error = 5.6096804037332652488437464491261e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.6MB, time=15.20
NO POLE
NO POLE
t[1] = 0.5033
x1[1] (analytic) = 2.0010881583334373664403266774516
x1[1] (numeric) = 2.0010881464350060868527654177757
absolute error = 1.18984312795875612596759e-08
relative error = 5.9459805556477383153327959727089e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007286160868734582786679574086
x2[1] (numeric) = 1.000728622057778819307323053982
absolute error = 5.9709053610286550965734e-09
relative error = 5.9665580308641034867857481781177e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.6MB, time=15.90
memory used=183.1MB, alloc=4.6MB, time=16.62
NO POLE
NO POLE
t[1] = 0.5034
x1[1] (analytic) = 2.0010880495230446330156811398021
x1[1] (numeric) = 2.0010880368925605346715399701205
absolute error = 1.26304840983441411696816e-08
relative error = 6.3118082691836533625018388531378e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007287074140267864916507635123
x2[1] (numeric) = 1.0007287137531326801313033605818
absolute error = 6.3391058936396525970695e-09
relative error = 6.3344899038826155090014570570618e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.6MB, time=17.33
NO POLE
NO POLE
t[1] = 0.5035
x1[1] (analytic) = 2.0010879407235323948305490116711
x1[1] (numeric) = 2.0010879273391428176472211066282
absolute error = 1.33843895771833279050429e-08
relative error = 6.6885564121404582880089166061388e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007287987648881637249751544417
x2[1] (numeric) = 1.0007288054832613560762594659013
absolute error = 6.7183731923512843114596e-09
relative error = 6.7134804161159181548536922047892e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.6MB, time=18.04
memory used=194.5MB, alloc=4.6MB, time=18.76
NO POLE
NO POLE
t[1] = 0.5036
x1[1] (analytic) = 2.0010878319348995638898070045447
x1[1] (numeric) = 2.0010878177747518411552606745417
absolute error = 1.41601477227345463300030e-08
relative error = 7.0762249896061592077284725905169e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007288901394617880106718572265
x2[1] (numeric) = 1.0007288972481734457471819720763
absolute error = 7.1087116577365101148498e-09
relative error = 7.1035339618763665025519451050984e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.6MB, time=19.48
NO POLE
NO POLE
t[1] = 0.5037
x1[1] (analytic) = 2.0010877231571450523071259024436
x1[1] (numeric) = 2.0010877081993865104622224135413
absolute error = 1.49577585418449034889023e-08
relative error = 7.4748140067771898727606461596395e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007289815377518582748644477049
x2[1] (numeric) = 1.0007289890478775496325146643772
absolute error = 7.5101256913576502166723e-09
relative error = 7.5046549364617712404177367729975e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.6MB, time=20.19
NO POLE
NO POLE
t[1] = 0.5038
x1[1] (analytic) = 2.0010876143902677723049596830596
x1[1] (numeric) = 2.0010875986130457307257711873582
absolute error = 1.57772220415791884957014e-08
relative error = 7.8843234689584117026768467709404e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007290729597625743379427469999
x2[1] (numeric) = 1.0007290808823822701045474403005
absolute error = 7.9226196957666046933006e-09
relative error = 7.9168477361556160820781788709467e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.6MB, time=20.90
memory used=209.8MB, alloc=4.6MB, time=21.62
NO POLE
NO POLE
t[1] = 0.5039
x1[1] (analytic) = 2.0010875056342666362145346399805
x1[1] (numeric) = 2.0010874890157284069946622143361
absolute error = 1.66185382292198724256444e-08
relative error = 8.3047533815631138198172308806550e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007291644054981369147362532235
x2[1] (numeric) = 1.0007291727516962114198093188421
absolute error = 8.3461980745050730656186e-09
relative error = 8.3401167582272752255934754358728e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.6MB, time=22.33
NO POLE
NO POLE
t[1] = 0.504
x1[1] (analytic) = 2.0010873968891405564758385060019
x1[1] (numeric) = 2.0010873794074334442087302969396
absolute error = 1.74817071122671082090623e-08
relative error = 8.7361037501130130846399853724113e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007292558749627476146876084142
x2[1] (numeric) = 1.000729264655827979719461529969
absolute error = 8.7808652321047739215548e-09
relative error = 8.7744664009322308565290980344462e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.6MB, time=23.04
memory used=221.2MB, alloc=4.6MB, time=23.76
NO POLE
NO POLE
t[1] = 0.5041
x1[1] (analytic) = 2.0010872881548884456376095775276
x1[1] (numeric) = 2.0010872697881597471988790502113
absolute error = 1.83667286984387305273163e-08
relative error = 9.1783745802382541321223212675093e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007293473681606089420261007159
x2[1] (numeric) = 1.0007293565947861830296906843049
absolute error = 9.2266255740876645835890e-09
relative error = 9.2199010635122906949795697301727e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.6MB, time=24.50
NO POLE
NO POLE
t[1] = 0.5042
x1[1] (analytic) = 2.0010871794315092163573258400565
x1[1] (numeric) = 2.0010871601579062206870701291755
absolute error = 1.92736029956702557108810e-08
relative error = 9.6315658776774094092131814096335e-07 %
h = 0.0001
x2[1] (analytic) = 1.0007294388850959242959412018029
x2[1] (numeric) = 1.0007294485685794312621020230465
absolute error = 9.6834835069661608212436e-09
relative error = 9.6764251461958055865554896192854e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.6MB, time=25.25
NO POLE
NO POLE
t[1] = 0.5043
x1[1] (analytic) = 2.0010870707190017814011940947576
x1[1] (numeric) = 2.0010870505166717692863124551899
absolute error = 2.02023300121148816395677e-08
relative error = 1.0095677648277479213337765761664e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007295304257728979707561395621
x2[1] (numeric) = 1.0007295405772163362141127481263
memory used=232.7MB, alloc=4.6MB, time=26.00
absolute error = 1.01514434382433566085642e-08
relative error = 1.0144043050197887137338034882707e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.6MB, time=26.77
NO POLE
NO POLE
t[1] = 0.5044
x1[1] (analytic) = 2.001086962017365053644139086132
x1[1] (numeric) = 2.0010869408644552975006514412442
absolute error = 2.11529097561434876448878e-08
relative error = 1.0570709897993891731953878005897e-06 %
h = 0.0001
x2[1] (analytic) = 1.000729621990195735156101506034
x2[1] (numeric) = 1.0007296326207055115693454326386
absolute error = 1.06305097764132439266046e-08
relative error = 1.0622759177720625392815569519974e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.6MB, time=27.50
NO POLE
NO POLE
t[1] = 0.5045
x1[1] (analytic) = 2.0010868533265979460697926307621
x1[1] (numeric) = 2.001086831201255709725158216206
absolute error = 2.21253422363446344145561e-08
relative error = 1.1056662632890503083159997192553e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007297135783686419370889006249
x2[1] (numeric) = 1.0007297246990555728980215115441
absolute error = 1.11206869309609326109192e-08
relative error = 1.1112577931953306560804897547404e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.6MB, time=28.22
memory used=247.9MB, alloc=4.6MB, time=28.94
NO POLE
NO POLE
t[1] = 0.5046
x1[1] (analytic) = 2.0010867446466993717704827471482
x1[1] (numeric) = 2.001086721527071910245918848014
absolute error = 2.31196274615245638991342e-08
relative error = 1.1553535859139597357355178072071e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007298051902958252944846085935
x2[1] (numeric) = 1.00072981681227513765735485267
absolute error = 1.16219793123628702440765e-08
relative error = 1.1613503717072630778370390441792e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.6MB, time=29.65
NO POLE
NO POLE
t[1] = 0.5047
x1[1] (analytic) = 2.0010866359776682439472227866313
x1[1] (numeric) = 2.0010866118419028032400235658178
absolute error = 2.41357654407071992208135e-08
relative error = 1.2061329583021886659950533936034e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007298968259814931048833148203
x2[1] (numeric) = 1.0007299089603728251919454080219
absolute error = 1.21343913320870620932016e-08
relative error = 1.2125540938242929922748422635434e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.6MB, time=30.37
NO POLE
NO POLE
memory used=259.4MB, alloc=4.6MB, time=31.08
t[1] = 0.5048
x1[1] (analytic) = 2.0010865273195034759097005654036
x1[1] (numeric) = 2.001086502145747292775555981065
absolute error = 2.51737561831341445843386e-08
relative error = 1.2580043810926511155132705437833e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007299884854298541408818528671
x2[1] (numeric) = 1.0007300011433572567341729454229
absolute error = 1.26579274025932910925558e-08
relative error = 1.2648694001616385466284748520794e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.6MB, time=31.78
NO POLE
NO POLE
t[1] = 0.5049
x1[1] (analytic) = 2.0010864186722039810762674976051
x1[1] (numeric) = 2.0010863924386042828115823075348
absolute error = 2.62335996982646851900703e-08
relative error = 1.3109678549351039110678919297901e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007300801686451180712529893331
x2[1] (numeric) = 1.0007300933612370554045908604969
absolute error = 1.31925919373333378711638e-08
relative error = 1.3182967314333246375394852470380e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.6MB, time=32.49
NO POLE
NO POLE
t[1] = 0.505
x1[1] (analytic) = 2.0010863100357686729739277295073
x1[1] (numeric) = 2.0010862827204726771981405803184
absolute error = 2.73152959957757871491889e-08
relative error = 1.3650233804901466943823990390358e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007301718756314954611192435145
x2[1] (numeric) = 1.0007301856140208462123200690121
absolute error = 1.37383893507512008254976e-08
relative error = 1.3728365284522047053555904195223e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.6MB, time=33.20
memory used=274.6MB, alloc=4.6MB, time=33.93
NO POLE
NO POLE
t[1] = 0.5051
x1[1] (analytic) = 2.0010862014101964652383272747832
x1[1] (numeric) = 2.001086172991351379676229873746
absolute error = 2.84188450855620974010372e-08
relative error = 1.4201709584292219268178971060078e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007302636063931977721267423749
x2[1] (numeric) = 1.0007302779017172560554429796008
absolute error = 1.42953240582833162372259e-08
relative error = 1.4284892321299825328338651781520e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.6MB, time=34.66
NO POLE
NO POLE
t[1] = 0.5052
x1[1] (analytic) = 2.0010860927954862716137431508637
x1[1] (numeric) = 2.0010860632512392938777995182601
absolute error = 2.95442469777359436326036e-08
relative error = 1.4764105894346148941701651247034e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007303553609344373626191108334
x2[1] (numeric) = 1.0007303702243349137213975468718
absolute error = 1.48634004763587784360384e-08
relative error = 1.4852552834772340482488184104528e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.6MB, time=35.40
memory used=286.1MB, alloc=4.6MB, time=36.14
NO POLE
NO POLE
t[1] = 0.5053
x1[1] (analytic) = 2.0010859841916370059530725163803
x1[1] (numeric) = 2.0010859535001353233257383162358
absolute error = 3.06915016826273342001445e-08
relative error = 1.5337422741994537115718513319656e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007304471392594274878113973781
x2[1] (numeric) = 1.0007304625818824498873714049317
absolute error = 1.54426230223995600075536e-08
relative error = 1.5431351236034291329061694699573e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.6MB, time=36.85
NO POLE
NO POLE
t[1] = 0.5054
x1[1] (analytic) = 2.0010858755986475822178218096944
x1[1] (numeric) = 2.0010858437380383714338637567464
absolute error = 3.18606092107839580529480e-08
relative error = 1.5921660134277093284999144758422e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007305389413723822999640350102
x2[1] (numeric) = 1.0007305549743684971206960813312
absolute error = 1.60329961148207320463210e-08
relative error = 1.6021291937169534330633677288452e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.6MB, time=37.55
NO POLE
NO POLE
t[1] = 0.5055
x1[1] (analytic) = 2.0010857670165169144780958885117
x1[1] (numeric) = 2.0010857339649473415069112292761
absolute error = 3.30515695729711846592356e-08
relative error = 1.6516818078341955338881463268398e-06 %
h = 0.0001
x2[1] (analytic) = 1.000730630767277516848556837528
x2[1] (numeric) = 1.0007306474018016898792412914528
absolute error = 1.66345241730306844539248e-08
relative error = 1.6622379351251301762575185729407e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.6MB, time=38.24
memory used=301.3MB, alloc=4.6MB, time=38.96
NO POLE
NO POLE
t[1] = 0.5056
x1[1] (analytic) = 2.001085658445243916912587170584
x1[1] (numeric) = 2.0010856241808611367405232363783
absolute error = 3.42643827801720639342057e-08
relative error = 1.7122896581445689613449656972017e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007307226169790470804630311551
x2[1] (numeric) = 1.0007307398641906645118093133561
absolute error = 1.72472116174313462822010e-08
relative error = 1.7234617892342419920418587452348e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.6MB, time=39.68
NO POLE
NO POLE
t[1] = 0.5057
x1[1] (analytic) = 2.0010855498848275038085647754956
x1[1] (numeric) = 2.0010855143857786602212386052799
absolute error = 3.54990488435873261702157e-08
relative error = 1.7739895650953290944763244232186e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007308144904811898401233215242
x2[1] (numeric) = 1.0007308323615440592585294430967
absolute error = 1.78710628694184061215725e-08
relative error = 1.7858011975495527371311944566608e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.6MB, time=40.39
memory used=312.8MB, alloc=4.6MB, time=41.11
NO POLE
NO POLE
t[1] = 0.5058
x1[1] (analytic) = 2.001085441335266589561863667536
x1[1] (numeric) = 2.0010854045796988149264816984319
absolute error = 3.67555677746353819691041e-08
relative error = 1.8367815294338182723137956406757e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007309063877881628697199960171
x2[1] (numeric) = 1.0007309248938705142512525305355
absolute error = 1.85060823513815325345184e-08
relative error = 1.8492566016753293249578748156362e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.6MB, time=41.81
NO POLE
NO POLE
t[1] = 0.5059
x1[1] (analytic) = 2.0010853327965600886768737996586
x1[1] (numeric) = 2.0010852947626205037245516230051
absolute error = 3.80339395849523221766535e-08
relative error = 1.9006655519182216948478896970603e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007309983089041848093510614748
x2[1] (numeric) = 1.000731017461178671513945595654
absolute error = 1.91522744867045945341792e-08
relative error = 1.9138284433148635596384241661724e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.6MB, time=42.52
NO POLE
NO POLE
t[1] = 0.506
x1[1] (analytic) = 2.0010852242687069157665292585244
x1[1] (numeric) = 2.0010851849345426293746114393322
absolute error = 3.93341642863919178191922e-08
relative error = 1.9656416333175674286664831308689e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007310902538334751972044172794
x2[1] (numeric) = 1.0007311100634771749630865253922
absolute error = 1.98096436997658821081128e-08
relative error = 1.9795171642704939743522759402319e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.6MB, time=43.22
memory used=328.0MB, alloc=4.6MB, time=43.98
NO POLE
NO POLE
t[1] = 0.5061
x1[1] (analytic) = 2.001085115751705985552297410631
x1[1] (numeric) = 2.001085075095464094526677368295
absolute error = 4.06562418910256200423360e-08
relative error = 2.0317097744117264126984410424894e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007311822225802544697320638176
x2[1] (numeric) = 1.0007312027007746704080588510256
absolute error = 2.04781944159383267872080e-08
relative error = 2.0463232064436276741332312083480e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.6MB, time=44.70
NO POLE
NO POLE
t[1] = 0.5062
x1[1] (analytic) = 2.0010850072455562128641680495278
x1[1] (numeric) = 2.0010849652453838017216079976571
absolute error = 4.20001724111425600518707e-08
relative error = 2.0988699759914124640624582109171e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007312742151487439618243463322
x2[1] (numeric) = 1.0007312953730798055515466060969
absolute error = 2.11579310615897222597647e-08
relative error = 2.1142470118347621830745149096488e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=335.7MB, alloc=4.6MB, time=45.41
memory used=339.5MB, alloc=4.6MB, time=46.15
NO POLE
NO POLE
t[1] = 0.5063
x1[1] (analytic) = 2.0010848987502565126406425441156
x1[1] (numeric) = 2.0010848553843006533910934873425
absolute error = 4.33659558592495490567731e-08
relative error = 2.1671222388581822840210093836901e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007313662315431659069842341678
x2[1] (numeric) = 1.0007313880804012299899292649194
absolute error = 2.18488580640829450307516e-08
relative error = 2.1832890225435072959484626051153e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.6MB, time=46.84
NO POLE
NO POLE
t[1] = 0.5064
x1[1] (analytic) = 2.0010847902658057999287229880316
x1[1] (numeric) = 2.0010847455122135518576447736587
absolute error = 4.47535922480710782143729e-08
relative error = 2.2364665638244354640395290426295e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007314582717677434375016354202
x2[1] (numeric) = 1.0007314808227475952136767616677
absolute error = 2.25509798517761751262475e-08
relative error = 2.2534496807686069342414009209189e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.6MB, time=47.55
NO POLE
NO POLE
t[1] = 0.5065
x1[1] (analytic) = 2.0010846817922029898839013501196
x1[1] (numeric) = 2.0010846356291213993345827724656
absolute error = 4.61630815905493185776540e-08
relative error = 2.3069029517134144919507460536431e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007315503358267005846277469922
x2[1] (numeric) = 1.0007315736001275546077445900726
absolute error = 2.32643008540231168430804e-08
relative error = 2.3247294288079610066050942364040e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=350.9MB, alloc=4.6MB, time=48.27
memory used=354.7MB, alloc=4.6MB, time=48.99
NO POLE
NO POLE
t[1] = 0.5066
x1[1] (analytic) = 2.0010845733294469977701486259847
x1[1] (numeric) = 2.0010845257350230979260275812894
absolute error = 4.75944238998441210446953e-08
relative error = 2.3784314033592047582241785653899e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007316424237242622787494400674
x2[1] (numeric) = 1.0007316664125497634519689837359
absolute error = 2.39888255011732195436685e-08
relative error = 2.3971287090586472737251208889055e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.6MB, time=49.70
NO POLE
NO POLE
t[1] = 0.5067
x1[1] (analytic) = 2.0010844648775367389599039906329
x1[1] (numeric) = 2.001084415829917549626887680381
absolute error = 4.90476191893330163102519e-08
relative error = 2.4510519196067345623408344998538e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007317345354646543495636810068
x2[1] (numeric) = 1.000731759260022878921462177082
absolute error = 2.47245582245718984960752e-08
relative error = 2.4706479640169432176073415626016e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=362.4MB, alloc=4.6MB, time=50.39
memory used=366.2MB, alloc=4.6MB, time=51.12
NO POLE
NO POLE
t[1] = 0.5068
x1[1] (analytic) = 2.0010843564364711289340639521961
x1[1] (numeric) = 2.00108430591380365632284913272
absolute error = 5.05226674726112148194761e-08
relative error = 2.5247645013117751192730880184588e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007318266710521035262519876743
x2[1] (numeric) = 1.0007318521425555600870077469617
absolute error = 2.54715034565607557592874e-08
relative error = 2.5452876362783479152833427127251e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=370.0MB, alloc=4.6MB, time=51.83
NO POLE
NO POLE
t[1] = 0.5069
x1[1] (analytic) = 2.0010842480062490832819715067401
x1[1] (numeric) = 2.0010841959866803197903647829629
absolute error = 5.20195687634916067237772e-08
relative error = 2.5995691493409405660696823581162e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007319188304908374376549212004
x2[1] (numeric) = 1.0007319450601564679154560349255
absolute error = 2.62296656304778011137251e-08
relative error = 2.6210481685376039169356079510855e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=373.8MB, alloc=4.6MB, time=52.55
NO POLE
NO POLE
t[1] = 0.507
x1[1] (analytic) = 2.0010841395868695177014052941589
x1[1] (numeric) = 2.0010840860485464416966434553363
absolute error = 5.35383230760047618388226e-08
relative error = 2.6754658645716879685459843366800e-06 %
h = 0.0001
x2[1] (analytic) = 1.00073201101378508461244661319
x2[1] (numeric) = 1.0007320380128342652701196501819
absolute error = 2.69990491806576730369919e-08
relative error = 2.6979300035887191284433301814709e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.6MB, time=53.23
memory used=381.4MB, alloc=4.6MB, time=53.94
NO POLE
NO POLE
t[1] = 0.5071
x1[1] (analytic) = 2.0010840311783313479985687551521
x1[1] (numeric) = 2.0010839760994009235996391504746
absolute error = 5.50789304243989296046775e-08
relative error = 2.7524546478923173280793559681221e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007321032209390744793093283805
x2[1] (numeric) = 1.0007321310005976169111690532574
absolute error = 2.77796585424318597248769e-08
relative error = 2.7759335843249886983498671871771e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=385.2MB, alloc=4.6MB, time=54.68
NO POLE
NO POLE
t[1] = 0.5072
x1[1] (analytic) = 2.0010839227806334900880792892867
x1[1] (numeric) = 2.0010838661392426669480402412021
absolute error = 5.66413908231400390480846e-08
relative error = 2.8305355002019715885097135165640e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007321954519570373671080627591
x2[1] (numeric) = 1.0007322240234551894960282203746
absolute error = 2.85714981521289201576155e-08
relative error = 2.8550593537390169092525435718474e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=389.1MB, alloc=4.6MB, time=55.40
memory used=392.9MB, alloc=4.6MB, time=56.15
NO POLE
NO POLE
t[1] = 0.5073
x1[1] (analytic) = 2.0010838143937748599929574141438
x1[1] (numeric) = 2.0010837561680705730812586672595
absolute error = 5.82257042869116987468843e-08
relative error = 2.9097084224106366431452993426271e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007322877068432045050651771445
x2[1] (numeric) = 1.000732317081415651579770388564
absolute error = 2.93745724470747052114195e-08
relative error = 2.9353077549227390736157917222628e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=396.7MB, alloc=4.6MB, time=56.87
NO POLE
NO POLE
t[1] = 0.5074
x1[1] (analytic) = 2.0010837060177543738446159255482
x1[1] (numeric) = 2.001083646185883543229419128975
absolute error = 5.98318708306151967965732e-08
relative error = 2.9899734154391413418735569686214e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007323799856018080229350662418
x2[1] (numeric) = 1.0007324101744876736155138815267
absolute error = 3.01888858655925788152849e-08
relative error = 3.0166792310674434340084245875178e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=400.5MB, alloc=4.6MB, time=57.57
NO POLE
NO POLE
memory used=404.3MB, alloc=4.6MB, time=58.31
t[1] = 0.5075
x1[1] (analytic) = 2.001083597652570947882849058883
x1[1] (numeric) = 2.0010835361926804785133482798789
absolute error = 6.14598904693695007790041e-08
relative error = 3.0713304802191574983772696427543e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007324722882370809511788631756
x2[1] (numeric) = 1.0007325033026799279548180162636
absolute error = 3.10144428470036391530880e-08
relative error = 3.0991742254637930677660528875724e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=408.1MB, alloc=4.6MB, time=59.03
NO POLE
NO POLE
t[1] = 0.5076
x1[1] (analytic) = 2.0010834892982234984558216514875
x1[1] (numeric) = 2.001083426188460279944563918263
absolute error = 6.31097632185112577332245e-08
relative error = 3.1537796176931998974558128503967e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007325646147532572211391795107
x2[1] (numeric) = 1.0007325964660010888480790904882
absolute error = 3.18512478316269399109775e-08
relative error = 3.1827931815018477960793695558531e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=411.9MB, alloc=4.6MB, time=59.75
NO POLE
NO POLE
t[1] = 0.5077
x1[1] (analytic) = 2.0010833809547109420200583061384
x1[1] (numeric) = 2.0010833161732218484252641776835
absolute error = 6.47814890935947941284549e-08
relative error = 3.2373208288146263024515861039013e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007326569651545716652148807651
x2[1] (numeric) = 1.000732689664459832444926450838
absolute error = 3.26993052607797115700729e-08
relative error = 3.2675365426710860975092840098403e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=415.8MB, alloc=4.6MB, time=60.49
memory used=419.6MB, alloc=4.6MB, time=61.23
NO POLE
NO POLE
t[1] = 0.5078
x1[1] (analytic) = 2.0010832726220321951404325556154
x1[1] (numeric) = 2.001083206146964084748316716408
absolute error = 6.64750681103921158392074e-08
relative error = 3.3219541145476374627816493640744e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007327493394452600170358974238
x2[1] (numeric) = 1.0007327828980648367946186419025
absolute error = 3.35586195767775827444787e-08
relative error = 3.3534047525604270259298088815590e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=423.4MB, alloc=4.6MB, time=61.97
NO POLE
NO POLE
t[1] = 0.5079
x1[1] (analytic) = 2.0010831643001861744901560283501
x1[1] (numeric) = 2.0010830961096858895972479058062
absolute error = 6.81905002848929081225439e-08
relative error = 3.4076794758672771215745294788236e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007328417376295589116380714609
x2[1] (numeric) = 1.0007328761668247818464396360824
absolute error = 3.44291952229348015646215e-08
relative error = 3.4403982548582521328993619950966e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=427.2MB, alloc=4.6MB, time=62.71
memory used=431.0MB, alloc=4.6MB, time=63.58
NO POLE
NO POLE
t[1] = 0.508
x1[1] (analytic) = 2.0010830559891717968507676151575
x1[1] (numeric) = 2.0010829860613861635462320176843
absolute error = 6.99277856333045355974732e-08
relative error = 3.4944969137594320234121620244129e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007329341597117058856380383748
x2[1] (numeric) = 1.000732969470748349450095144298
absolute error = 3.53110366435644571059232e-08
relative error = 3.5285174933524273944617559111510e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=434.8MB, alloc=4.6MB, time=64.32
NO POLE
NO POLE
t[1] = 0.5081
x1[1] (analytic) = 2.0010829476889879791121226370521
x1[1] (numeric) = 2.0010828760020638070600804105629
absolute error = 7.16869241720520422264892e-08
relative error = 3.5824064292208319221770788561939e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007330266056959393774081447462
x2[1] (numeric) = 1.0007330628098442233561090075617
absolute error = 3.62041482839787008628155e-08
relative error = 3.6177629119303251423773479237501e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=438.6MB, alloc=4.6MB, time=65.04
NO POLE
NO POLE
t[1] = 0.5082
x1[1] (analytic) = 2.0010828393996336382723820141458
x1[1] (numeric) = 2.0010827659317177204942307148985
absolute error = 7.34679159177781512992473e-08
relative error = 3.6714080232590495890046968136521e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007331190755864987272514013242
x2[1] (numeric) = 1.0007331561841210892162196694315
absolute error = 3.71085345904889682681073e-08
relative error = 3.7081349545788459997854629051986e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=442.5MB, alloc=4.6MB, time=65.74
memory used=446.3MB, alloc=4.6MB, time=66.48
NO POLE
NO POLE
t[1] = 0.5083
x1[1] (analytic) = 2.00108273112110769143800143563
x1[1] (numeric) = 2.0010826558503468040947360172484
absolute error = 7.52707608873432654183816e-08
relative error = 3.7615016968925008203408378756677e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007332115693876241775764716484
x2[1] (numeric) = 1.0007332495935876345837767293623
absolute error = 3.80242000104062002577139e-08
relative error = 3.7996340653844408212989315723888e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=450.1MB, alloc=4.6MB, time=67.20
NO POLE
NO POLE
t[1] = 0.5084
x1[1] (analytic) = 2.0010826228534090558237205308397
x1[1] (numeric) = 2.0010825457579499579982540433786
absolute error = 7.70954590978254664874611e-08
relative error = 3.8526874511504444461043911809050e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007333040871035568730726962129
x2[1] (numeric) = 1.0007333430382525489141375769705
absolute error = 3.89511489920410648807576e-08
relative error = 3.8922606885331326375316566757833e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=453.9MB, alloc=4.6MB, time=67.93
memory used=457.7MB, alloc=4.6MB, time=68.66
NO POLE
NO POLE
t[1] = 0.5085
x1[1] (analytic) = 2.0010825145965366487525520414014
x1[1] (numeric) = 2.0010824356545260822320363403151
absolute error = 7.89420105665205157010863e-08
relative error = 3.9449652870729823379551872415735e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007333966287385388608851521817
x2[1] (numeric) = 1.0007334365181245235650641072287
absolute error = 3.98893859847041789550470e-08
relative error = 3.9860152683105386040598897603221e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=461.5MB, alloc=4.6MB, time=69.36
NO POLE
NO POLE
t[1] = 0.5086
x1[1] (analytic) = 2.0010824063504893876557709944627
x1[1] (numeric) = 2.0010823255400740767139174573385
absolute error = 8.08104153109418535371242e-08
relative error = 4.0383352057110594176669847707204e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007334891942968130907897486592
x2[1] (numeric) = 1.000733530033212251797119516607
absolute error = 4.08389154387063297679478e-08
relative error = 4.0808982491018919548184507239656e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=465.4MB, alloc=4.6MB, time=70.04
NO POLE
NO POLE
t[1] = 0.5087
x1[1] (analytic) = 2.0010822981152661900729038770055
x1[1] (numeric) = 2.0010822154145928412523041259208
absolute error = 8.27006733488205997510847e-08
relative error = 4.1327972081264636656057204078781e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007335817837826234153683575261
x2[1] (numeric) = 1.0007336235835244287740651801764
absolute error = 4.17997418053586968226503e-08
relative error = 4.1769100753920639599323629358158e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=469.2MB, alloc=4.6MB, time=70.75
memory used=473.0MB, alloc=4.6MB, time=71.48
NO POLE
NO POLE
t[1] = 0.5088
x1[1] (analytic) = 2.0010821898908659736517178112409
x1[1] (numeric) = 2.001082105278081275546164438606
absolute error = 8.46127846981055533726349e-08
relative error = 4.2283512953918261293128468036515e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007336743972002145901839798449
x2[1] (numeric) = 1.000733717169069751563257609692
absolute error = 4.27718695369730736298471e-08
relative error = 4.2740511917655858879852060469785e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=476.8MB, alloc=4.6MB, time=72.21
NO POLE
NO POLE
t[1] = 0.5089
x1[1] (analytic) = 2.0010820816772876561482097310871
x1[1] (numeric) = 2.0010819951305382791850170268329
absolute error = 8.65467493769631927042542e-08
relative error = 4.3249974685906209321939043506320e-06 %
h = 0.0001
x2[1] (analytic) = 1.000733767034553832273955947845
x2[1] (numeric) = 1.0007338107898569191360454926709
absolute error = 4.37553030868620895448259e-08
relative error = 4.3723220429066709727246292369598e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=480.6MB, alloc=4.6MB, time=72.94
memory used=484.4MB, alloc=4.6MB, time=73.68
NO POLE
NO POLE
t[1] = 0.509
x1[1] (analytic) = 2.0010819734745301554265955597291
x1[1] (numeric) = 2.0010818849719627516489202377008
absolute error = 8.85025674037776753220283e-08
relative error = 4.4227357288171652823122319777927e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007338596958477230287351624915
x2[1] (numeric) = 1.0007339044458946323681668124826
absolute error = 4.47500469093394316499911e-08
relative error = 4.4717230735992363842063469727913e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=488.2MB, alloc=4.6MB, time=74.39
NO POLE
NO POLE
t[1] = 0.5091
x1[1] (analytic) = 2.0010818652825923894592993882611
x1[1] (numeric) = 2.0010817748023535923084613096774
absolute error = 9.04802387971508380785837e-08
relative error = 4.5215660771766194812878973307819e-06 %
h = 0.0001
x2[1] (analytic) = 1.000733952381086134320079366647
x2[1] (numeric) = 1.0007339981371915940401460494667
absolute error = 4.57561054597200666828197e-08
relative error = 4.5722547287269252043771199385040e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=492.1MB, alloc=4.6MB, time=75.10
NO POLE
NO POLE
t[1] = 0.5092
x1[1] (analytic) = 2.0010817571014732763269426554107
x1[1] (numeric) = 2.0010816646217097004247455472497
absolute error = 9.24797635759021971081610e-08
relative error = 4.6214885147849869333017617497009e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007340450902733145172284538324
x2[1] (numeric) = 1.0007340918637565088376914630957
absolute error = 4.67734831943204630092633e-08
relative error = 4.6739174532731284070978533101140e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=495.9MB, alloc=4.6MB, time=75.82
memory used=499.7MB, alloc=4.6MB, time=76.56
NO POLE
NO POLE
t[1] = 0.5093
x1[1] (analytic) = 2.001081648931171734218333328345
x1[1] (numeric) = 2.001081554430029975149385494517
absolute error = 9.45011417590689478338280e-08
relative error = 4.7225030427691141542047303828645e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007341378234135128932798125935
x2[1] (numeric) = 1.0007341856255980833520924551983
absolute error = 4.78021845704588126426048e-08
relative error = 4.7767116923210068426076247652005e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=503.5MB, alloc=4.6MB, time=77.26
NO POLE
NO POLE
t[1] = 0.5094
x1[1] (analytic) = 2.0010815407716866814304550845588
x1[1] (numeric) = 2.0010814442273133155244901077262
absolute error = 9.65443733659059649768326e-08
relative error = 4.8246096622666907807321878020169e-06 %
h = 0.0001
x2[1] (analytic) = 1.000734230580510979625363706482
x2[1] (numeric) = 1.00073427942272502608061701426
absolute error = 4.88422140464552533077780e-08
relative error = 4.8806378910535132264294146248903e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=507.3MB, alloc=4.6MB, time=78.00
memory used=511.1MB, alloc=4.6MB, time=78.78
NO POLE
NO POLE
t[1] = 0.5095
x1[1] (analytic) = 2.0010814326230170363684564948442
x1[1] (numeric) = 2.001081334013558620482653926749
absolute error = 9.86094584158858025680952e-08
relative error = 4.9278083744262495798236044925118e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007343233615699657948186896566
x2[1] (numeric) = 1.0007343732551460474269092408173
absolute error = 4.98935760816320905511607e-08
relative error = 4.9856964947534141327185503293835e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=514.9MB, alloc=4.6MB, time=79.53
NO POLE
NO POLE
t[1] = 0.5096
x1[1] (analytic) = 2.0010813244851617175456402073423
x1[1] (numeric) = 2.0010812237887647888469462455018
absolute error = 1.006963969286986939618405e-07
relative error = 5.0320991804071664580473095864766e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007344161665947233873670581104
x2[1] (numeric) = 1.0007344671228698597013869539618
absolute error = 5.09562751363140198958514e-08
relative error = 5.0918879488033119920548274640785e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=518.8MB, alloc=4.6MB, time=80.29
NO POLE
NO POLE
t[1] = 0.5097
x1[1] (analytic) = 2.0010812163581196435834521326761
x1[1] (numeric) = 2.0010811135529307193309002813069
absolute error = 1.028051889242525518513692e-07
relative error = 5.1374820813796604711304551907059e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007345089955895052932903365348
x2[1] (numeric) = 1.0007345610259051771216393789707
absolute error = 5.20303156718283490424359e-08
relative error = 5.1992126986856670936788898114983e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=522.6MB, alloc=4.6MB, time=81.05
memory used=526.4MB, alloc=4.6MB, time=81.83
NO POLE
NO POLE
t[1] = 0.5098
x1[1] (analytic) = 2.0010811082418897332114706301652
x1[1] (numeric) = 2.0010810033060553105385023431959
absolute error = 1.049358344226729682869693e-07
relative error = 5.2439570785247938335941576825665e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007346018485585653076048008237
x2[1] (numeric) = 1.0007346549642607158128249160798
absolute error = 5.31157021505052201152561e-08
relative error = 5.3076711899828195921740504433488e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=530.2MB, alloc=4.6MB, time=82.59
NO POLE
NO POLE
t[1] = 0.5099
x1[1] (analytic) = 2.001081000136470905267395695121
x1[1] (numeric) = 2.0010808930481374609641809991549
absolute error = 1.070883334443032146959661e-07
relative error = 5.3515241730344719284937713633361e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007346947255061581302370362269
x2[1] (numeric) = 1.0007347489379451938080689904159
absolute error = 5.42124390356778319541890e-08
relative error = 5.4172638683770115185943061617752e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=534.0MB, alloc=4.6MB, time=83.36
memory used=537.8MB, alloc=4.6MB, time=84.14
NO POLE
NO POLE
t[1] = 0.51
x1[1] (analytic) = 2.0010808920418620786970381472244
x1[1] (numeric) = 2.0010807827791760689927962423111
absolute error = 1.092626860097042419049133e-07
relative error = 5.4601833661114433172644147691658e-06 %
h = 0.0001
x2[1] (analytic) = 1.0007347876264365393661995311595
x2[1] (numeric) = 1.0007348429469673310488619831043
absolute error = 5.53205307916826624519448e-08
relative error = 5.5279911796504087960393875122002e-06 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
Iterations = 100
Total Elapsed Time = 1 Minutes 24 Seconds
Elapsed Time(since restart) = 1 Minutes 24 Seconds
Expected Time Remaining = 10 Hours 24 Minutes 6 Seconds
Optimized Time Remaining = 10 Hours 24 Minutes 0 Seconds
Time to Timeout = 13 Minutes 35 Seconds
Percent Done = 0.2244 %
> quit
memory used=538.7MB, alloc=4.6MB, time=84.29