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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
> DEBUGMASSIVE,
> INFO,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_clock_start_sec,
> glob_html_log,
> glob_current_iter,
> glob_small_float,
> glob_look_poles,
> glob_clock_sec,
> years_in_century,
> sec_in_min,
> djd_debug2,
> glob_max_iter,
> glob_relerr,
> glob_abserr,
> glob_hmin_init,
> glob_hmax,
> glob_disp_incr,
> glob_optimal_done,
> glob_almost_1,
> djd_debug,
> glob_iter,
> glob_warned,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmin,
> glob_start,
> glob_not_yet_start_msg,
> glob_initial_pass,
> days_in_year,
> glob_smallish_float,
> glob_max_order,
> glob_display_flag,
> glob_dump,
> glob_max_opt_iter,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_percent_done,
> glob_max_sec,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_last_good_h,
> glob_reached_optimal_h,
> min_in_hour,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_dump_analytic,
> glob_large_float,
> centuries_in_millinium,
> glob_log10normmin,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_h,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_0D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_type_pole,
> array_norms,
> array_t,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2,
> array_x1,
> array_m1,
> array_x1_init,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_higher,
> array_x1_higher_work,
> array_poles,
> array_complex_pole,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_x2(ind_var);
> omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x2[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_x1(ind_var);
> omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms,
glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float,
glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2,
glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax,
glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter,
glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start,
glob_not_yet_start_msg, glob_initial_pass, days_in_year,
glob_smallish_float, glob_max_order, glob_display_flag, glob_dump,
glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done,
glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes,
glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_dump_analytic, glob_large_float,
centuries_in_millinium, glob_log10normmin, glob_log10_abserr,
glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr,
glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h,
hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0,
array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t,
array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1,
array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole,
array_real_pole, array_x1_higher_work2, array_x1_higher,
array_x2_higher_work, array_x2_higher_work2, glob_last;
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_x2(ind_var);
omniout_float(ALWAYS, "x2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x2[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x2[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_x1(ind_var);
omniout_float(ALWAYS, "x1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x1[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGMASSIVE,
> INFO,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_clock_start_sec,
> glob_html_log,
> glob_current_iter,
> glob_small_float,
> glob_look_poles,
> glob_clock_sec,
> years_in_century,
> sec_in_min,
> djd_debug2,
> glob_max_iter,
> glob_relerr,
> glob_abserr,
> glob_hmin_init,
> glob_hmax,
> glob_disp_incr,
> glob_optimal_done,
> glob_almost_1,
> djd_debug,
> glob_iter,
> glob_warned,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmin,
> glob_start,
> glob_not_yet_start_msg,
> glob_initial_pass,
> days_in_year,
> glob_smallish_float,
> glob_max_order,
> glob_display_flag,
> glob_dump,
> glob_max_opt_iter,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_percent_done,
> glob_max_sec,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_last_good_h,
> glob_reached_optimal_h,
> min_in_hour,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_dump_analytic,
> glob_large_float,
> centuries_in_millinium,
> glob_log10normmin,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_h,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_0D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_type_pole,
> array_norms,
> array_t,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2,
> array_x1,
> array_m1,
> array_x1_init,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_higher,
> array_x1_higher_work,
> array_poles,
> array_complex_pole,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_t[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms,
glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float,
glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2,
glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax,
glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter,
glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start,
glob_not_yet_start_msg, glob_initial_pass, days_in_year,
glob_smallish_float, glob_max_order, glob_display_flag, glob_dump,
glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done,
glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes,
glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_dump_analytic, glob_large_float,
centuries_in_millinium, glob_log10normmin, glob_log10_abserr,
glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr,
glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h,
hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0,
array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t,
array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1,
array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole,
array_real_pole, array_x1_higher_work2, array_x1_higher,
array_x2_higher_work, array_x2_higher_work2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_t[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(t_start,t_end)
> global
> DEBUGMASSIVE,
> INFO,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_clock_start_sec,
> glob_html_log,
> glob_current_iter,
> glob_small_float,
> glob_look_poles,
> glob_clock_sec,
> years_in_century,
> sec_in_min,
> djd_debug2,
> glob_max_iter,
> glob_relerr,
> glob_abserr,
> glob_hmin_init,
> glob_hmax,
> glob_disp_incr,
> glob_optimal_done,
> glob_almost_1,
> djd_debug,
> glob_iter,
> glob_warned,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmin,
> glob_start,
> glob_not_yet_start_msg,
> glob_initial_pass,
> days_in_year,
> glob_smallish_float,
> glob_max_order,
> glob_display_flag,
> glob_dump,
> glob_max_opt_iter,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_percent_done,
> glob_max_sec,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_last_good_h,
> glob_reached_optimal_h,
> min_in_hour,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_dump_analytic,
> glob_large_float,
> centuries_in_millinium,
> glob_log10normmin,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_h,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_0D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_type_pole,
> array_norms,
> array_t,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2,
> array_x1,
> array_m1,
> array_x1_init,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_higher,
> array_x1_higher_work,
> array_poles,
> array_complex_pole,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> 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 DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms,
glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float,
glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2,
glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax,
glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter,
glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start,
glob_not_yet_start_msg, glob_initial_pass, days_in_year,
glob_smallish_float, glob_max_order, glob_display_flag, glob_dump,
glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done,
glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes,
glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_dump_analytic, glob_large_float,
centuries_in_millinium, glob_log10normmin, glob_log10_abserr,
glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr,
glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h,
hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0,
array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t,
array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1,
array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole,
array_real_pole, array_x1_higher_work2, array_x1_higher,
array_x2_higher_work, array_x2_higher_work2, 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
> DEBUGMASSIVE,
> INFO,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_clock_start_sec,
> glob_html_log,
> glob_current_iter,
> glob_small_float,
> glob_look_poles,
> glob_clock_sec,
> years_in_century,
> sec_in_min,
> djd_debug2,
> glob_max_iter,
> glob_relerr,
> glob_abserr,
> glob_hmin_init,
> glob_hmax,
> glob_disp_incr,
> glob_optimal_done,
> glob_almost_1,
> djd_debug,
> glob_iter,
> glob_warned,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmin,
> glob_start,
> glob_not_yet_start_msg,
> glob_initial_pass,
> days_in_year,
> glob_smallish_float,
> glob_max_order,
> glob_display_flag,
> glob_dump,
> glob_max_opt_iter,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_percent_done,
> glob_max_sec,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_last_good_h,
> glob_reached_optimal_h,
> min_in_hour,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_dump_analytic,
> glob_large_float,
> centuries_in_millinium,
> glob_log10normmin,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_h,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_0D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_type_pole,
> array_norms,
> array_t,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2,
> array_x1,
> array_m1,
> array_x1_init,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_higher,
> array_x1_higher_work,
> array_poles,
> array_complex_pole,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 2 - 1;
> while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1];
> rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1];
> rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]);
> rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]);
> rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]);
> rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]);
> rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float)) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]);
> rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]);
> rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]);
> rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]);
> rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4
> ;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3
> ;
> #BOTTOM RADII COMPLEX EQ = 2
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 2
> if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 2
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if array_pole[1] > array_poles[2,1] then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 2
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms,
glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float,
glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2,
glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax,
glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter,
glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start,
glob_not_yet_start_msg, glob_initial_pass, days_in_year,
glob_smallish_float, glob_max_order, glob_display_flag, glob_dump,
glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done,
glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes,
glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_dump_analytic, glob_large_float,
centuries_in_millinium, glob_log10normmin, glob_log10_abserr,
glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr,
glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h,
hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0,
array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t,
array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1,
array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole,
array_real_pole, array_x1_higher_work2, array_x1_higher,
array_x2_higher_work, array_x2_higher_work2, glob_last;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or
abs(array_x2_higher[1, m - 1]) < glob_small_float or
abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or
abs(array_x1_higher[1, m - 1]) < glob_small_float or
abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_x2_higher[1, m]) or
glob_large_float <= abs(array_x2_higher[1, m - 1]) or
glob_large_float <= abs(array_x2_higher[1, m - 2]) or
glob_large_float <= abs(array_x2_higher[1, m - 3]) or
glob_large_float <= abs(array_x2_higher[1, m - 4]) or
glob_large_float <= abs(array_x2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3];
rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4];
rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= abs(array_x1_higher[1, m]) or
glob_large_float <= abs(array_x1_higher[1, m - 1]) or
glob_large_float <= abs(array_x1_higher[1, m - 2]) or
glob_large_float <= abs(array_x1_higher[1, m - 3]) or
glob_large_float <= abs(array_x1_higher[1, m - 4]) or
glob_large_float <= abs(array_x1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3];
rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4];
rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[2, 1] := rad_c;
array_complex_pole[2, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGMASSIVE,
> INFO,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_clock_start_sec,
> glob_html_log,
> glob_current_iter,
> glob_small_float,
> glob_look_poles,
> glob_clock_sec,
> years_in_century,
> sec_in_min,
> djd_debug2,
> glob_max_iter,
> glob_relerr,
> glob_abserr,
> glob_hmin_init,
> glob_hmax,
> glob_disp_incr,
> glob_optimal_done,
> glob_almost_1,
> djd_debug,
> glob_iter,
> glob_warned,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmin,
> glob_start,
> glob_not_yet_start_msg,
> glob_initial_pass,
> days_in_year,
> glob_smallish_float,
> glob_max_order,
> glob_display_flag,
> glob_dump,
> glob_max_opt_iter,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_percent_done,
> glob_max_sec,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_last_good_h,
> glob_reached_optimal_h,
> min_in_hour,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_dump_analytic,
> glob_large_float,
> centuries_in_millinium,
> glob_log10normmin,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_h,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_0D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_type_pole,
> array_norms,
> array_t,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2,
> array_x1,
> array_m1,
> array_x1_init,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_higher,
> array_x1_higher_work,
> array_poles,
> array_complex_pole,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 3
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms,
glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float,
glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2,
glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax,
glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter,
glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start,
glob_not_yet_start_msg, glob_initial_pass, days_in_year,
glob_smallish_float, glob_max_order, glob_display_flag, glob_dump,
glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done,
glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes,
glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_dump_analytic, glob_large_float,
centuries_in_millinium, glob_log10normmin, glob_log10_abserr,
glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr,
glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h,
hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0,
array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t,
array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1,
array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole,
array_real_pole, array_x1_higher_work2, array_x1_higher,
array_x2_higher_work, array_x2_higher_work2, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x2[iii]) then
array_norms[iii] := abs(array_x2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x1[iii]) then
array_norms[iii] := abs(array_x1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGMASSIVE,
> INFO,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_clock_start_sec,
> glob_html_log,
> glob_current_iter,
> glob_small_float,
> glob_look_poles,
> glob_clock_sec,
> years_in_century,
> sec_in_min,
> djd_debug2,
> glob_max_iter,
> glob_relerr,
> glob_abserr,
> glob_hmin_init,
> glob_hmax,
> glob_disp_incr,
> glob_optimal_done,
> glob_almost_1,
> djd_debug,
> glob_iter,
> glob_warned,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmin,
> glob_start,
> glob_not_yet_start_msg,
> glob_initial_pass,
> days_in_year,
> glob_smallish_float,
> glob_max_order,
> glob_display_flag,
> glob_dump,
> glob_max_opt_iter,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_percent_done,
> glob_max_sec,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_last_good_h,
> glob_reached_optimal_h,
> min_in_hour,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_dump_analytic,
> glob_large_float,
> centuries_in_millinium,
> glob_log10normmin,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_h,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_0D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_type_pole,
> array_norms,
> array_t,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2,
> array_x1,
> array_m1,
> array_x1_init,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_higher,
> array_x1_higher_work,
> array_poles,
> array_complex_pole,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1
> array_tmp1[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp4[1] := (array_const_2D0[1] * (array_x2[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp6[1] := array_x1_higher[3,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp8[1] := array_x1_higher[2,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp10[1] := array_tmp9[1] + array_x1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2);
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> # emit pre mult $eq_no = 2 i = 1
> array_tmp12[1] := (array_const_4D0[1] * (array_x2[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1]));
> # emit pre mult $eq_no = 2 i = 1
> array_tmp16[1] := (array_const_2D0[1] * (array_x1[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2
> array_tmp1[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp4[2] := ats(2,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp6[2] := array_x1_higher[3,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp8[2] := array_x1_higher[2,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2]));
> #emit pre add $eq_no = 1 i = 2
> array_tmp10[2] := array_tmp9[2] + array_x1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> # emit pre mult $eq_no = 2 i = 2
> array_tmp12[2] := ats(2,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2]));
> # emit pre mult $eq_no = 2 i = 2
> array_tmp16[2] := ats(2,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2]));
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3
> array_tmp1[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp4[3] := ats(3,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp6[3] := array_x1_higher[3,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp8[3] := array_x1_higher[2,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3]));
> #emit pre add $eq_no = 1 i = 3
> array_tmp10[3] := array_tmp9[3] + array_x1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> # emit pre mult $eq_no = 2 i = 3
> array_tmp12[3] := ats(3,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3]));
> # emit pre mult $eq_no = 2 i = 3
> array_tmp16[3] := ats(3,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3]));
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4
> array_tmp1[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp4[4] := ats(4,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp6[4] := array_x1_higher[3,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp8[4] := array_x1_higher[2,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4]));
> #emit pre add $eq_no = 1 i = 4
> array_tmp10[4] := array_tmp9[4] + array_x1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> # emit pre mult $eq_no = 2 i = 4
> array_tmp12[4] := ats(4,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4]));
> # emit pre mult $eq_no = 2 i = 4
> array_tmp16[4] := ats(4,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4]));
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5
> array_tmp1[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp4[5] := ats(5,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp6[5] := array_x1_higher[3,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp8[5] := array_x1_higher[2,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5]));
> #emit pre add $eq_no = 1 i = 5
> array_tmp10[5] := array_tmp9[5] + array_x1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> # emit pre mult $eq_no = 2 i = 5
> array_tmp12[5] := ats(5,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5]));
> # emit pre mult $eq_no = 2 i = 5
> array_tmp16[5] := ats(5,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5]));
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit diff $eq_no = 1
> array_tmp1[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1);
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
> #emit mult $eq_no = 1
> array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1);
> #emit sub $eq_no = 1
> array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk]));
> #emit diff $eq_no = 1
> array_tmp6[kkk] := array_x1_higher[3,kkk];
> #emit sub $eq_no = 1
> array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk]));
> #emit diff $eq_no = 1
> array_tmp8[kkk] := array_x1_higher[2,kkk];
> #emit sub $eq_no = 1
> array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk]));
> #emit add $eq_no = 1
> array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x2[kkk + order_d] := temporary;
> array_x2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> #emit mult $eq_no = 2
> array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1);
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 2
> array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1);
> #emit sub $eq_no = 2
> array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk]));
> #emit mult $eq_no = 2
> array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1);
> #emit sub $eq_no = 2
> array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk]));
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x1[kkk + order_d] := temporary;
> array_x1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms,
glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float,
glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2,
glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax,
glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter,
glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start,
glob_not_yet_start_msg, glob_initial_pass, days_in_year,
glob_smallish_float, glob_max_order, glob_display_flag, glob_dump,
glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done,
glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes,
glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_dump_analytic, glob_large_float,
centuries_in_millinium, glob_log10normmin, glob_log10_abserr,
glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr,
glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h,
hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0,
array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t,
array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1,
array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole,
array_real_pole, array_x1_higher_work2, array_x1_higher,
array_x2_higher_work, array_x2_higher_work2, glob_last;
array_tmp1[1] := array_x2_higher[2, 1];
array_tmp2[1] := array_const_3D0[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_const_2D0[1]*array_x2[1];
array_tmp5[1] := array_tmp3[1] - array_tmp4[1];
array_tmp6[1] := array_x1_higher[3, 1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
array_tmp8[1] := array_x1_higher[2, 1];
array_tmp9[1] := array_tmp7[1] - array_tmp8[1];
array_tmp10[1] := array_tmp9[1] + array_x1[1];
if 1 <= glob_max_terms then
temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2);
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 1] := temporary
end if;
kkk := 2;
array_tmp12[1] := array_const_4D0[1]*array_x2[1];
array_tmp13[1] := array_x2_higher[2, 1];
array_tmp14[1] := array_const_2D0[1]*array_tmp13[1];
array_tmp15[1] := array_tmp12[1] - array_tmp14[1];
array_tmp16[1] := array_const_2D0[1]*array_x1[1];
array_tmp17[1] := array_tmp15[1] - array_tmp16[1];
if 1 <= glob_max_terms then
temporary := array_tmp17[1]*glob_h*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 1] := temporary
end if;
kkk := 2;
array_tmp1[2] := array_x2_higher[2, 2];
array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1);
array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1);
array_tmp5[2] := array_tmp3[2] - array_tmp4[2];
array_tmp6[2] := array_x1_higher[3, 2];
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
array_tmp8[2] := array_x1_higher[2, 2];
array_tmp9[2] := array_tmp7[2] - array_tmp8[2];
array_tmp10[2] := array_tmp9[2] + array_x1[2];
if 2 <= glob_max_terms then
temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 2] := temporary
end if;
kkk := 3;
array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1);
array_tmp13[2] := array_x2_higher[2, 2];
array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1);
array_tmp15[2] := array_tmp12[2] - array_tmp14[2];
array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1);
array_tmp17[2] := array_tmp15[2] - array_tmp16[2];
if 2 <= glob_max_terms then
temporary := array_tmp17[2]*glob_h*factorial_3(1, 2);
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 2] := temporary
end if;
kkk := 3;
array_tmp1[3] := array_x2_higher[2, 3];
array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1);
array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1);
array_tmp5[3] := array_tmp3[3] - array_tmp4[3];
array_tmp6[3] := array_x1_higher[3, 3];
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
array_tmp8[3] := array_x1_higher[2, 3];
array_tmp9[3] := array_tmp7[3] - array_tmp8[3];
array_tmp10[3] := array_tmp9[3] + array_x1[3];
if 3 <= glob_max_terms then
temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if;
kkk := 4;
array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1);
array_tmp13[3] := array_x2_higher[2, 3];
array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1);
array_tmp15[3] := array_tmp12[3] - array_tmp14[3];
array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1);
array_tmp17[3] := array_tmp15[3] - array_tmp16[3];
if 3 <= glob_max_terms then
temporary := array_tmp17[3]*glob_h*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 3] := temporary
end if;
kkk := 4;
array_tmp1[4] := array_x2_higher[2, 4];
array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1);
array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1);
array_tmp5[4] := array_tmp3[4] - array_tmp4[4];
array_tmp6[4] := array_x1_higher[3, 4];
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
array_tmp8[4] := array_x1_higher[2, 4];
array_tmp9[4] := array_tmp7[4] - array_tmp8[4];
array_tmp10[4] := array_tmp9[4] + array_x1[4];
if 4 <= glob_max_terms then
temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 4] := temporary
end if;
kkk := 5;
array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1);
array_tmp13[4] := array_x2_higher[2, 4];
array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1);
array_tmp15[4] := array_tmp12[4] - array_tmp14[4];
array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1);
array_tmp17[4] := array_tmp15[4] - array_tmp16[4];
if 4 <= glob_max_terms then
temporary := array_tmp17[4]*glob_h*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 4] := temporary
end if;
kkk := 5;
array_tmp1[5] := array_x2_higher[2, 5];
array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1);
array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1);
array_tmp5[5] := array_tmp3[5] - array_tmp4[5];
array_tmp6[5] := array_x1_higher[3, 5];
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
array_tmp8[5] := array_x1_higher[2, 5];
array_tmp9[5] := array_tmp7[5] - array_tmp8[5];
array_tmp10[5] := array_tmp9[5] + array_x1[5];
if 5 <= glob_max_terms then
temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 5] := temporary
end if;
kkk := 6;
array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1);
array_tmp13[5] := array_x2_higher[2, 5];
array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1);
array_tmp15[5] := array_tmp12[5] - array_tmp14[5];
array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1);
array_tmp17[5] := array_tmp15[5] - array_tmp16[5];
if 5 <= glob_max_terms then
temporary := array_tmp17[5]*glob_h*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 5] := temporary
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_x2_higher[2, kkk];
array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1);
array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1);
array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := array_x1_higher[3, kkk];
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
array_tmp8[kkk] := array_x1_higher[2, kkk];
array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk];
array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp10[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x2[kkk + order_d] := temporary;
array_x2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1);
array_tmp13[kkk] := array_x2_higher[2, kkk];
array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1);
array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk];
array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1);
array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp17[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x1[kkk + order_d] := temporary;
array_x1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_x1 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c1 + 6.0 * c3 * exp(-t);
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0*c2*exp(2.0*t) - c3*exp(-t)
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> t_start,t_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGMASSIVE,
> INFO,
> glob_iolevel,
> DEBUGL,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_clock_start_sec,
> glob_html_log,
> glob_current_iter,
> glob_small_float,
> glob_look_poles,
> glob_clock_sec,
> years_in_century,
> sec_in_min,
> djd_debug2,
> glob_max_iter,
> glob_relerr,
> glob_abserr,
> glob_hmin_init,
> glob_hmax,
> glob_disp_incr,
> glob_optimal_done,
> glob_almost_1,
> djd_debug,
> glob_iter,
> glob_warned,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_hmin,
> glob_start,
> glob_not_yet_start_msg,
> glob_initial_pass,
> days_in_year,
> glob_smallish_float,
> glob_max_order,
> glob_display_flag,
> glob_dump,
> glob_max_opt_iter,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_percent_done,
> glob_max_sec,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_log10_relerr,
> glob_last_good_h,
> glob_reached_optimal_h,
> min_in_hour,
> glob_max_minutes,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_dump_analytic,
> glob_large_float,
> centuries_in_millinium,
> glob_log10normmin,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_h,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_0D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_type_pole,
> array_norms,
> array_t,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2,
> array_x1,
> array_m1,
> array_x1_init,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_higher,
> array_x1_higher_work,
> array_poles,
> array_complex_pole,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> INFO := 2;
> glob_iolevel := 5;
> DEBUGL := 3;
> ALWAYS := 1;
> glob_max_terms := 30;
> glob_clock_start_sec := 0.0;
> glob_html_log := true;
> glob_current_iter := 0;
> glob_small_float := 0.1e-50;
> glob_look_poles := false;
> glob_clock_sec := 0.0;
> years_in_century := 100.0;
> sec_in_min := 60.0;
> djd_debug2 := true;
> glob_max_iter := 1000;
> glob_relerr := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_hmax := 1.0;
> glob_disp_incr := 0.1;
> glob_optimal_done := false;
> glob_almost_1 := 0.9990;
> djd_debug := true;
> glob_iter := 0;
> glob_warned := false;
> glob_no_eqs := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_hmin := 0.00000000001;
> glob_start := 0;
> glob_not_yet_start_msg := true;
> glob_initial_pass := true;
> days_in_year := 365.0;
> glob_smallish_float := 0.1e-100;
> glob_max_order := 30;
> glob_display_flag := true;
> glob_dump := false;
> glob_max_opt_iter := 10;
> glob_normmax := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_percent_done := 0.0;
> glob_max_sec := 10000.0;
> glob_warned2 := false;
> glob_optimal_clock_start_sec := 0.0;
> glob_log10_relerr := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_reached_optimal_h := false;
> min_in_hour := 60.0;
> glob_max_minutes := 0.0;
> glob_orig_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_hours := 0.0;
> glob_dump_analytic := false;
> glob_large_float := 9.0e100;
> centuries_in_millinium := 10.0;
> glob_log10normmin := 0.1;
> glob_log10_abserr := 0.1e-10;
> glob_not_yet_finished := true;
> glob_optimal_expect_sec := 0.1;
> glob_log10relerr := 0.0;
> glob_log10abserr := 0.0;
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_h := 0.1;
> hours_in_day := 24.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_max_order := 2;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/complicatedrevpostode.ode#################");
> omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_pole:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_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_type_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_t:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_x1_init:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_tmp10:= Array(1..(max_terms + 1),[]);
> array_tmp11:= Array(1..(max_terms + 1),[]);
> array_tmp12:= Array(1..(max_terms + 1),[]);
> array_tmp13:= Array(1..(max_terms + 1),[]);
> array_tmp14:= Array(1..(max_terms + 1),[]);
> array_tmp15:= Array(1..(max_terms + 1),[]);
> array_tmp16:= Array(1..(max_terms + 1),[]);
> array_tmp17:= Array(1..(max_terms + 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> 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_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_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2_init[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
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher[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_x2_higher_work2[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_t := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_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_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_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_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[1] := exact_soln_x1(t_start);
> array_x2_init[1] := exact_soln_x2(t_start);
> array_x2_init[2] := exact_soln_x2p(t_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> if glob_html_log then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_t[1] := t_start;
> array_t[2] := glob_h;
> order_diff := 2;
> #Start Series array_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_x2();
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> start_array_x1();
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> order_diff := 2;
> #Jump Series array_x2
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x2
> order_diff := 2;
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> order_diff := 1;
> #Jump Series array_x1
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x1
> order_diff := 1;
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 3
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 3
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if glob_html_log then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-02T01:53:37-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"complicatedrev")
> ;
> logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;")
> ;
> logitem_float(html_log_file,t_start)
> ;
> logitem_float(html_log_file,t_end)
> ;
> logitem_float(html_log_file,array_t[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 4
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 4
> ;
> log_revs(html_log_file," 076 | ")
> ;
> logitem_str(html_log_file,"complicatedrev diffeq.mxt")
> ;
> logitem_str(html_log_file,"complicatedrev maple results")
> ;
> logitem_str(html_log_file,"sub iter once eqs reversed")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4
> ;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then # if number 4
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;# end if 4
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3
> ;
> if glob_html_log then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp;
global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms,
glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float,
glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2,
glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax,
glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter,
glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start,
glob_not_yet_start_msg, glob_initial_pass, days_in_year,
glob_smallish_float, glob_max_order, glob_display_flag, glob_dump,
glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done,
glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr,
glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes,
glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_dump_analytic, glob_large_float,
centuries_in_millinium, glob_log10normmin, glob_log10_abserr,
glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr,
glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h,
hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0,
array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t,
array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1,
array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole,
array_real_pole, array_x1_higher_work2, array_x1_higher,
array_x2_higher_work, array_x2_higher_work2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
INFO := 2;
glob_iolevel := 5;
DEBUGL := 3;
ALWAYS := 1;
glob_max_terms := 30;
glob_clock_start_sec := 0.;
glob_html_log := true;
glob_current_iter := 0;
glob_small_float := 0.1*10^(-50);
glob_look_poles := false;
glob_clock_sec := 0.;
years_in_century := 100.0;
sec_in_min := 60.0;
djd_debug2 := true;
glob_max_iter := 1000;
glob_relerr := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_hmax := 1.0;
glob_disp_incr := 0.1;
glob_optimal_done := false;
glob_almost_1 := 0.9990;
djd_debug := true;
glob_iter := 0;
glob_warned := false;
glob_no_eqs := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_hmin := 0.1*10^(-10);
glob_start := 0;
glob_not_yet_start_msg := true;
glob_initial_pass := true;
days_in_year := 365.0;
glob_smallish_float := 0.1*10^(-100);
glob_max_order := 30;
glob_display_flag := true;
glob_dump := false;
glob_max_opt_iter := 10;
glob_normmax := 0.;
glob_unchanged_h_cnt := 0;
glob_percent_done := 0.;
glob_max_sec := 10000.0;
glob_warned2 := false;
glob_optimal_clock_start_sec := 0.;
glob_log10_relerr := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_reached_optimal_h := false;
min_in_hour := 60.0;
glob_max_minutes := 0.;
glob_orig_start_sec := 0.;
glob_optimal_start := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_hours := 0.;
glob_dump_analytic := false;
glob_large_float := 0.90*10^101;
centuries_in_millinium := 10.0;
glob_log10normmin := 0.1;
glob_log10_abserr := 0.1*10^(-10);
glob_not_yet_finished := true;
glob_optimal_expect_sec := 0.1;
glob_log10relerr := 0.;
glob_log10abserr := 0.;
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_h := 0.1;
hours_in_day := 24.0;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_max_order := 2;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/complicatedrevpostode.ode#################");
omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
diff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_pole := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_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_type_pole := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_t := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_x2 := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_x1_init := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_tmp10 := Array(1 .. max_terms + 1, []);
array_tmp11 := Array(1 .. max_terms + 1, []);
array_tmp12 := Array(1 .. max_terms + 1, []);
array_tmp13 := Array(1 .. max_terms + 1, []);
array_tmp14 := Array(1 .. max_terms + 1, []);
array_tmp15 := Array(1 .. max_terms + 1, []);
array_tmp16 := Array(1 .. max_terms + 1, []);
array_tmp17 := Array(1 .. max_terms + 1, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_t[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2_init[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;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher[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_x2_higher_work2[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_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1
end do;
array_x1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
end do;
array_x2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1
end do;
array_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_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_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_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x2_higher[r_order, term_no] := array_x2_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x1_higher[r_order, term_no] := array_x1_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_x2();
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_x1();
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_t[1] <= t_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 2;
order_diff := 2;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
order_diff := 1;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x1[term_no] := array_x1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x1_higher[ord, term_no] :=
array_x1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
ff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-02T01:53:37-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"complicatedrev");
logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \
2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
logitem_float(html_log_file, t_start);
logitem_float(html_log_file, t_end);
logitem_float(html_log_file, array_t[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 076 | ");
logitem_str(html_log_file, "complicatedrev diffeq.mxt");
logitem_str(html_log_file, "complicatedrev maple results");
logitem_str(html_log_file, "sub iter once eqs reversed");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/complicatedrevpostode.ode#################
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
#END FIRST INPUT BLOCK
!
#BEGIN SECOND INPUT BLOCK
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.001
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.001
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.001
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = 0.00082652209612614425075269168613102
absolute error = 1.7377596846004174084e-16
relative error = 2.1024963431042189816430962969600e-11 %
h = 0.001
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = 0.0012906639784542818918618739547211
absolute error = 4.633444453781957526860e-13
relative error = 3.5899696069572120796765728479236e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.502
x2[1] (analytic) = 0.0008274309894041739636559251804687
x2[1] (numeric) = 0.00082743208206711503358407744411689
absolute error = 1.09266294106992815226364819e-09
relative error = 0.00013205487286096759163327430459812 %
h = 0.001
x1[1] (analytic) = 0.0012895738591632036100858259251
x1[1] (numeric) = 0.0012895716796697751322509839346479
absolute error = 2.1794934284778348419904521e-09
relative error = 0.00016900880961499130103998997246766 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.503
x2[1] (analytic) = 0.0008283422476198008492141699458837
x2[1] (numeric) = 0.00082834662209419532515247999857985
absolute error = 4.37447439447593831005269615e-09
relative error = 0.00052809987744145214230170552587512 %
h = 0.001
x1[1] (analytic) = 0.0012884848299094197347162072617323
x1[1] (numeric) = 0.0012884761133078092129236615748211
absolute error = 8.7166016105217925456869112e-09
relative error = 0.00067650013474621724202878276122865 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.504
x2[1] (analytic) = 0.00082925587496274761468760841422102
x2[1] (numeric) = 0.00082926573062464187676195249676034
absolute error = 9.85566189426207434408253932e-09
relative error = 0.0011884946723717594353916049289451 %
h = 0.001
x1[1] (analytic) = 0.0012873968891405564758385060019091
x1[1] (numeric) = 0.0012873772731260255561388750919475
absolute error = 1.96160145309196996309099616e-08
relative error = 0.0015236959710237459080535094232935 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.505
x2[1] (analytic) = 0.00083017187563149546111924351454314
x2[1] (numeric) = 0.0008301894292660833587342720599604
absolute error = 1.755363458789761502854541726e-08
relative error = 0.0021144578735029911161583922341777 %
h = 0.001
x1[1] (analytic) = 0.0012863100357686729739277295072664
x1[1] (numeric) = 0.0012862747677288049168478543730644
absolute error = 3.52680398680570798751342020e-08
relative error = 0.0027417993242182557854751824962821 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3.8MB, alloc=2.9MB, time=0.17
t[1] = 0.506
x2[1] (analytic) = 0.00083109025383347519720441727943742
x2[1] (numeric) = 0.00083111813963898378021103730559235
absolute error = 2.788580550858300662002615493e-08
relative error = 0.0033553281824636172738729172433782 %
h = 0.001
x1[1] (analytic) = 0.0012852242687069157665292585243653
x1[1] (numeric) = 0.0012851346937267006448141946499636
absolute error = 8.95749802151217150638744017e-08
relative error = 0.0069695991895052295674023577236862 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.507
x2[1] (analytic) = 0.00083201101378508461244661319002326
x2[1] (numeric) = 0.00083208182025711992659294685537073
absolute error = 7.080647203531414633366534747e-08
relative error = 0.0085102806167424183765694805023606 %
h = 0.001
x1[1] (analytic) = 0.001284139586869517701405294158948
x1[1] (numeric) = 0.0012816032012667107580533020335611
absolute error = 2.5363856028069433519921253869e-06
relative error = 0.19751634703437167860653061977856 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.508
x2[1] (analytic) = 0.00083293415971170588563803837477598
x2[1] (numeric) = 0.00083486689850480914716087654457917
absolute error = 1.93273879310326152283816980319e-06
relative error = 0.23203980417518458136622086027346 %
h = 0.001
x1[1] (analytic) = 0.0012830559891717968507676151575396
x1[1] (numeric) = 0.0011445592494289191531884065137392
absolute error = 0.0001384967397428776975792086438004
relative error = 10.794286524649350533293680493259 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.509
x2[1] (analytic) = 0.00083385969584772302873516249155556
x2[1] (numeric) = 0.00092687683083470305397401705731068
absolute error = 9.301713498698002523885456575512e-05
relative error = 11.155010303312049881472952177155 %
h = 0.001
x1[1] (analytic) = 0.001281973474530155426595559729063
x1[1] (numeric) = -0.0050876137298401921977037822387805
absolute error = 0.0063695872043703476242993419678435
relative error = 496.85795618390682919220616232654 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.51
x2[1] (analytic) = 0.00083478762643653936619953115948893
x2[1] (numeric) = 0.0046589937378618315002240136718923
absolute error = 0.0038242061114252921340244825124034
relative error = 458.10527016909595292703358234922 %
h = 0.001
x1[1] (analytic) = 0.0012808920418620786970381472243591
x1[1] (numeric) = -0.24131402437289095671277172187697
absolute error = 0.24259491641475303540980986910133
relative error = 18939.528741398385565485550762183 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.511
x2[1] (analytic) = 0.00083571795573059504987431312643056
x2[1] (numeric) = 0.13285816078867771248944683425825
absolute error = 0.13202244283294711743957252113182
relative error = 15797.487887828310799736820128395 %
h = 0.001
x1[1] (analytic) = 0.0012798116900861339038992560756415
x1[1] (numeric) = -7.7093942279778686438373784130089
absolute error = 7.7106740396679547777412776690845
relative error = 602485.0452138791518531421981286 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.512
x2[1] (analytic) = 0.00083665068799138460946718195917937
x2[1] (numeric) = 3.848764768360869453897499526031
absolute error = 3.8479281176728780692880323440718
relative error = 459920.51078221333123823971899632 %
h = 0.001
x1[1] (analytic) = 0.0012787324181219691812047754809758
x1[1] (numeric) = -205.62452745932470778191386248986
absolute error = 205.62580619174282975109506726534
relative error = 16080440.542341020722247847680653 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
NO POLE
Radius of convergence = 9.530e-05
Order of pole = 1.449
t[1] = 0.513
x2[1] (analytic) = 0.00083758582748947453871027492802935
x2[1] (numeric) = 95.03997140458233662383395828203
absolute error = 95.039133818754847149295248007102
relative error = 11346793.45084180635823719951838 %
h = 0.001
x1[1] (analytic) = 0.0012776542248903124748506494008434
x1[1] (numeric) = -4614.1765933388366477251758552195
absolute error = 4614.1778709930615380376507058689
relative error = 361144492.86067143827350427059414 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 6.634e-05
Order of pole = 0.2405
t[1] = 0.514
x2[1] (analytic) = 0.0008385233785045209172681139251402
x2[1] (numeric) = 1992.6637388793779558995202832394
absolute error = 1992.6629003559994513786030151255
relative error = 237639516.25413816240454496582944 %
h = 0.001
x1[1] (analytic) = 0.0012765771093129704633307325147448
x1[1] (numeric) = -87182.96718468238078720867603815
absolute error = 87182.968461259490100179139368883
relative error = 6829432223.5011488387443148255895 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 9.347e-05
Order of pole = 16.65
t[1] = 0.515
x2[1] (analytic) = 0.00083946334532528706846451570820467
x2[1] (numeric) = 35463.481349374228164985292732259
absolute error = 35463.480509910882839698224267743
relative error = 4224541870.3980451264878519214906 %
h = 0.001
x1[1] (analytic) = 0.0012755010703128274795433788656077
x1[1] (numeric) = -1385013.8243610767550654844287504
absolute error = 1385013.8256365778253783119082938
relative error = 108585861499.66078912881341962994 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 0.0003875
Order of pole = 180.9
memory used=7.6MB, alloc=4.1MB, time=0.38
t[1] = 0.516
x2[1] (analytic) = 0.00084040573224966125289966149752755
x2[1] (numeric) = 534723.84790466957895035491098952
absolute error = 534723.84706426384670069365808986
relative error = 63626868135.80802784577150418021 %
h = 0.001
x1[1] (analytic) = 0.0012744261068138444336756849984992
x1[1] (numeric) = -18432473.242678055858975289924739
absolute error = 18432473.243952481965789134358415
relative error = 1446335189259.0282151448527669851 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.517
x2[1] (analytic) = 0.0008413505435846743980286389764889
x2[1] (numeric) = 6805672.8427367871910800556581839
absolute error = 6805672.8418954366474953812601553
relative error = 808898608765.26629591003009895997 %
h = 0.001
x1[1] (analytic) = 0.0012733522177410577371643104777951
x1[1] (numeric) = -204280317.45416562057307061203871
absolute error = 204280317.45543897279081166977587
relative error = 16042718943689.808866691108116321 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.518
x2[1] (analytic) = 0.00084229778364651786377291305301299
x2[1] (numeric) = 72704196.59553744274731642534695
absolute error = 72704196.594695144963669907483177
relative error = 8631649994369.0325267923053004535 %
h = 0.001
x1[1] (analytic) = 0.0012722794020205782277317997435378
x1[1] (numeric) = -1869185610.9990685417338471914189
absolute error = 1869185611.0003408211358677696466
relative error = 146916283328314.70722635113676919 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.519
x2[1] (analytic) = 0.00084324745676056124423632533367627
x2[1] (numeric) = 646913806.76858365663383533572403
absolute error = 646913806.76774040917707477447979
relative error = 76716959129997.179650868112208331 %
h = 0.001
x1[1] (analytic) = 0.0012712076585795900954973303432135
x1[1] (numeric) = -13958789929.958012959304013896182
absolute error = 13958789929.959284166962593486277
relative error = 1098073146094511.7253913579901584 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.52
x2[1] (analytic) = 0.00084419956726137020559736614303792
x2[1] (numeric) = 4747258637.5844548551973869526829
absolute error = 4747258637.5836106556301255824773
relative error = 562338435328032.51616216893304551 %
h = 0.001
x1[1] (analytic) = 0.00127013698634634981016081364961
x1[1] (numeric) = -83835909426.063292532867110345569
absolute error = 83835909426.064562669853456695379
relative error = 6600540754838203.1208627605382563 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 3.560e-05
Order of pole = 38.68
t[1] = 0.521
x2[1] (analytic) = 0.00084515411949272436024960708923766
x2[1] (numeric) = 28393092936.383396962744004738756
absolute error = 28393092936.382551808624512014396
relative error = 3359516599578850.9120275925160686 %
h = 0.001
x1[1] (analytic) = 0.0012690673842501850492592752487639
x1[1] (numeric) = -398022389772.65971946563416331421
absolute error = 398022389772.66098853301841349926
relative error = 31363377131296166.698088651723839 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 0.0001169
Order of pole = 228.7
t[1] = 0.522
x2[1] (analytic) = 0.00084611111780763517726232663345645
x2[1] (numeric) = 136671615850.64154313074210004024
absolute error = 136671615850.64069701962429240506
relative error = 16152915731065151.271615074867864 %
h = 0.001
x1[1] (analytic) = 0.0012679988512214936274944432542899
x1[1] (numeric) = -1469402384393.40254974984770924
absolute error = 1469402384393.4038177486989307336
relative error = 115883573788564031.31663473669231 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.523
x2[1] (analytic) = 0.00084707056656836392923350586605222
x2[1] (numeric) = 524315431733.21614790863155058981
absolute error = 524315431733.21530083806498222588
relative error = 61897491475510941.811060006420899 %
h = 0.001
x1[1] (analytic) = 0.0012669313861917424271304738755899
x1[1] (numeric) = -4198510280127.8065888182437736909
absolute error = 4198510280127.8078557496299654333
relative error = 331392080572577166.94861286814447 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.524
x2[1] (analytic) = 0.00084803247014643967560751672664236
x2[1] (numeric) = 1605595799032.6572100156258602256
absolute error = 1605595799032.6563619831557137859
relative error = 189331877676263902.31171389903844 %
h = 0.001
x1[1] (analytic) = 0.0012658649880934663294607446375807
x1[1] (numeric) = -9556189501036.6680043320599734608
absolute error = 9556189501036.6692701970480669271
relative error = 754913801307464477.36671125618277 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 0.001167
Order of pole = 280.4
t[1] = 0.525
x2[1] (analytic) = 0.00084899683292267728252997022968994
x2[1] (numeric) = 4020473916672.2860943242908248939
absolute error = 4020473916672.2852453274579022166
relative error = 473555820324061382.49275585960482 %
h = 0.001
x1[1] (analytic) = 0.0012647996558602671473426467186411
x1[1] (numeric) = -18097458069571.86542017725871785
absolute error = 18097458069571.866684976914578117
relative error = 1430855707915471016.1510171161615 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 0.0001137
Order of pole = 11.65
memory used=11.4MB, alloc=4.2MB, time=0.62
t[1] = 0.526
x2[1] (analytic) = 0.00084996365928719547931233787183942
x2[1] (numeric) = 8416124951971.5064426398063244774
absolute error = 8416124951971.5055926761470372819
relative error = 990174681001010735.15966424812374 %
h = 0.001
x1[1] (analytic) = 0.0012637353884268125587993089414852
x1[1] (numeric) = -18080977850166.451559871822635303
absolute error = 18080977850166.452823607211062116
relative error = 1430756629572187294.2232910188971 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.527
x2[1] (analytic) = 0.00085093295363943495157910530292247
x2[1] (numeric) = 10619053727748.775740450074613078
absolute error = 10619053727748.774889517120973643
relative error = 1247930719139639395.2845057128129 %
h = 0.001
x1[1] (analytic) = 0.0012626721847288350416871870185942
x1[1] (numeric) = 208388532861669.09174743790579605
absolute error = 208388532861669.09048476572106721
relative error = 16503771555435153245.503965934719 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.528
x2[1] (analytic) = 0.00085190472038817647117036353980059
x2[1] (numeric) = -76377295454035.304669209461938995
absolute error = 76377295454035.305521114182327171
relative error = 8965473911123939455.2496080780862 %
h = 0.001
x1[1] (analytic) = 0.0012616100437031308094284527197097
x1[1] (numeric) = 4028911219777281.6723537642880636
absolute error = 4028911219777281.6710921542443605
relative error = 319346793399920325283.54610079869 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.529
x2[1] (analytic) = 0.00085287896395155906287288949160932
x2[1] (numeric) = -1584199293909485.2191174470730754
absolute error = 1584199293909485.219970326037027
relative error = 185747258505424098216.8567063679 %
h = 0.001
x1[1] (analytic) = 0.001260548964287558747807118693686
x1[1] (numeric) = 59645665455178133.700293949005246
absolute error = 59645665455178133.699033400040958
relative error = 4731721428123093107440.8879292078 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.53
x2[1] (analytic) = 0.00085385568875709820805291434710783
x2[1] (numeric) = -23044614641880801.120824519976832
absolute error = 23044614641880801.121678375665589
relative error = 2698888693407352834375.9881218953 %
h = 0.001
x1[1] (analytic) = 0.0012594889454210393528278357407412
x1[1] (numeric) = 789441831498582105.60231663497849
absolute error = 789441831498582105.60105714603307
relative error = 62679536360255753682248.344868604 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.531
x2[1] (analytic) = 0.00085483489924170408526392545030159
x2[1] (numeric) = -297700552474111974.70144902897774
absolute error = 297700552474111974.70230386387698
relative error = 34825502882274967990297.17199346 %
h = 0.001
x1[1] (analytic) = 0.0012584299860435536696363003938124
x1[1] (numeric) = 9419807278531444728.2307140802689
absolute error = 9419807278531444728.2294556502829
relative error = 748536460748753139692563.58284364 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.532
x2[1] (analytic) = 0.00085581659985169984790299465988337
x2[1] (numeric) = -3471766895682267226.6209457098289
absolute error = 3471766895682267226.6218015264288
relative error = 405667160029832588191634.20157905 %
h = 0.001
x1[1] (analytic) = 0.001257372085096142232500211729337
x1[1] (numeric) = 101081058865388804662.54687367722
absolute error = 101081058865388804662.54561630513
relative error = 8039072925470574645346776.8560099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.533
x2[1] (analytic) = 0.0008568007950428399389892738519192
x2[1] (numeric) = -36500192779859514087.336456621742
absolute error = 36500192779859514087.337313422537
relative error = 4260055895260287280767385.65163 %
h = 0.001
x1[1] (analytic) = 0.0012563152415209040058497173883259
x1[1] (numeric) = 971671203008010545373.90298913125
absolute error = 971671203008010545373.90173281601
relative error = 77342944739864701520548792.014237 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.534
x2[1] (analytic) = 0.00085778748928032844313844618417794
x2[1] (numeric) = -344763967424345606117.35198703553
absolute error = 344763967424345606117.35284482302
relative error = 40192235458411464216896436.725986 %
h = 0.001
x1[1] (analytic) = 0.0012552594542609953263762898480893
x1[1] (numeric) = 8331108755382093997844.817964788
absolute error = 8331108755382093997844.8167095285
relative error = 663696156766796838428306550.02122 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
NO POLE
Radius of convergence = 0.0003058
Order of pole = 310.8
t[1] = 0.535
x2[1] (analytic) = 0.00085877668703883747580706999516187
x2[1] (numeric) = -2914574886945155522813.1246417025
absolute error = 2914574886945155522813.1255004792
relative error = 339386819755779682547215014.86589 %
h = 0.001
x1[1] (analytic) = 0.0012542047222606288461889750434006
x1[1] (numeric) = 63444812881827322429418.049838158
absolute error = 63444812881827322429418.048583953
relative error = 5058569127970739060693491388.9891 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.536
x2[1] (analytic) = 0.00085976839280252560988090076182799
x2[1] (numeric) = -21977161734593959798322.193332718
absolute error = 21977161734593959798322.194192486
relative error = 2556172327172504643561522940.6447 %
h = 0.001
x1[1] (analytic) = 0.0012531510444650724770269564932605
x1[1] (numeric) = 428038360735937613695808.71233172
absolute error = 428038360735937613695808.71107857
relative error = 34156964767056681443137624102.043 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.3MB, time=0.85
NO POLE
NO POLE
t[1] = 0.537
x2[1] (analytic) = 0.00086076261106505633968142538779503
x2[1] (numeric) = -147594906722031812720483.02090421
absolute error = 147594906722031812720483.02176497
relative error = 17146993238868341895702273750.884 %
h = 0.001
x1[1] (analytic) = 0.0012520984198206483355273791457368
x1[1] (numeric) = 2565132925887698907547833.2990847
absolute error = 2565132925887698907547833.2978326
relative error = 204866716967435417287671514248.52 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.538
x2[1] (analytic) = 0.0008617593463296165824649922390997
x2[1] (numeric) = -886284898338716046806321.12008458
absolute error = 886284898338716046806321.12094634
relative error = 102845986192497716400303751820.17 %
h = 0.001
x1[1] (analytic) = 0.0012510468472747316895473782086164
x1[1] (numeric) = 13867043360108630895489782.873343
absolute error = 13867043360108630895489782.872092
relative error = 1108435178931665394371383900078.4 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.539
x2[1] (analytic) = 0.00086275860310893521748906978789598
x2[1] (numeric) = -4835122702791031967582892.6683127
absolute error = 4835122702791031967582892.6691755
relative error = 560425904229497528400235909032.57 %
h = 0.001
x1[1] (analytic) = 0.0012499963257757499055392592878095
x1[1] (numeric) = 70350186225748130153879863.743503
absolute error = 70350186225748130153879863.742253
relative error = 5628031440979531005162062267178.4 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 4.342e-05
Order of pole = 7.198
t[1] = 0.54
x2[1] (analytic) = 0.0008637603859253016627203164664802
x2[1] (numeric) = -24858034430362983879728442.259866
absolute error = 24858034430362983879728442.26073
relative error = 2877885445479635188585245344284.6 %
h = 0.001
x1[1] (analytic) = 0.0012489468542731813969777772086
x1[1] (numeric) = 356950605722257851507598948.66393
absolute error = 356950605722257851507598948.66268
relative error = 28580127689258926579437053952018 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 9.568e-05
Order of pole = 61.16
t[1] = 0.541
x2[1] (analytic) = 0.00086476469931058448925929437526969
x2[1] (numeric) = -127200742934307154159662141.92313
absolute error = 127200742934307154159662141.92399
relative error = 14709289479058902074523271982624 %
h = 0.001
x1[1] (analytic) = 0.0012478984317175545738384619469313
x1[1] (numeric) = 1895145680929461501567251596.5581
absolute error = 1895145680929461501567251596.5569
relative error = 1.5186698153960039952798340153173e+32 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.542
x2[1] (analytic) = 0.00086577154780625007355680982946525
x2[1] (numeric) = -672065666098214441207771350.90056
absolute error = 672065666098214441207771350.90143
relative error = 77626213035198423021416083240120 %
h = 0.001
x1[1] (analytic) = 0.001246851057060446793125941148968
x1[1] (numeric) = 10211682922641022570422368549.784
absolute error = 10211682922641022570422368549.783
relative error = 8.1899781572274551595030358583525e+32 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.543
x2[1] (analytic) = 0.00086678093596338128749701437068642
x2[1] (numeric) = -3571921968778738599744148503.7726
absolute error = 3571921968778738599744148503.7735
relative error = 4.1209050875221843116265932774054e+32 %
h = 0.001
x1[1] (analytic) = 0.0012458047292544833104512097671668
x1[1] (numeric) = 50989848709111945273759000647.705
absolute error = 50989848709111945273759000647.704
relative error = 4.0929246383279811068905285829752e+33 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.544
x2[1] (analytic) = 0.00086779286834269622642255081248739
x2[1] (numeric) = -17635360651247484324761069901.842
absolute error = 17635360651247484324761069901.843
relative error = 2.0322085251665357540110571666253e+33 %
h = 0.001
x1[1] (analytic) = 0.00124475944725333623265679839004
x1[1] (numeric) = 209308394696559569053895112815.48
absolute error = 209308394696559569053895112815.48
relative error = 1.6815168196426683189508152492371e+34 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.545
x2[1] (analytic) = 0.00086880734951456697517718013294248
x2[1] (numeric) = -72091855217655734366068732132.198
absolute error = 72091855217655734366068732132.199
relative error = 8.2977952773921598355168830041327e+33 %
h = 0.001
x1[1] (analytic) = 0.0012437152100117234714887928906918
x1[1] (numeric) = 507695167407203124076201562387.98
absolute error = 507695167407203124076201562387.98
relative error = 4.0820853787131661992055669161699e+34 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 0.0002099
Order of pole = 72.05
t[1] = 0.546
x2[1] (analytic) = 0.00086982438405903841224147657403825
x2[1] (numeric) = -173674618527119777865356493368.03
absolute error = 173674618527119777865356493368.03
relative error = 1.9966630242838972469166590487744e+34 %
h = 0.001
x1[1] (analytic) = 0.0012426720164854076983146590660609
x1[1] (numeric) = -2038824696603027221866061391504.1
absolute error = 2038824696603027221866061391504.1
relative error = 1.6406780466251599147448345103381e+35 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=1.09
NO POLE
NO POLE
t[1] = 0.547
x2[1] (analytic) = 0.00087084397656584705203733015703041
x2[1] (numeric) = 742895166451449508478869070552.21
absolute error = 742895166451449508478869070552.21
relative error = 8.5307493241331162725508940022443e+34 %
h = 0.001
x1[1] (analytic) = 0.0012416298656311952998858269846059
x1[1] (numeric) = -46426739093838342823868197241364
absolute error = 46426739093838342823868197241364
relative error = 3.7391770590373833326580896636108e+36 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.548
x2[1] (analytic) = 0.0008718661316344399254771479758239
x2[1] (numeric) = 16613889867063091210172183428212
absolute error = 16613889867063091210172183428212
relative error = 1.9055551379106718177226399005637e+36 %
h = 0.001
x1[1] (analytic) = 0.0012405887564069353351439908049313
x1[1] (numeric) = -5.2078761025166113535027250827395e+32
absolute error = 5.2078761025166113535027250827395e+32
relative error = 4.1979069015585489488458050722047e+37 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.549
x2[1] (analytic) = 0.00087289085387399349883379808742284
x2[1] (numeric) = 1.8555396819436862183297832333337e+32
absolute error = 1.8555396819436862183297832333337e+32
relative error = 2.1257407769924272525656712605514e+37 %
h = 0.001
x1[1] (analytic) = 0.0012395486877715184930700808715671
x1[1] (numeric) = -4.8658790120476665950009646954474e+33
absolute error = 4.8658790120476665950009646954474e+33
relative error = 3.9255247172223834404821535533903e+38 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.55
x2[1] (analytic) = 0.00087391814790343263100749258018221
x2[1] (numeric) = 1.7226529906994720272543097480685e+33
absolute error = 1.7226529906994720272543097480685e+33
relative error = 1.9711834510270680715072698198015e+38 %
h = 0.001
x1[1] (analytic) = 0.0012385096586848760515748659367868
x1[1] (numeric) = -4.0997660674376877732734577125954e+34
absolute error = 4.0997660674376877732734577125954e+34
relative error = 3.3102414976650772686936356475767e+39 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.551
x2[1] (analytic) = 0.0008749480183514495692659594675856
x2[1] (numeric) = 1.4413463999623131253119244409390e+34
absolute error = 1.4413463999623131253119244409390e+34
relative error = 1.6473508936885806663947198962633e+39 %
h = 0.001
x1[1] (analytic) = 0.0012374716681079788374301443989802
x1[1] (numeric) = -3.1723244358050155898812802891035e+35
absolute error = 3.1723244358050155898812802891035e+35
relative error = 2.5635531847410393377204969442104e+40 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.552
x2[1] (analytic) = 0.00087598046985652298353440642818536
x2[1] (numeric) = 1.1089522158592725949721176493768e+35
absolute error = 1.1089522158592725949721176493768e+35
relative error = 1.2659554111302368423117445991817e+40 %
h = 0.001
x1[1] (analytic) = 0.0012364347150028361872394844886841
x1[1] (numeric) = -2.2685791336849822624297430149174e+36
absolute error = 2.2685791336849822624297430149174e+36
relative error = 1.8347747003203307000623688539782e+41 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.553
x2[1] (analytic) = 0.00087701550706693703931193309178555
x2[1] (numeric) = 7.9040722915796569740431090377779e+35
absolute error = 7.9040722915796569740431090377779e+35
relative error = 9.0124658320053959939259204755806e+40 %
h = 0.001
x1[1] (analytic) = 0.0012353987983324949094474743729255
x1[1] (numeric) = -1.5095292224034438926228771451801e+37
absolute error = 1.5095292224034438926228771451801e+37
relative error = 1.2218963013732587366039930575378e+42 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.554
x2[1] (analytic) = 0.00087805313464080050929120255853851
x2[1] (numeric) = 5.2571558079547644152423193008139e+36
absolute error = 5.2571558079547644152423193008139e+36
relative error = 5.9872866465027708481374516468066e+41 %
h = 0.001
x1[1] (analytic) = 0.0012343639170610382473864441870416
x1[1] (numeric) = -9.4570451831048801319996977359934e+37
absolute error = 9.4570451831048801319996977359934e+37
relative error = 7.6614724818120532271767784660222e+42 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.555
x2[1] (analytic) = 0.00087909335724606592375833713197844
x2[1] (numeric) = 3.3009832203067912539813012769618e+37
absolute error = 3.3009832203067912539813012769618e+37
relative error = 3.7549859671875750089028344566231e+42 %
h = 0.001
x1[1] (analytic) = 0.0012333300701535848433596230406101
x1[1] (numeric) = -5.6798572535330703244873441964760e+38
absolute error = 5.6798572535330703244873441964760e+38
relative error = 4.6053018498330830134198770581258e+43 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.556
x2[1] (analytic) = 0.00088013617956054875985015784974602
x2[1] (numeric) = 1.9899010927491380458888180533748e+38
absolute error = 1.9899010927491380458888180533748e+38
relative error = 2.2609013684026646377494039278007e+43 %
h = 0.001
x1[1] (analytic) = 0.0012322972565762877037596950805625
x1[1] (numeric) = -3.3387962804542805611859924924515e+39
absolute error = 3.3387962804542805611859924924515e+39
relative error = 2.7094081907887344483128857061890e+44 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.3MB, time=1.33
NO POLE
NO POLE
t[1] = 0.557
x2[1] (analytic) = 0.00088118160627194666974604230748542
x2[1] (numeric) = 1.1730599093150617765957628371400e+39
absolute error = 1.1730599093150617765957628371400e+39
relative error = 1.3312351290195188398087848025415e+44 %
h = 0.001
x1[1] (analytic) = 0.0012312654752963331652217197299492
x1[1] (numeric) = -1.9465631240143861855132373507554e+40
absolute error = 1.9465631240143861855132373507554e+40
relative error = 1.5809451032856254813892425039252e+45 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 7.409e-05
Order of pole = 35.39
t[1] = 0.558
x2[1] (analytic) = 0.00088222964207785874787183049273793
x2[1] (numeric) = 6.8380483340048683774335473601477e+39
absolute error = 6.8380483340048683774335473601477e+39
relative error = 7.7508712106970842973023269982535e+44 %
h = 0.001
x1[1] (analytic) = 0.0012302347252819398618093822551908
x1[1] (numeric) = -1.1199027394228693951106010691967e+41
absolute error = 1.1199027394228693951106010691967e+41
relative error = 9.1031631314602580379885164670517e+45 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.559
x2[1] (analytic) = 0.00088328029168580483719336387723487
x2[1] (numeric) = 3.9211576234463187242686762218825e+40
absolute error = 3.9211576234463187242686762218825e+40
relative error = 4.4393129342470706619072172274257e+45 %
h = 0.001
x1[1] (analytic) = 0.00122920500550235769323354184798
x1[1] (numeric) = -6.2047025932490207049817642871715e+41
absolute error = 6.2047025932490207049817642871715e+41
relative error = 5.0477361916641818389650003332843e+46 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.56
x2[1] (analytic) = 0.00088433355981324487467739885842914
x2[1] (numeric) = 2.1630544115884961953541852346008e+41
absolute error = 2.1630544115884961953541852346008e+41
relative error = 2.4459711921882664408741618447104e+46 %
h = 0.001
x1[1] (analytic) = 0.0012281763149278667941020454402963
x1[1] (numeric) = -3.1914625948378813318380404820238e+42
absolute error = 3.1914625948378813318380404820238e+42
relative error = 2.5985378125658791872284847789117e+47 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.561
x2[1] (analytic) = 0.00088538945118759827599779179502061
x2[1] (numeric) = 1.1093427606551960601998447075342e+42
absolute error = 1.1093427606551960601998447075342e+42
relative error = 1.2529432772970163402770215044478e+47 %
h = 0.001
x1[1] (analytic) = 0.0012271486525297765041997765022611
x1[1] (numeric) = -1.4490982384840528134570113217892e+43
absolute error = 1.4490982384840528134570113217892e+43
relative error = 1.1808660959670415717553623979297e+48 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.562
x2[1] (analytic) = 0.00088644797054626335956500934725191
x2[1] (numeric) = 5.0344038888645337075486087438096e+42
absolute error = 5.0344038888645337075486087438096e+42
relative error = 5.6792999207411352669319834782364e+47 %
h = 0.001
x1[1] (analytic) = 0.0012261220172804243397979091027969
x1[1] (numeric) = -5.1886925824970336226824803564450e+43
absolute error = 5.1886925824970336226824803564450e+43
relative error = 4.2317913791367277266872373848867e+48 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 0.0001112
Order of pole = 20.75
t[1] = 0.563
x2[1] (analytic) = 0.00088750912263663680995717461150232
x2[1] (numeric) = 1.8023253611685577571600748147999e+43
absolute error = 1.8023253611685577571600748147999e+43
relative error = 2.0307682650226280459050907171822e+48 %
h = 0.001
x1[1] (analytic) = 0.0012250964081531749659913385422579
x1[1] (numeric) = -7.1710464586995159459036459624407e+43
absolute error = 7.1710464586995159459036459624407e+43
relative error = 5.8534548064750453541367282842641e+48 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 7.221e-05
Order of pole = 10.86
t[1] = 0.564
x2[1] (analytic) = 0.00088857291221613318083101663081396
x2[1] (numeric) = 2.4259668645623557801352660236288e+43
absolute error = 2.4259668645623557801352660236288e+43
relative error = 2.7301832311227067814793039364087e+48 %
h = 0.001
x1[1] (analytic) = 0.0012240718241224191700632608943781
x1[1] (numeric) = 1.1574263562365199010318002425107e+45
absolute error = 1.1574263562365199010318002425107e+45
relative error = 9.4555428319438707252964415819686e+49 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.565
x2[1] (analytic) = 0.00088963934405220443739124826907637
x2[1] (numeric) = -4.1413018969797786111451927000158e+44
absolute error = 4.1413018969797786111451927000158e+44
relative error = 4.6550345650369135997211770405507e+49 %
h = 0.001
x1[1] (analytic) = 0.00122304826416357283587587482203
x1[1] (numeric) = 1.7557792400527687448103988235585e+46
absolute error = 1.7557792400527687448103988235585e+46
relative error = 1.4355764130481995760484465983179e+51 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.566
x2[1] (analytic) = 0.00089070842292235953849705515730068
x2[1] (numeric) = -6.2242725438754744400350241917297e+45
absolute error = 6.2242725438754744400350241917297e+45
relative error = 6.9880023402653128011532026095229e+50 %
h = 0.001
x1[1] (analytic) = 0.001222025727253075919286180057411
x1[1] (numeric) = 1.7620043161420033069605273349766e+47
absolute error = 1.7620043161420033069605273349766e+47
relative error = 1.4418717027363371542977335928792e+52 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=26.7MB, alloc=4.3MB, time=1.56
t[1] = 0.567
x2[1] (analytic) = 0.00089178015361418405848453645636232
x2[1] (numeric) = -6.2141071752097569666088393566103e+46
absolute error = 6.2141071752097569666088393566103e+46
relative error = 6.9682052802199965166189847573389e+51 %
h = 0.001
x1[1] (analytic) = 0.0012210042123683914245858479623694
x1[1] (numeric) = 1.5111828972596486947701778356762e+48
absolute error = 1.5111828972596486947701778356762e+48
relative error = 1.2376557606860302345494036962019e+53 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.568
x2[1] (analytic) = 0.00089285454092535984878409653241629
x2[1] (numeric) = -5.3060398252158809707396469081545e+47
absolute error = 5.3060398252158809707396469081545e+47
relative error = 5.9427819224805299075885320262646e+52 %
h = 0.001
x1[1] (analytic) = 0.0012199837184880043819641406086574
x1[1] (numeric) = 1.1763192844019761307956268538499e+49
absolute error = 1.1763192844019761307956268538499e+49
relative error = 9.6420900260853965953780541957631e+53 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.569
x2[1] (analytic) = 0.00089393158966368473941194530952011
x2[1] (numeric) = -4.1179096084541391241054471485886e+48
absolute error = 4.1179096084541391241054471485886e+48
relative error = 4.6065153710513581263231385534888e+53 %
h = 0.001
x1[1] (analytic) = 0.0012189642445914208259928558409419
x1[1] (numeric) = 8.5177628724472357333257217805781e+49
absolute error = 8.5177628724472357333257217805781e+49
relative error = 6.9877052671895774757523014343295e+54 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.57
x2[1] (analytic) = 0.00089501130464709228041502404947533
x2[1] (numeric) = -2.9781501641580982926819264023201e+49
absolute error = 2.9781501641580982926819264023201e+49
relative error = 3.3275000535690426262334893649923e+54 %
h = 0.001
x1[1] (analytic) = 0.0012179457896591667751322768074366
x1[1] (numeric) = 5.8321391716182165243656133848141e+50
absolute error = 5.8321391716182165243656133848141e+50
relative error = 4.7885047274971885513334860490382e+55 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.571
x2[1] (analytic) = 0.00089609369070367152334883261215016
x2[1] (numeric) = -2.0397258833796450993649500299965e+50
absolute error = 2.0397258833796450993649500299965e+50
relative error = 2.2762417641596366889588345449381e+55 %
h = 0.001
x1[1] (analytic) = 0.0012169283526727872122571054640167
x1[1] (numeric) = 3.8298145741817899014545709204468e+51
absolute error = 3.8298145741817899014545709204468e+51
relative error = 3.1471159051970633723447357469897e+56 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.572
x2[1] (analytic) = 0.00089717875267168684286779387121317
x2[1] (numeric) = -1.3408563099943228462922517660030e+51
absolute error = 1.3408563099943228462922517660030e+51
relative error = 1.4945252615506323223481151456817e+56 %
h = 0.001
x1[1] (analytic) = 0.0012159119326148450662013605776668
x1[1] (numeric) = 2.4406515362741576292103795590223e+52
absolute error = 2.4406515362741576292103795590223e+52
relative error = 2.0072601237044227357479230161324e+57 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.573
x2[1] (analytic) = 0.00089826649539959779850795090092798
x2[1] (numeric) = -8.5528634610705944862683893186664e+51
absolute error = 8.5528634610705944862683893186664e+51
relative error = 9.5215211798207118750045392232150e+56 %
h = 0.001
x1[1] (analytic) = 0.0012148965284689201943212217740738
x1[1] (numeric) = 1.5202235678608787521377880015141e+53
absolute error = 1.5202235678608787521377880015141e+53
relative error = 1.2513193776072013158575006432788e+58 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.574
x2[1] (analytic) = 0.00089935692374607903674195281006981
x2[1] (numeric) = -5.3276543688642093012574115002706e+52
absolute error = 5.3276543688642093012574115002706e+52
relative error = 5.9238487281256520092105665062035e+57 %
h = 0.001
x1[1] (analytic) = 0.0012138821392196083660748021921261
x1[1] (numeric) = 9.2570621658676472834064895360310e+53
absolute error = 9.2570621658676472834064895360310e+53
relative error = 7.6259975056712770625052448494990e+58 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.575
x2[1] (analytic) = 0.00090045004258004023338644567976864
x2[1] (numeric) = -3.2408818039140228044448331934073e+53
absolute error = 3.2408818039140228044448331934073e+53
relative error = 3.5991800218344079821589597192459e+58 %
h = 0.001
x1[1] (analytic) = 0.0012128687638525202476178333250037
x1[1] (numeric) = 5.4726711960066224015198422044698e+54
absolute error = 5.4726711960066224015198422044698e+54
relative error = 4.5121709447140781136913519544988e+59 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 8.287e-05
Order of pole = 44.99
t[1] = 0.576
x2[1] (analytic) = 0.00090154585678064607644214596380192
x2[1] (numeric) = -1.9128471401725350634317086798115e+54
absolute error = 1.9128471401725350634317086798115e+54
relative error = 2.1217413687676092969344047917474e+59 %
h = 0.001
x1[1] (analytic) = 0.0012118564013542803874142466434628
x1[1] (numeric) = 3.1031377015220580801033398774309e+55
absolute error = 3.1031377015220580801033398774309e+55
relative error = 2.5606480256689015958235101457987e+60 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.577
memory used=30.5MB, alloc=4.3MB, time=1.79
x2[1] (analytic) = 0.00090264437123733628944703493319481
x2[1] (numeric) = -1.0830031259993200683646363988051e+55
absolute error = 1.0830031259993200683646363988051e+55
relative error = 1.1998115321039998501240429761896e+60 %
h = 0.001
x1[1] (analytic) = 0.0012108450507125262028606376118103
x1[1] (numeric) = 1.6610425221115017734463373981237e+56
absolute error = 1.6610425221115017734463373981237e+56
relative error = 1.3718043618661654688336698857089e+61 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.578
x2[1] (analytic) = 0.00090374559084984569542327429258224
x2[1] (numeric) = -5.7923535769912255219744191938231e+55
absolute error = 5.7923535769912255219744191938231e+55
relative error = 6.4092745078228610451255820554276e+60 %
h = 0.001
x1[1] (analytic) = 0.0012098347109159069679235987209479
x1[1] (numeric) = 8.2060930899503125274936483247462e+56
absolute error = 8.2060930899503125274936483247462e+56
relative error = 6.7828216663893523943154890279843e+61 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.579
x2[1] (analytic) = 0.00090484952052822432149860496429206
x2[1] (numeric) = -2.8609726586177813939954436750353e+56
absolute error = 2.8609726586177813939954436750353e+56
relative error = 3.1618214893318729760650217704806e+61 %
h = 0.001
x1[1] (analytic) = 0.0012088253809540828017889091757341
x1[1] (numeric) = 3.5737760382361641920914785963704e+57
absolute error = 3.5737760382361641920914785963704e+57
relative error = 2.9564038731677772198661007769200e+62 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.58
x2[1] (analytic) = 0.00090595616519285754428315322816622
x2[1] (numeric) = -1.2449978815061120073683373794633e+57
absolute error = 1.2449978815061120073683373794633e+57
relative error = 1.3742363365241630230990374100745e+62 %
h = 0.001
x1[1] (analytic) = 0.0012078170598177236585215698857712
x1[1] (numeric) = 1.1834306117011450248147940616412e+58
absolute error = 1.1834306117011450248147940616412e+58
relative error = 9.7980948528723473498446437501943e+62 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 7.054e-05
Order of pole = 5.63
t[1] = 0.581
x2[1] (analytic) = 0.00090706552977448627608273092139788
x2[1] (numeric) = -4.1009381579274677288208541912904e+57
absolute error = 4.1009381579274677288208541912904e+57
relative error = 4.5211046206849452961255053807970e+62 %
h = 0.001
x1[1] (analytic) = 0.0012068097464985083177356734195659
x1[1] (numeric) = 4.9158190708782411993261744499246e+57
absolute error = 4.9158190708782411993261744499246e+57
relative error = 4.0734002067361637919702258649170e+62 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 5.144e-05
Order of pole = 1.61
t[1] = 0.582
x2[1] (analytic) = 0.00090817761921422719202987924377588
x2[1] (numeric) = -1.3764404433401996478927625577277e+57
absolute error = 1.3764404433401996478927625577277e+57
relative error = 1.5156070951529531093604096058848e+62 %
h = 0.001
x1[1] (analytic) = 0.0012058034399891233762730995918507
x1[1] (numeric) = -4.1783158310013619174562996225764e+59
absolute error = 4.1783158310013619174562996225764e+59
relative error = 3.4651715963250621387003757068289e+64 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.583
x2[1] (analytic) = 0.00090929243846359299821406888034318
x2[1] (numeric) = 1.4880362600581185880347151894486e+59
absolute error = 1.4880362600581185880347151894486e+59
relative error = 1.6364771080384364298545807586215e+64 %
h = 0.001
x1[1] (analytic) = 0.0012047981392832622408900283626774
x1[1] (numeric) = -5.4711006233959855894363711515958e+60
absolute error = 5.4711006233959855894363711515958e+60
relative error = 4.5410931881508038724405194768252e+65 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.584
x2[1] (analytic) = 0.00091040999248451274089263264624774
x2[1] (numeric) = 1.9300132430361618402214430292855e+60
absolute error = 1.9300132430361618402214430292855e+60
relative error = 2.1199385540234982404362204221787e+65 %
h = 0.001
x1[1] (analytic) = 0.0012037938433756241219502627347115
x1[1] (numeric) = -5.1739401427306391912768564985913e+61
absolute error = 5.1739401427306391912768564985913e+61
relative error = 4.2980284134217789335943795406151e+66 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.585
x2[1] (analytic) = 0.00091153028624935215686417067814311
x2[1] (numeric) = 1.8177609467006611604627154451172e+61
absolute error = 1.8177609467006611604627154451172e+61
relative error = 1.9941860123816078855848369973268e+66 %
h = 0.001
x1[1] (analytic) = 0.0012027905512619130281243553419666
x1[1] (numeric) = -4.2510572335481436371702240130992e+62
absolute error = 4.2510572335481436371702240130992e+62
relative error = 3.5343287566468892971290472412034e+67 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.586
x2[1] (analytic) = 0.0009126533247409340650863323435399
x2[1] (numeric) = 1.4903756675927179844930831829429e+62
absolute error = 1.4903756675927179844930831829429e+62
relative error = 1.6330140122107989759349129747956e+67 %
h = 0.001
x1[1] (analytic) = 0.0012017882619388367620935334290215
x1[1] (numeric) = -3.2095476108022800455768938587771e+63
absolute error = 3.2095476108022800455768938587771e+63
relative error = 2.6706431677276818243777301664304e+68 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.587
x2[1] (analytic) = 0.00091377911295255879962004351467114
x2[1] (numeric) = 1.1243462369502534914511383972012e+63
absolute error = 1.1243462369502534914511383972012e+63
relative error = 1.2304354750649972750890661739801e+68 %
h = 0.001
x1[1] (analytic) = 0.0012007869744041059172574179245617
x1[1] (numeric) = -2.2870791849151302458501096617625e+64
absolute error = 2.2870791849151302458501096617625e+64
relative error = 1.9046502282805824460053098896670e+69 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=2.03
NO POLE
NO POLE
t[1] = 0.588
x2[1] (analytic) = 0.00091490765588802468398241265737402
x2[1] (numeric) = 8.0118923017946421777450514613766e+63
absolute error = 8.0118923017946421777450514613766e+63
relative error = 8.7570502336852405190101976323188e+68 %
h = 0.001
x1[1] (analytic) = 0.0011997866876564328754445333168804
x1[1] (numeric) = -1.5629565678008495831816850257672e+65
absolute error = 1.5629565678008495831816850257672e+65
relative error = 1.3026953740033602431499287891374e+70 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.589
x2[1] (analytic) = 0.00091603895856164854699071431886538
x2[1] (numeric) = 5.4762562415555361135822530536608e+64
absolute error = 5.4762562415555361135822530536608e+64
relative error = 5.9781914190137463449025339654806e+69 %
h = 0.001
x1[1] (analytic) = 0.0011987874006955308056246060417651
x1[1] (numeric) = -1.0341097134354206938215479800156e+66
absolute error = 1.0341097134354206938215479800156e+66
relative error = 8.6262978142365786209645964569143e+70 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.59
x2[1] (analytic) = 0.00091717302599828628018001406175885
x2[1] (numeric) = 3.6230418852219134339158494260653e+65
absolute error = 3.6230418852219134339158494260653e+65
relative error = 3.9502272554063130686279994019155e+70 %
h = 0.001
x1[1] (analytic) = 0.0011977891125221126636216500949856
x1[1] (numeric) = -6.6516002029969479587038167170453e+66
absolute error = 6.6516002029969479587038167170453e+66
relative error = 5.5532314774435313787592546101951e+71 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.591
x2[1] (analytic) = 0.00091830986323335343687716468589885
x2[1] (numeric) = 2.3292514846201026170126830694318e+66
absolute error = 2.3292514846201026170126830694318e+66
relative error = 2.5364548262814554631612768957381e+71 %
h = 0.001
x1[1] (analytic) = 0.0011967918221378901928268395823847
x1[1] (numeric) = -4.1578916226152450201242728216474e+67
absolute error = 4.1578916226152450201242728216474e+67
relative error = 3.4741978894773791353878735820395e+72 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.592
x2[1] (analytic) = 0.00091944947531284587301406970523356
x2[1] (numeric) = 1.4548366059964883097726377014911e+67
absolute error = 1.4548366059964883097726377014911e+67
relative error = 1.5822909741739480666894786112207e+72 %
h = 0.001
x1[1] (analytic) = 0.0011957955285455729259101689203614
x1[1] (numeric) = -2.5170844193402301366549004981790e+68
absolute error = 2.5170844193402301366549004981790e+68
relative error = 2.1049455021810625638570947561428e+73 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.593
x2[1] (analytic) = 0.00092059186729336042976327650467993
x2[1] (numeric) = 8.7998648046171344928540264292756e+67
absolute error = 8.7998648046171344928540264292756e+67
relative error = 9.5589208608693100273025295188011e+72 %
h = 0.001
x1[1] (analytic) = 0.001194800230748867187529902398324
x1[1] (numeric) = -1.4677151183780838290829407608899e+69
absolute error = 1.4677151183780838290829407608899e+69
relative error = 1.2284188440925904945620816109595e+74 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.594
x2[1] (analytic) = 0.00092173704424211565807912839241284
x2[1] (numeric) = 5.1279543047820128922466442898460e+68
absolute error = 5.1279543047820128922466442898460e+68
relative error = 5.5633592430891130681035339330519e+73 %
h = 0.001
x1[1] (analytic) = 0.0011938059277524750980388158124784
x1[1] (numeric) = -8.1831317210789717805782561923994e+69
absolute error = 8.1831317210789717805782561923994e+69
relative error = 6.8546583082268547809552551361832e+74 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.595
x2[1] (analytic) = 0.00092288501123697258522787188690669
x2[1] (numeric) = 2.8579102890795473554490271730013e+69
absolute error = 2.8579102890795473554490271730013e+69
relative error = 3.0967133004457379782201978888659e+74 %
h = 0.001
x1[1] (analytic) = 0.0011928126185620935781862338771108
x1[1] (numeric) = -4.3124854774878951646519863228473e+70
absolute error = 4.3124854774878951646519863228473e+70
relative error = 3.6153922337663487119714040838299e+75 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.596
x2[1] (analytic) = 0.00092403577336645552339028303603533
x2[1] (numeric) = 1.5055052064378101951615934808220e+70
absolute error = 1.5055052064378101951615934808220e+70
relative error = 1.6292715605078144877306596721691e+75 %
h = 0.001
x1[1] (analytic) = 0.0011918203021844133548148681153206
x1[1] (numeric) = -2.0994896005525668548011801626882e+71
absolute error = 2.0994896005525668548011801626882e+71
relative error = 1.7615823431641018858190686179219e+76 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.597
x2[1] (analytic) = 0.00092518933572977292042054435826881
x2[1] (numeric) = 7.3224242801927720218823847443467e+70
absolute error = 7.3224242801927720218823847443467e+70
relative error = 7.9145143565851564492655003774011e+75 %
h = 0.001
x1[1] (analytic) = 0.0011908289776271179675514609259555
x1[1] (numeric) = -8.9217291718118612335310348792867e+71
absolute error = 8.9217291718118612335310348792867e+71
relative error = 7.4920323064270488949435598672783e+76 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=38.1MB, alloc=4.4MB, time=2.27
t[1] = 0.598
x2[1] (analytic) = 0.00092634570343683825284527212416087
x2[1] (numeric) = 3.1035207533019070951412139108633e+71
absolute error = 3.1035207533019070951412139108633e+71
relative error = 3.3502835299905040865330934159545e+76 %
h = 0.001
x1[1] (analytic) = 0.0011898386438988827764902425173134
x1[1] (numeric) = -2.7112285306233839106350033281485e+72
absolute error = 2.7112285306233839106350033281485e+72
relative error = 2.2786522731680539549209282557749e+77 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.599
x2[1] (analytic) = 0.0009275048816082909611867621605716
x2[1] (numeric) = 9.3472236197729701929881478446902e+71
absolute error = 9.3472236197729701929881478446902e+71
relative error = 1.0077816090374543006540576385845e+77 %
h = 0.001
x1[1] (analytic) = 0.001188849300009373970868208390983
x1[1] (numeric) = 2.0946281308220220861936040218879e+72
absolute error = 2.0946281308220220861936040218879e+72
relative error = 1.7618954150080301430134911247571e+77 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.6
x2[1] (analytic) = 0.00092866687537551742769469116109009
x2[1] (numeric) = -8.2971446950140066344438697293588e+71
absolute error = 8.2971446950140066344438697293588e+71
relative error = 8.9344682307732340583419286343589e+76 %
h = 0.001
x1[1] (analytic) = 0.0011878609449692475787312260510186
x1[1] (numeric) = 1.3603092904579727828001945828630e+74
absolute error = 1.3603092904579727828001945828630e+74
relative error = 1.1451755327246571804827170807987e+79 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
Iterations = 100
Total Elapsed Time = 2 Seconds
Elapsed Time(since restart) = 2 Seconds
Expected Time Remaining = 1 Minutes 39 Seconds
Optimized Time Remaining = 1 Minutes 38 Seconds
Time to Timeout = 14 Minutes 57 Seconds
Percent Done = 2.244 %
> quit
memory used=39.1MB, alloc=4.4MB, time=2.33