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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGL,
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_abserr,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> glob_max_opt_iter,
> glob_warned2,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_normmax,
> glob_max_order,
> glob_html_log,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_initial_pass,
> days_in_year,
> glob_dump,
> glob_log10normmin,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_log10_relerr,
> glob_optimal_done,
> glob_max_sec,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_large_float,
> glob_h,
> glob_almost_1,
> min_in_hour,
> glob_start,
> glob_no_eqs,
> glob_look_poles,
> glob_hmin_init,
> djd_debug2,
> glob_percent_done,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_hmin,
> glob_disp_incr,
> centuries_in_millinium,
> glob_display_flag,
> glob_iter,
> glob_current_iter,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> sec_in_min,
> glob_smallish_float,
> glob_clock_start_sec,
> glob_clock_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_1,
> array_const_0D0,
> array_const_2,
> #END CONST
> array_x2,
> array_x1,
> array_t,
> array_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_complex_pole,
> array_x1_higher,
> array_real_pole,
> array_x1_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_x2(ind_var);
> omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x2[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_x1(ind_var);
> omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_x2(ind_var);
omniout_float(ALWAYS, "x2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x2[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x2[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_x1(ind_var);
omniout_float(ALWAYS, "x1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x1[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGL,
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_abserr,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> glob_max_opt_iter,
> glob_warned2,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_normmax,
> glob_max_order,
> glob_html_log,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_initial_pass,
> days_in_year,
> glob_dump,
> glob_log10normmin,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_log10_relerr,
> glob_optimal_done,
> glob_max_sec,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_large_float,
> glob_h,
> glob_almost_1,
> min_in_hour,
> glob_start,
> glob_no_eqs,
> glob_look_poles,
> glob_hmin_init,
> djd_debug2,
> glob_percent_done,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_hmin,
> glob_disp_incr,
> centuries_in_millinium,
> glob_display_flag,
> glob_iter,
> glob_current_iter,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> sec_in_min,
> glob_smallish_float,
> glob_clock_start_sec,
> glob_clock_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_1,
> array_const_0D0,
> array_const_2,
> #END CONST
> array_x2,
> array_x1,
> array_t,
> array_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_complex_pole,
> array_x1_higher,
> array_real_pole,
> array_x1_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_t[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_t[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(t_start,t_end)
> global
> DEBUGL,
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_abserr,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> glob_max_opt_iter,
> glob_warned2,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_normmax,
> glob_max_order,
> glob_html_log,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_initial_pass,
> days_in_year,
> glob_dump,
> glob_log10normmin,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_log10_relerr,
> glob_optimal_done,
> glob_max_sec,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_large_float,
> glob_h,
> glob_almost_1,
> min_in_hour,
> glob_start,
> glob_no_eqs,
> glob_look_poles,
> glob_hmin_init,
> djd_debug2,
> glob_percent_done,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_hmin,
> glob_disp_incr,
> centuries_in_millinium,
> glob_display_flag,
> glob_iter,
> glob_current_iter,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> sec_in_min,
> glob_smallish_float,
> glob_clock_start_sec,
> glob_clock_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_1,
> array_const_0D0,
> array_const_2,
> #END CONST
> array_x2,
> array_x1,
> array_t,
> array_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_complex_pole,
> array_x1_higher,
> array_real_pole,
> array_x1_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(t_start, t_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start),
convfloat(array_t[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),
convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(t_end), convfloat(t_start),
convfloat(array_t[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_abserr,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> glob_max_opt_iter,
> glob_warned2,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_normmax,
> glob_max_order,
> glob_html_log,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_initial_pass,
> days_in_year,
> glob_dump,
> glob_log10normmin,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_log10_relerr,
> glob_optimal_done,
> glob_max_sec,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_large_float,
> glob_h,
> glob_almost_1,
> min_in_hour,
> glob_start,
> glob_no_eqs,
> glob_look_poles,
> glob_hmin_init,
> djd_debug2,
> glob_percent_done,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_hmin,
> glob_disp_incr,
> centuries_in_millinium,
> glob_display_flag,
> glob_iter,
> glob_current_iter,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> sec_in_min,
> glob_smallish_float,
> glob_clock_start_sec,
> glob_clock_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_1,
> array_const_0D0,
> array_const_2,
> #END CONST
> array_x2,
> array_x1,
> array_t,
> array_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_complex_pole,
> array_x1_higher,
> array_real_pole,
> array_x1_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 2 - 1;
> while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1];
> rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1];
> rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]);
> rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]);
> rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]);
> rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]);
> rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float)) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]);
> rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]);
> rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]);
> rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]);
> rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4
> ;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3
> ;
> #BOTTOM RADII COMPLEX EQ = 2
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 2
> if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 2
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if array_pole[1] > array_poles[2,1] then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 2
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or
abs(array_x2_higher[1, m - 1]) < glob_small_float or
abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or
abs(array_x1_higher[1, m - 1]) < glob_small_float or
abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_x2_higher[1, m]) or
glob_large_float <= abs(array_x2_higher[1, m - 1]) or
glob_large_float <= abs(array_x2_higher[1, m - 2]) or
glob_large_float <= abs(array_x2_higher[1, m - 3]) or
glob_large_float <= abs(array_x2_higher[1, m - 4]) or
glob_large_float <= abs(array_x2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3];
rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4];
rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= abs(array_x1_higher[1, m]) or
glob_large_float <= abs(array_x1_higher[1, m - 1]) or
glob_large_float <= abs(array_x1_higher[1, m - 2]) or
glob_large_float <= abs(array_x1_higher[1, m - 3]) or
glob_large_float <= abs(array_x1_higher[1, m - 4]) or
glob_large_float <= abs(array_x1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3];
rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4];
rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[2, 1] := rad_c;
array_complex_pole[2, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_abserr,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> glob_max_opt_iter,
> glob_warned2,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_normmax,
> glob_max_order,
> glob_html_log,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_initial_pass,
> days_in_year,
> glob_dump,
> glob_log10normmin,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_log10_relerr,
> glob_optimal_done,
> glob_max_sec,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_large_float,
> glob_h,
> glob_almost_1,
> min_in_hour,
> glob_start,
> glob_no_eqs,
> glob_look_poles,
> glob_hmin_init,
> djd_debug2,
> glob_percent_done,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_hmin,
> glob_disp_incr,
> centuries_in_millinium,
> glob_display_flag,
> glob_iter,
> glob_current_iter,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> sec_in_min,
> glob_smallish_float,
> glob_clock_start_sec,
> glob_clock_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_1,
> array_const_0D0,
> array_const_2,
> #END CONST
> array_x2,
> array_x1,
> array_t,
> array_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_complex_pole,
> array_x1_higher,
> array_real_pole,
> array_x1_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 3
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x2[iii]) then
array_norms[iii] := abs(array_x2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x1[iii]) then
array_norms[iii] := abs(array_x1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_abserr,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> glob_max_opt_iter,
> glob_warned2,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_normmax,
> glob_max_order,
> glob_html_log,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_initial_pass,
> days_in_year,
> glob_dump,
> glob_log10normmin,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_log10_relerr,
> glob_optimal_done,
> glob_max_sec,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_large_float,
> glob_h,
> glob_almost_1,
> min_in_hour,
> glob_start,
> glob_no_eqs,
> glob_look_poles,
> glob_hmin_init,
> djd_debug2,
> glob_percent_done,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_hmin,
> glob_disp_incr,
> centuries_in_millinium,
> glob_display_flag,
> glob_iter,
> glob_current_iter,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> sec_in_min,
> glob_smallish_float,
> glob_clock_start_sec,
> glob_clock_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_1,
> array_const_0D0,
> array_const_2,
> #END CONST
> array_x2,
> array_x1,
> array_t,
> array_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_complex_pole,
> array_x1_higher,
> array_real_pole,
> array_x1_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1
> array_tmp1[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp4[1] := (array_const_2D0[1] * (array_x2[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp6[1] := array_x1_higher[3,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp8[1] := array_x1_higher[2,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp10[1] := array_tmp9[1] + array_x1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2);
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> # emit pre mult $eq_no = 2 i = 1
> array_tmp12[1] := (array_const_4D0[1] * (array_x2[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1]));
> # emit pre mult $eq_no = 2 i = 1
> array_tmp16[1] := (array_const_2D0[1] * (array_x1[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2
> array_tmp1[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp4[2] := ats(2,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp6[2] := array_x1_higher[3,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp8[2] := array_x1_higher[2,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2]));
> #emit pre add $eq_no = 1 i = 2
> array_tmp10[2] := array_tmp9[2] + array_x1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> # emit pre mult $eq_no = 2 i = 2
> array_tmp12[2] := ats(2,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2]));
> # emit pre mult $eq_no = 2 i = 2
> array_tmp16[2] := ats(2,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2]));
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3
> array_tmp1[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp4[3] := ats(3,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp6[3] := array_x1_higher[3,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp8[3] := array_x1_higher[2,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3]));
> #emit pre add $eq_no = 1 i = 3
> array_tmp10[3] := array_tmp9[3] + array_x1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> # emit pre mult $eq_no = 2 i = 3
> array_tmp12[3] := ats(3,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3]));
> # emit pre mult $eq_no = 2 i = 3
> array_tmp16[3] := ats(3,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3]));
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4
> array_tmp1[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp4[4] := ats(4,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp6[4] := array_x1_higher[3,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp8[4] := array_x1_higher[2,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4]));
> #emit pre add $eq_no = 1 i = 4
> array_tmp10[4] := array_tmp9[4] + array_x1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> # emit pre mult $eq_no = 2 i = 4
> array_tmp12[4] := ats(4,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4]));
> # emit pre mult $eq_no = 2 i = 4
> array_tmp16[4] := ats(4,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4]));
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5
> array_tmp1[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp4[5] := ats(5,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp6[5] := array_x1_higher[3,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp8[5] := array_x1_higher[2,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5]));
> #emit pre add $eq_no = 1 i = 5
> array_tmp10[5] := array_tmp9[5] + array_x1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> # emit pre mult $eq_no = 2 i = 5
> array_tmp12[5] := ats(5,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5]));
> # emit pre mult $eq_no = 2 i = 5
> array_tmp16[5] := ats(5,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5]));
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit diff $eq_no = 1
> array_tmp1[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1);
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
> #emit mult $eq_no = 1
> array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1);
> #emit sub $eq_no = 1
> array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk]));
> #emit diff $eq_no = 1
> array_tmp6[kkk] := array_x1_higher[3,kkk];
> #emit sub $eq_no = 1
> array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk]));
> #emit diff $eq_no = 1
> array_tmp8[kkk] := array_x1_higher[2,kkk];
> #emit sub $eq_no = 1
> array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk]));
> #emit add $eq_no = 1
> array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x2[kkk + order_d] := temporary;
> array_x2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> #emit mult $eq_no = 2
> array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1);
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 2
> array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1);
> #emit sub $eq_no = 2
> array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk]));
> #emit mult $eq_no = 2
> array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1);
> #emit sub $eq_no = 2
> array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk]));
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x1[kkk + order_d] := temporary;
> array_x1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
array_tmp1[1] := array_x2_higher[2, 1];
array_tmp2[1] := array_const_3D0[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_const_2D0[1]*array_x2[1];
array_tmp5[1] := array_tmp3[1] - array_tmp4[1];
array_tmp6[1] := array_x1_higher[3, 1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
array_tmp8[1] := array_x1_higher[2, 1];
array_tmp9[1] := array_tmp7[1] - array_tmp8[1];
array_tmp10[1] := array_tmp9[1] + array_x1[1];
if 1 <= glob_max_terms then
temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2);
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 1] := temporary
end if;
kkk := 2;
array_tmp12[1] := array_const_4D0[1]*array_x2[1];
array_tmp13[1] := array_x2_higher[2, 1];
array_tmp14[1] := array_const_2D0[1]*array_tmp13[1];
array_tmp15[1] := array_tmp12[1] - array_tmp14[1];
array_tmp16[1] := array_const_2D0[1]*array_x1[1];
array_tmp17[1] := array_tmp15[1] - array_tmp16[1];
if 1 <= glob_max_terms then
temporary := array_tmp17[1]*glob_h*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 1] := temporary
end if;
kkk := 2;
array_tmp1[2] := array_x2_higher[2, 2];
array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1);
array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1);
array_tmp5[2] := array_tmp3[2] - array_tmp4[2];
array_tmp6[2] := array_x1_higher[3, 2];
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
array_tmp8[2] := array_x1_higher[2, 2];
array_tmp9[2] := array_tmp7[2] - array_tmp8[2];
array_tmp10[2] := array_tmp9[2] + array_x1[2];
if 2 <= glob_max_terms then
temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 2] := temporary
end if;
kkk := 3;
array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1);
array_tmp13[2] := array_x2_higher[2, 2];
array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1);
array_tmp15[2] := array_tmp12[2] - array_tmp14[2];
array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1);
array_tmp17[2] := array_tmp15[2] - array_tmp16[2];
if 2 <= glob_max_terms then
temporary := array_tmp17[2]*glob_h*factorial_3(1, 2);
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 2] := temporary
end if;
kkk := 3;
array_tmp1[3] := array_x2_higher[2, 3];
array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1);
array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1);
array_tmp5[3] := array_tmp3[3] - array_tmp4[3];
array_tmp6[3] := array_x1_higher[3, 3];
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
array_tmp8[3] := array_x1_higher[2, 3];
array_tmp9[3] := array_tmp7[3] - array_tmp8[3];
array_tmp10[3] := array_tmp9[3] + array_x1[3];
if 3 <= glob_max_terms then
temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if;
kkk := 4;
array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1);
array_tmp13[3] := array_x2_higher[2, 3];
array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1);
array_tmp15[3] := array_tmp12[3] - array_tmp14[3];
array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1);
array_tmp17[3] := array_tmp15[3] - array_tmp16[3];
if 3 <= glob_max_terms then
temporary := array_tmp17[3]*glob_h*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 3] := temporary
end if;
kkk := 4;
array_tmp1[4] := array_x2_higher[2, 4];
array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1);
array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1);
array_tmp5[4] := array_tmp3[4] - array_tmp4[4];
array_tmp6[4] := array_x1_higher[3, 4];
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
array_tmp8[4] := array_x1_higher[2, 4];
array_tmp9[4] := array_tmp7[4] - array_tmp8[4];
array_tmp10[4] := array_tmp9[4] + array_x1[4];
if 4 <= glob_max_terms then
temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 4] := temporary
end if;
kkk := 5;
array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1);
array_tmp13[4] := array_x2_higher[2, 4];
array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1);
array_tmp15[4] := array_tmp12[4] - array_tmp14[4];
array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1);
array_tmp17[4] := array_tmp15[4] - array_tmp16[4];
if 4 <= glob_max_terms then
temporary := array_tmp17[4]*glob_h*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 4] := temporary
end if;
kkk := 5;
array_tmp1[5] := array_x2_higher[2, 5];
array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1);
array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1);
array_tmp5[5] := array_tmp3[5] - array_tmp4[5];
array_tmp6[5] := array_x1_higher[3, 5];
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
array_tmp8[5] := array_x1_higher[2, 5];
array_tmp9[5] := array_tmp7[5] - array_tmp8[5];
array_tmp10[5] := array_tmp9[5] + array_x1[5];
if 5 <= glob_max_terms then
temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 5] := temporary
end if;
kkk := 6;
array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1);
array_tmp13[5] := array_x2_higher[2, 5];
array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1);
array_tmp15[5] := array_tmp12[5] - array_tmp14[5];
array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1);
array_tmp17[5] := array_tmp15[5] - array_tmp16[5];
if 5 <= glob_max_terms then
temporary := array_tmp17[5]*glob_h*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 5] := temporary
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_x2_higher[2, kkk];
array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1);
array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1);
array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := array_x1_higher[3, kkk];
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
array_tmp8[kkk] := array_x1_higher[2, kkk];
array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk];
array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp10[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x2[kkk + order_d] := temporary;
array_x2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1);
array_tmp13[kkk] := array_x2_higher[2, kkk];
array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1);
array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk];
array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1);
array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp17[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x1[kkk + order_d] := temporary;
array_x1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_x1 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c1 + 6.0 * c3 * exp(-t);
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0*c2*exp(2.0*t) - c3*exp(-t)
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> t_start,t_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGL,
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_abserr,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> glob_max_opt_iter,
> glob_warned2,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_normmax,
> glob_max_order,
> glob_html_log,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_relerr,
> glob_log10_abserr,
> glob_initial_pass,
> days_in_year,
> glob_dump,
> glob_log10normmin,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_log10_relerr,
> glob_optimal_done,
> glob_max_sec,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_large_float,
> glob_h,
> glob_almost_1,
> min_in_hour,
> glob_start,
> glob_no_eqs,
> glob_look_poles,
> glob_hmin_init,
> djd_debug2,
> glob_percent_done,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_hmin,
> glob_disp_incr,
> centuries_in_millinium,
> glob_display_flag,
> glob_iter,
> glob_current_iter,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> sec_in_min,
> glob_smallish_float,
> glob_clock_start_sec,
> glob_clock_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_4D0,
> array_const_1,
> array_const_0D0,
> array_const_2,
> #END CONST
> array_x2,
> array_x1,
> array_t,
> array_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_x1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_complex_pole,
> array_x1_higher,
> array_real_pole,
> array_x1_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> INFO := 2;
> ALWAYS := 1;
> glob_max_terms := 30;
> glob_iolevel := 5;
> glob_abserr := 0.1e-10;
> glob_not_yet_start_msg := true;
> glob_not_yet_finished := true;
> hours_in_day := 24.0;
> glob_max_opt_iter := 10;
> glob_warned2 := false;
> glob_warned := false;
> glob_optimal_clock_start_sec := 0.0;
> glob_last_good_h := 0.1;
> glob_hmax := 1.0;
> glob_reached_optimal_h := false;
> years_in_century := 100.0;
> djd_debug := true;
> glob_optimal_expect_sec := 0.1;
> glob_log10relerr := 0.0;
> glob_normmax := 0.0;
> glob_max_order := 30;
> glob_html_log := true;
> glob_optimal_start := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_iter := 1000;
> glob_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_initial_pass := true;
> days_in_year := 365.0;
> glob_dump := false;
> glob_log10normmin := 0.1;
> glob_curr_iter_when_opt := 0;
> glob_max_hours := 0.0;
> glob_log10_relerr := 0.1e-10;
> glob_optimal_done := false;
> glob_max_sec := 10000.0;
> glob_max_trunc_err := 0.1e-10;
> glob_dump_analytic := false;
> glob_large_float := 9.0e100;
> glob_h := 0.1;
> glob_almost_1 := 0.9990;
> min_in_hour := 60.0;
> glob_start := 0;
> glob_no_eqs := 0;
> glob_look_poles := false;
> glob_hmin_init := 0.001;
> djd_debug2 := true;
> glob_percent_done := 0.0;
> glob_log10abserr := 0.0;
> glob_orig_start_sec := 0.0;
> glob_hmin := 0.00000000001;
> glob_disp_incr := 0.1;
> centuries_in_millinium := 10.0;
> glob_display_flag := true;
> glob_iter := 0;
> glob_current_iter := 0;
> glob_max_minutes := 0.0;
> MAX_UNCHANGED := 10;
> glob_unchanged_h_cnt := 0;
> glob_small_float := 0.1e-50;
> sec_in_min := 60.0;
> glob_smallish_float := 0.1e-100;
> glob_clock_start_sec := 0.0;
> glob_clock_sec := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_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 := 0.00005 ;");
> 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_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_t:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= 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_type_pole:= Array(1..(max_terms + 1),[]);
> array_x1_init:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_tmp5:= Array(1..(max_terms + 1),[]);
> array_tmp6:= Array(1..(max_terms + 1),[]);
> array_tmp7:= Array(1..(max_terms + 1),[]);
> array_tmp8:= Array(1..(max_terms + 1),[]);
> array_tmp9:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work2 := 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),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> 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_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[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_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_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 <=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_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_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_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_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_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_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_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_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 := 0.00005 ;
> 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,"2012-06-02T02:11:39-05:00")
> ;
> 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 DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
DEBUGMASSIVE := 4;
INFO := 2;
ALWAYS := 1;
glob_max_terms := 30;
glob_iolevel := 5;
glob_abserr := 0.1*10^(-10);
glob_not_yet_start_msg := true;
glob_not_yet_finished := true;
hours_in_day := 24.0;
glob_max_opt_iter := 10;
glob_warned2 := false;
glob_warned := false;
glob_optimal_clock_start_sec := 0.;
glob_last_good_h := 0.1;
glob_hmax := 1.0;
glob_reached_optimal_h := false;
years_in_century := 100.0;
djd_debug := true;
glob_optimal_expect_sec := 0.1;
glob_log10relerr := 0.;
glob_normmax := 0.;
glob_max_order := 30;
glob_html_log := true;
glob_optimal_start := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_iter := 1000;
glob_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_initial_pass := true;
days_in_year := 365.0;
glob_dump := false;
glob_log10normmin := 0.1;
glob_curr_iter_when_opt := 0;
glob_max_hours := 0.;
glob_log10_relerr := 0.1*10^(-10);
glob_optimal_done := false;
glob_max_sec := 10000.0;
glob_max_trunc_err := 0.1*10^(-10);
glob_dump_analytic := false;
glob_large_float := 0.90*10^101;
glob_h := 0.1;
glob_almost_1 := 0.9990;
min_in_hour := 60.0;
glob_start := 0;
glob_no_eqs := 0;
glob_look_poles := false;
glob_hmin_init := 0.001;
djd_debug2 := true;
glob_percent_done := 0.;
glob_log10abserr := 0.;
glob_orig_start_sec := 0.;
glob_hmin := 0.1*10^(-10);
glob_disp_incr := 0.1;
centuries_in_millinium := 10.0;
glob_display_flag := true;
glob_iter := 0;
glob_current_iter := 0;
glob_max_minutes := 0.;
MAX_UNCHANGED := 10;
glob_unchanged_h_cnt := 0;
glob_small_float := 0.1*10^(-50);
sec_in_min := 60.0;
glob_smallish_float := 0.1*10^(-100);
glob_clock_start_sec := 0.;
glob_clock_sec := 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 := 0.00005 ;");
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_x2 := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_t := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_norms := 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_type_pole := Array(1 .. max_terms + 1, []);
array_x1_init := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_tmp5 := Array(1 .. max_terms + 1, []);
array_tmp6 := Array(1 .. max_terms + 1, []);
array_tmp7 := Array(1 .. max_terms + 1, []);
array_tmp8 := Array(1 .. max_terms + 1, []);
array_tmp9 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work2 := 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, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
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_t[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp10[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp15[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp16[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp17[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[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_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_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_init[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_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_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_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_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[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_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_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_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_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_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 := 0.00005;
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, "2012-06-02T02:11:39-05:00");
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 := 0.00005 ;
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 = 5e-05
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 5e-05
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 5e-05
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50005
x2[1] (analytic) = 0.00082566083422809021229815693339498
x2[1] (numeric) = 0.0008256608342280902112128809789913
absolute error = 1.08527595440368e-21
relative error = 1.3144331296982299010145367931419e-16 %
h = 5e-05
x1[1] (analytic) = 0.0012917006010880372652167092040327
x1[1] (numeric) = 0.001291700601088095146219364060659
absolute error = 5.78810026548566263e-17
relative error = 4.4809921591816061521273028438937e-12 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5001
x2[1] (analytic) = 0.00082570611074256394598966051590164
x2[1] (numeric) = 0.00082570611347206562644713699489435
absolute error = 2.72950168045747647899271e-12
relative error = 3.3056576001391273795257349110012e-07 %
h = 5e-05
x1[1] (analytic) = 0.001291646017422585871235266471237
x1[1] (numeric) = 0.0012916460119643116371280973748446
absolute error = 5.4582742341071690963924e-12
relative error = 4.2258282536254619845612697292069e-07 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50015
x2[1] (analytic) = 0.00082575139314954126995470805844824
x2[1] (numeric) = 0.00082575140406802564281686871319886
absolute error = 1.091848437286216065475062e-11
relative error = 1.3222483744432331394992543106801e-06 %
h = 5e-05
x1[1] (analytic) = 0.0012915914364862495213788540506512
x1[1] (numeric) = 0.001291591414653326414540770995122
absolute error = 2.18329231068380830555292e-11
relative error = 1.6903892740442863466810236789852e-06 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5002
x2[1] (analytic) = 0.0008257966814495432344339416603249
x2[1] (numeric) = 0.00082579670601776504825521809306856
absolute error = 2.456822181382127643274366e-11
relative error = 2.9750933087665129214883467185353e-06 %
h = 5e-05
x1[1] (analytic) = 0.0012915368582788917633066026400632
x1[1] (numeric) = 0.0012915368091547605399638597636327
absolute error = 4.91241312233427428764305e-11
relative error = 3.8035407900635369168021387272216e-06 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50025
x2[1] (analytic) = 0.00082584197564309094518702663178858
x2[1] (numeric) = 0.00082584201932344272793081978780986
absolute error = 4.368035178274379315602128e-11
relative error = 5.2891900715908138154263162587966e-06 %
h = 5e-05
x1[1] (analytic) = 0.0012914822828003761515000894181426
x1[1] (numeric) = 0.0012914821954673861157167421604024
absolute error = 8.73329900357833472577402e-11
relative error = 6.7622290447853065221893849845794e-06 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3.8MB, alloc=2.9MB, time=0.17
t[1] = 0.5003
x2[1] (analytic) = 0.00082588727573070556349803310856235
x2[1] (numeric) = 0.00082588734398721787879028945562029
absolute error = 6.825651231529225634705794e-11
relative error = 8.2646281545992046697870150154137e-06 %
h = 5e-05
x1[1] (analytic) = 0.0012914277100505662472629969306448
x1[1] (numeric) = 0.0012914275735899751963934017782433
absolute error = 1.364605910508695951524015e-10
relative error = 1.0566645735480342058201119878555e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50035
x2[1] (analytic) = 0.00082593258171290830618081821305085
x2[1] (numeric) = 0.00082593268001125006720421780581691
absolute error = 9.829834176102339959276606e-11
relative error = 1.1901497039523694324166328783172e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012913731400293256187207719936699
x1[1] (numeric) = 0.0012913729435212996524334089100879
absolute error = 1.965080259662873630835820e-10
relative error = 1.5216982595892066392731728962904e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5004
x2[1] (analytic) = 0.00082597789359022044558440876232671
x2[1] (numeric) = 0.00082597802739769922901785675780158
absolute error = 1.3380747878343344799547487e-10
relative error = 1.6199886198142885101723757319479e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012913185727365178408202846139762
x1[1] (numeric) = 0.0012913183052601311701163150872154
absolute error = 2.674763866707039695267608e-10
relative error = 2.0713431396241535032098315877769e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50045
x2[1] (analytic) = 0.00082602321136316330959838452294175
x2[1] (numeric) = 0.00082602338614872566961108883300895
absolute error = 1.7478556236001270431006720e-10
relative error = 2.1159885092280750123100989569948e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012912640081720064953294869263476
x1[1] (numeric) = 0.0012912636588052412515340347370404
absolute error = 3.493667652437954521893072e-10
relative error = 2.7056183943234097981506726047895e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5005
x2[1] (analytic) = 0.00082606853503225828165826201261726
x2[1] (numeric) = 0.00082606875626649006395840449911754
absolute error = 2.2123423178230014248650028e-10
relative error = 2.6781583173805411188280210146852e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012912094463356551708370721480129
x1[1] (numeric) = 0.001291209004155401214563226252667
absolute error = 4.421802539562738458953459e-10
relative error = 3.4245432080066062523454204021962e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50055
x2[1] (analytic) = 0.00082611386459802680075087884886784
x2[1] (numeric) = 0.00082611413775315345668888896468016
absolute error = 2.7315512665593801011581232e-10
relative error = 3.3065069884627917407609282961215e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012911548872273274627521335501181
x1[1] (numeric) = 0.0012911543413093821928376689204337
absolute error = 5.459179452699144646296844e-10
relative error = 4.2281367686431357189388814628772e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5006
x2[1] (analytic) = 0.00082615920006099036141977864461309
x2[1] (numeric) = 0.00082615953061087726214621842539718
absolute error = 3.3054988690072643978078409e-10
relative error = 4.0010434656701024581949552109456e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012911003308468869733038234462486
x1[1] (numeric) = 0.0012910996702659551357206357053896
absolute error = 6.605809318375831877408590e-10
relative error = 5.1164182678528196924791464428897e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
Complex estimate of poles used
NO POLE
Radius of convergence = 9.530e-05
Order of pole = 1.45
t[1] = 0.50065
x2[1] (analytic) = 0.0008262045414216705137705964508309
x2[1] (numeric) = 0.00082620493484182326444866576350163
absolute error = 3.9342015275067806931267073e-10
relative error = 4.7617766912017975331931690868870e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012910457771941973115410121980021
x1[1] (numeric) = 0.0012910449910238908082772618940204
absolute error = 7.861703065032637503039817e-10
relative error = 6.0894069009065749447894853936796e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 6.634e-05
Order of pole = 0.243
t[1] = 0.5007
x2[1] (analytic) = 0.00082624988868058886347644474630742
x2[1] (numeric) = 0.00082625035044815361754911570174268
absolute error = 4.6176756475407267095543526e-10
relative error = 5.5887156062611279976306896949143e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012909912262691220933319472376107
x1[1] (numeric) = 0.0012909903035819597912469095932504
absolute error = 9.226871623020850376443603e-10
relative error = 7.1471218667270802802276184754481e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 9.350e-05
Order of pole = 16.66
t[1] = 0.50075
x2[1] (analytic) = 0.00082629524183826707178329997453724
x2[1] (numeric) = 0.00082629577743203084529508941356178
absolute error = 5.3559376377351178943902454e-10
relative error = 6.4818691510551498159393858391484e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012909366780715249413639121076118
x1[1] (numeric) = 0.0012909356079389324810155280827534
absolute error = 1.0701325924603483840248584e-09
relative error = 8.2895823678894434103714976133245e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 0.0003883
Order of pole = 181.4
t[1] = 0.5008
x2[1] (analytic) = 0.00082634060089522685551538962782877
x2[1] (numeric) = 0.00082634121579561784148877859176918
absolute error = 6.1490039098597338896394041e-10
relative error = 7.4412462647946021227707970268687e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012908821326012694851428855175656
x1[1] (numeric) = 0.0012908809040935790895880100038865
absolute error = 1.2285076903955548755136791e-09
relative error = 9.5168076106218679482770050054311e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.2MB, time=0.40
NO POLE
NO POLE
t[1] = 0.50085
x2[1] (analytic) = 0.00082638596585198998708057987866837
x2[1] (numeric) = 0.00082638666554107786994708898284107
absolute error = 6.9968908788286650910417270e-10
relative error = 8.4668558856937855356441671362775e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012908275898582193609932004178204
x1[1] (numeric) = 0.0012908261920446696445605432805914
absolute error = 1.3978135497164326571372290e-09
relative error = 0.00010828816804806320523134541790187 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5009
x2[1] (analytic) = 0.00082643133670907829447576375839823
x2[1] (numeric) = 0.00082643212667057456456169342423452
absolute error = 7.8996149627008592966583629e-10
relative error = 9.5587069509704405430127772053782e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012907730498422382120572030903234
x1[1] (numeric) = 0.0012907714717909739890929581838272
absolute error = 1.5780512642229642449064962e-09
relative error = 0.00012225629163979198019899719555733 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50095
x2[1] (analytic) = 0.00082647671346701366129224988326191
x2[1] (numeric) = 0.00082647759918627192935909458690167
absolute error = 8.8571925826806684470363976e-10
relative error = 0.00010716808396845625970175393146151 %
h = 5e-05
x1[1] (analytic) = 0.0012907185125531896882949122564762
x1[1] (numeric) = 0.0012907167433312617818810668579742
absolute error = 1.7692219279064138453985020e-09
relative error = 0.00013707263905331994964691660082604 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = 0.00082652308309033433856069834427694
absolute error = 9.8696401631183954661640508e-10
relative error = 0.00011941169158543597534158781585741 %
h = 5e-05
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = 0.001290662006664302497128986429335
absolute error = 1.9713266349493546917727001e-09
relative error = 0.00015273740249711971124783660771257 %
h = 5e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 2.210e-05
Order of pole = 14.49
t[1] = 0.50105
x2[1] (analytic) = 0.0008265674846875133855587774461534
x2[1] (numeric) = 0.00082656857838492653664290094548412
absolute error = 1.09369741315108412349933072e-09
relative error = 0.00013231798170291686525991667208559 %
h = 5e-05
x1[1] (analytic) = 0.0012906094461553451502178419190542
x1[1] (numeric) = 0.0012906072617888654245214289948781
absolute error = 2.1843664797256964129241761e-09
relative error = 0.00016925077421622819452641104815716 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 2.336e-05
Order of pole = 24.84
t[1] = 0.5011
x2[1] (analytic) = 0.00082661287915112178821202023981947
x2[1] (numeric) = 0.00082661408507221363839719704923771
absolute error = 1.20592109185018517680941824e-09
relative error = 0.00014588704365320178705696758450004 %
h = 5e-05
x1[1] (analytic) = 0.0012905549170462764699083942648711
x1[1] (numeric) = 0.0012905525087037196691959618481976
absolute error = 2.4083425568007124324166735e-09
relative error = 0.00018661294649225334348077323939715 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 1.141e-05
Order of pole = 2.46
t[1] = 0.50115
x2[1] (analytic) = 0.00082665827951766534070374927443031
x2[1] (numeric) = 0.00082665960315436112899031384330714
absolute error = 1.32363669578828656456887683e-09
relative error = 0.00016011896675862193473133214038365 %
h = 5e-05
x1[1] (analytic) = 0.0012905003906635950827826351381346
x1[1] (numeric) = 0.001290497747407634151715323712609
absolute error = 2.6432559609310673114255256e-09
relative error = 0.00020482411164338079573977004314158 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5012
x2[1] (analytic) = 0.00082670368578766620467820114309252
x2[1] (numeric) = 0.00082670513263353486402435507813827
absolute error = 1.44684586865934615393504575e-09
relative error = 0.00017501384033153563118979833302682 %
h = 5e-05
x1[1] (analytic) = 0.0012904458670071646728838326718726
x1[1] (numeric) = 0.0012904429778993776080398574894025
absolute error = 2.8891077870648439751824701e-09
relative error = 0.0002238844620243805535657308320619 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50125
x2[1] (analytic) = 0.00082674909796164659740637187785192
x2[1] (numeric) = 0.00082675067351190106959692671965234
absolute error = 1.57555025447219055484180042e-09
relative error = 0.00019057175367432711813593685869316 %
h = 5e-05
x1[1] (analytic) = 0.0012903913460768489310708824436005
x1[1] (numeric) = 0.0012903882001777185894998475956791
absolute error = 3.1458991303415710348479214e-09
relative error = 0.00024379419002661366312352445869106 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5013
x2[1] (analytic) = 0.00082679451604012879179140950883443
x2[1] (numeric) = 0.00082679622579162634236126301599356
absolute error = 1.70975149755056985350715913e-09
relative error = 0.00020679279607940534561175300696596 %
h = 5e-05
x1[1] (analytic) = 0.0012903368278725115550179667024679
x1[1] (numeric) = 0.0012903334142414254627683205900583
absolute error = 3.4136310860922496461124096e-09
relative error = 0.00026455348807803885871951801637687 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
memory used=11.4MB, alloc=4.3MB, time=0.62
NO POLE
t[1] = 0.50135
x2[1] (analytic) = 0.00082683994002363511637400717118929
x2[1] (numeric) = 0.00082684178947487764958623358631015
absolute error = 1.84945124253321222641512086e-09
relative error = 0.00022367705682920274675308798412464 %
h = 5e-05
x1[1] (analytic) = 0.0012902823123940162492142136134444
x1[1] (numeric) = 0.0012902786200892664098346456101133
absolute error = 3.6923047498393795680033311e-09
relative error = 0.00028616254864321914591847241354952 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5014
x2[1] (analytic) = 0.00082688536991268795533779675988916
x2[1] (numeric) = 0.00082688736456382232921608864264273
absolute error = 1.99465113437387829188275357e-09
relative error = 0.00024122462519617398048417150809564 %
h = 5e-05
x1[1] (analytic) = 0.0012902277996412267249633565185424
x1[1] (numeric) = 0.0012902238177200094279729425426769
absolute error = 3.9819212172969904139758655e-09
relative error = 0.0003086215642233287879403327220334 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50145
x2[1] (analytic) = 0.00082693080570780974851474313244131
x2[1] (numeric) = 0.00082693295106062808993114507299581
absolute error = 2.14535281834141640194055450e-09
relative error = 0.0002594355904427947876085798671822 %
h = 5e-05
x1[1] (analytic) = 0.0012901732896140067003833932150759
x1[1] (numeric) = 0.0012901690071324223297169055925665
absolute error = 4.2824815843706664876225094e-09
relative error = 0.00033193072735615979575782052203881 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5015
x2[1] (analytic) = 0.00082697624740952299139053885956424
x2[1] (numeric) = 0.00082697854896746301120785883420776
absolute error = 2.30155794001981731997464352e-09
relative error = 0.00027831004182156077227291004636589 %
h = 5e-05
x1[1] (analytic) = 0.0012901187823122199004062452509559
x1[1] (numeric) = 0.0012901141883252727428317147811532
absolute error = 4.5939869471575745304698027e-09
relative error = 0.00035609023061612864474084966933865 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50155
x2[1] (analytic) = 0.00082702169501835023510999952388432
x2[1] (numeric) = 0.0008270241582864955433790033090115
absolute error = 2.46326814530826900378512718e-09
relative error = 0.00029784806857498619584955683714112 %
h = 5e-05
x1[1] (analytic) = 0.0012900642777357300567774172370197
x1[1] (numeric) = 0.0012900593612973281102863389190148
absolute error = 4.9164384019464910783180049e-09
relative error = 0.00038110026661428296183864119182014 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5016
x2[1] (analytic) = 0.00082706714853481408648245956670656
x2[1] (numeric) = 0.00082706977901989450769385489220588
absolute error = 2.63048508042121139532549932e-09
relative error = 0.00031804975993560277129593468950195 %
h = 5e-05
x1[1] (analytic) = 0.001290009775884400908055656176395
x1[1] (numeric) = 0.0012900045260473556902258254181453
absolute error = 5.2498370452178298307582497e-09
relative error = 0.00040696102799830821465741053608137 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50165
x2[1] (analytic) = 0.00082711260795943720798716868291399
x2[1] (numeric) = 0.00082711541116982909637838805970475
absolute error = 2.80321039188839121937679076e-09
relative error = 0.00033891520512595845826254094678894 %
h = 5e-05
x1[1] (analytic) = 0.0012899552767580961996126108108966
x1[1] (numeric) = 0.0012899496825741225559435859508189
absolute error = 5.5941839736436690248600777e-09
relative error = 0.00043367270745253440173574659510224 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5017
x2[1] (analytic) = 0.00082715807329274231777868876405026
x2[1] (numeric) = 0.000827161054738468872695479921465
absolute error = 2.98144572655491679115741474e-09
relative error = 0.00036044449335861625894978717254087 %
h = 5e-05
x1[1] (analytic) = 0.0012899007803566796836324909844552
x1[1] (numeric) = 0.0012898948308763955958536779527188
absolute error = 5.9494802840877788130317364e-09
relative error = 0.00046123549769794274401802974202934 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50175
x2[1] (analytic) = 0.0008272035445352521896922913896394
x2[1] (numeric) = 0.00082720670972798377100512425976157
absolute error = 3.16519273158131283287012217e-09
relative error = 0.00038263771383615301471358170812616 %
h = 5e-05
x1[1] (analytic) = 0.0012898462866800151191117270235781
x1[1] (numeric) = 0.0012898399709529415134630819697096
absolute error = 6.3157270736056486450538685e-09
relative error = 0.00048964959149217237752609908408452 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5018
x2[1] (analytic) = 0.00082724902168748965324935586679766
x2[1] (numeric) = 0.00082725237614054409682465505427742
absolute error = 3.35445305444357529918747976e-09
relative error = 0.0004054949557511582034196463826453 %
h = 5e-05
x1[1] (analytic) = 0.0012897917957279662718586291348401
x1[1] (numeric) = 0.0012897851028025268273439748476288
absolute error = 6.6929254394445146542872113e-09
relative error = 0.00051891518162952704722937931891312 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50185
x2[1] (analytic) = 0.00082729450474997759366276781819127
x2[1] (numeric) = 0.00082729805397832052688897949547691
absolute error = 3.54922834293322621167728564e-09
relative error = 0.00042901630828623273754655038521288 %
h = 5e-05
x1[1] (analytic) = 0.0012897373075003969144930468194044
x1[1] (numeric) = 0.0012897302264239178711059987644746
absolute error = 7.0810764790433870480549298e-09
relative error = 0.00054903246094098180211367758897854 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.4MB, time=0.84
NO POLE
NO POLE
t[1] = 0.5019
x2[1] (analytic) = 0.00082733999372323895184231831839524
x2[1] (numeric) = 0.00082734374324348410921082048773105
absolute error = 3.74952024515736850216933581e-09
relative error = 0.00045320186061398776303744405863382 %
h = 5e-05
x1[1] (analytic) = 0.0012896828219971708264460283045716
x1[1] (numeric) = 0.0012896753418158807933685261043666
absolute error = 7.4801812900330775022002050e-09
relative error = 0.00058000162229418969144886067311321 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50195
x2[1] (analytic) = 0.00082738548860779672440010357870682
x2[1] (numeric) = 0.00082738944393820626314096864366339
absolute error = 3.95533040953874086506495657e-09
relative error = 0.00047805170189704345890047549475362 %
h = 5e-05
x1[1] (analytic) = 0.0012896283392181517939594799923581
x1[1] (numeric) = 0.0012896204489771815577329201726557
absolute error = 7.8902409702362265598197024e-09
relative error = 0.00061182285859348846225562315449888 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.502
x2[1] (analytic) = 0.0008274309894041739636559251804687
x2[1] (numeric) = 0.00082743515606465877942854377118556
absolute error = 4.16666048481577261859071686e-09
relative error = 0.0005035659212880278375578725667491 %
h = 5e-05
x1[1] (analytic) = 0.0012895738591632036100858259251
x1[1] (numeric) = 0.0012895655479065859427547917515594
absolute error = 8.3112566176673310341735406e-09
relative error = 0.00064449636277990725797155683773415 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50205
x2[1] (analytic) = 0.00082747649611289377764269085695601
x2[1] (numeric) = 0.0008274808796250138202812658546917
absolute error = 4.38351212004263857499773569e-09
relative error = 0.00052974460792957554594367308720935 %
h = 5e-05
x1[1] (analytic) = 0.0012895193818321900746876672680847
x1[1] (numeric) = 0.0012895106386028595419162514956996
absolute error = 8.7432293305327714157723851e-09
relative error = 0.00067802232783117331831673211962611 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5021
x2[1] (analytic) = 0.00082752200873447933011181582388164
x2[1] (numeric) = 0.00082752661462144391942573553188116
absolute error = 4.60588696458931391970799952e-09
relative error = 0.00055658785095432666735008564466675 %
h = 5e-05
x1[1] (analytic) = 0.0012894649072249749944374418092067
x1[1] (numeric) = 0.0012894557210647677635981581669182
absolute error = 9.1861602072308392836422885e-09
relative error = 0.00071240094676171868035900174476368 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50215
x2[1] (analytic) = 0.00082756752726945384053862465857453
x2[1] (numeric) = 0.00082757236105612198216772406767919
absolute error = 4.83378666814162909940910466e-09
relative error = 0.00058409573948492552402246359913447 %
h = 5e-05
x1[1] (analytic) = 0.0012894104353414221828170834756492
x1[1] (numeric) = 0.0012894007952910758310523627077468
absolute error = 9.6400503463517647207679024e-09
relative error = 0.00074763241262268688077923772367162 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5022
x2[1] (analytic) = 0.0008276130517183405841277537278848
x2[1] (numeric) = 0.00082761811893122128545247282672549
absolute error = 5.06721288070132471909884069e-09
relative error = 0.00061226836263401948050287473211411 %
h = 5e-05
x1[1] (analytic) = 0.0012893559661813954601176818675888
x1[1] (numeric) = 0.0012893458612805487823739481529073
absolute error = 1.01049008466777437337146815e-08
relative error = 0.00078371691850193965933671184794605 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50225
x2[1] (analytic) = 0.00082765858208166289181855416487103
x2[1] (numeric) = 0.00082766388824891547792500224590075
absolute error = 5.30616725258610644808102972e-09
relative error = 0.00064110580950425774772224880647601 %
h = 5e-05
x1[1] (analytic) = 0.0012893014997447586534391418089226
x1[1] (numeric) = 0.0012892909190319514704734653782179
absolute error = 1.05807128071829656764307047e-08
relative error = 0.00082065465752406366353483059904026 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5023
x2[1] (analytic) = 0.00082770411835994415029049539432325
x2[1] (numeric) = 0.0008277096690113785799904303083615
absolute error = 5.55065143442969993491403825e-09
relative error = 0.00067060816918829018784108542859691 %
h = 5e-05
x1[1] (analytic) = 0.0012892470360313755966898429150187
x1[1] (numeric) = 0.0012892359685440485630491646862818
absolute error = 1.10674873270336406782287369e-08
relative error = 0.00085844582285037715448743519091747 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50235
x2[1] (analytic) = 0.00082774966055370780196856920717682
x2[1] (numeric) = 0.00082775546122078498387430052055384
absolute error = 5.80066707718190573131337702e-09
relative error = 0.00070077553076876611983870434215 %
h = 5e-05
x1[1] (analytic) = 0.0012891925750411101305862991774863
x1[1] (numeric) = 0.0012891810098156045425592232283333
absolute error = 1.15652255055880270759491530e-08
relative error = 0.00089709060767893671398587734498348 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=19.0MB, alloc=4.4MB, time=1.06
t[1] = 0.5024
x2[1] (analytic) = 0.00082779520866347734502869438387111
x2[1] (numeric) = 0.00082780126487930945368291939367687
absolute error = 6.05621583210865422500980576e-09
relative error = 0.00073160798331833312585102036918086 %
h = 5e-05
x1[1] (analytic) = 0.0012891381167738261026528185659675
x1[1] (numeric) = 0.0012891260428453837061939682616174
absolute error = 1.20739284423964588503043501e-08
relative error = 0.00093658920524454395276708177356707 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50245
x2[1] (analytic) = 0.00082784076268977633340312186670805
x2[1] (numeric) = 0.0008278470799891271254637034310668
absolute error = 6.31729935079206058156435875e-09
relative error = 0.00076310561589963585825682499586731 %
h = 5e-05
x1[1] (analytic) = 0.0012890836612293873672211626469477
x1[1] (numeric) = 0.0012890710676321501658480962416781
absolute error = 1.25935972372013730664052696e-08
relative error = 0.00097694180881875221998280604355632 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5025
x2[1] (analytic) = 0.00082788632263312837678584048126422
x2[1] (numeric) = 0.000827892906552413507265535622973
absolute error = 6.58391928513047969514170878e-09
relative error = 0.00079526851756531484751255670592886 %
h = 5e-05
x1[1] (analytic) = 0.0012890292084076577854302062195851
x1[1] (numeric) = 0.0012890160841746678480928877489317
absolute error = 1.31242329899373373184706534e-08
relative error = 0.0010181486117098733138703087145388 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50255
x2[1] (analytic) = 0.00082793188849405714063798320691191
x2[1] (numeric) = 0.00082793874457134447919913145019748
absolute error = 6.85607728733856114824328557e-09
relative error = 0.00082809677735800531073554188242706 %
h = 5e-05
x1[1] (analytic) = 0.0012889747583085012252255969685576
x1[1] (numeric) = 0.0012889610924717004941484182488993
absolute error = 1.36658368007310771787196583e-08
relative error = 0.0010602098072629841936246366669017 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5026
x2[1] (analytic) = 0.00082797746027308634619323399650282
x2[1] (numeric) = 0.00082798459404809629349741439806942
absolute error = 7.13377500994730418040156660e-09
relative error = 0.00086159048431033596103568822964852 %
h = 5e-05
x1[1] (analytic) = 0.001288920310931781561359415133927
x1[1] (numeric) = 0.0012889060925220116598557646854744
absolute error = 1.42184097699015036504484526e-08
relative error = 0.0011031255888599336924727425564524 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50265
x2[1] (analytic) = 0.00082802303797073977046323514526932
x2[1] (numeric) = 0.00082803045498484557457590098222676
absolute error = 7.41701410580411266583695744e-09
relative error = 0.00089574972744492781759561246550527 %
h = 5e-05
x1[1] (analytic) = 0.0012888658662773626753898331980192
x1[1] (numeric) = 0.001288851084324364715649207906601
absolute error = 1.47819529979597406252914182e-08
relative error = 0.0011468961499193492319496433066746 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5027
x2[1] (analytic) = 0.00082806862158754124624299520899781
x2[1] (numeric) = 0.00082807632738376931909309528767692
absolute error = 7.70579622807285010007867911e-09
relative error = 0.00093057459577439301649918399069987 %
h = 5e-05
x1[1] (analytic) = 0.0012888114243451084556807755893193
x1[1] (numeric) = 0.0012887960678775228465284309217365
absolute error = 1.53564675856091523446675828e-08
relative error = 0.0011915216838966435373768306794499 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50275
x2[1] (analytic) = 0.00082811421112401466211629747152829
x2[1] (numeric) = 0.00082812221124704489601089302260907
absolute error = 8.00012303023389459555108078e-09
relative error = 0.00096606517830133362230846623777141 %
h = 5e-05
x1[1] (analytic) = 0.0012887569851348827974015784033818
x1[1] (numeric) = 0.0012887410431802490520307129904753
absolute error = 1.59419546337453708654129065e-08
relative error = 0.0012370023842840213545431449706798 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5028
x2[1] (analytic) = 0.00082815980658068396246110896163522
x2[1] (numeric) = 0.0008281681065768500466549950884305
absolute error = 8.29999616608419388612679528e-09
relative error = 0.0010022215640183404403890372043692 %
h = 5e-05
x1[1] (analytic) = 0.0012887025486465496025266491407532
x1[1] (numeric) = 0.0012886860102313061462031195417074
absolute error = 1.65384152434563235295990458e-08
relative error = 0.001283338444610486167588322805248 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50285
x2[1] (analytic) = 0.0008282054079580731474549900193436
x2[1] (numeric) = 0.00082821401337536288477533066749994
absolute error = 8.60541728973732034064815634e-09
relative error = 0.001039043841907991829983670752911 %
h = 5e-05
x1[1] (analytic) = 0.0012886481148799727798351264619085
x1[1] (numeric) = 0.0012886309690294567575746879226867
absolute error = 1.71458505160222604385392218e-08
relative error = 0.0013305300584418469180894303294862 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5029
x2[1] (analytic) = 0.0008282510152567062730805044117353
x2[1] (numeric) = 0.00082825993164476189660648983003084
absolute error = 8.91638805562352598541829554e-09
relative error = 0.0010765321009428525180343600479695 %
h = 5e-05
x1[1] (analytic) = 0.0012885936838350162449105399591989
x1[1] (numeric) = 0.0012885759195734633291286089773842
absolute error = 1.77642615529157819309818147e-08
relative error = 0.0013785774193807247253503927635229 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=1.29
NO POLE
NO POLE
t[1] = 0.50295
x2[1] (analytic) = 0.00082829662847710745113062999829971
x2[1] (numeric) = 0.00082830586138722594092816566163796
absolute error = 9.23291011848979753566333825e-09
relative error = 0.0011146864300854724137526645624312 %
h = 5e-05
x1[1] (analytic) = 0.0012885392555115439201404699458103
x1[1] (numeric) = 0.0012885208618620881182744044535006
absolute error = 1.83936494558018660654923097e-08
relative error = 0.0014274807210665596078948315375385 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.503
x2[1] (analytic) = 0.0008283422476198008492141699458837
x2[1] (numeric) = 0.00082835180260493424912560591300064
absolute error = 9.55498513339991143596711694e-09
relative error = 0.0011535069182883854239383618775362 %
h = 5e-05
x1[1] (analytic) = 0.0012884848299094197347162072617323
x1[1] (numeric) = 0.0012884657958940931968201002375121
absolute error = 1.90340153265378961070242202e-08
relative error = 0.0014772401571756172061624203269484 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50305
x2[1] (analytic) = 0.00082838787268531069076116449329504
x2[1] (numeric) = 0.00082839775530006642525007417311659
absolute error = 9.88261475573448890967982155e-09
relative error = 0.0011929936544941082690463855628223 %
h = 5e-05
x1[1] (analytic) = 0.0012884304070285076246324130967366
x1[1] (numeric) = 0.001288410721668240450944395417125
absolute error = 1.96853602671736880176796116e-08
relative error = 0.0015278559214209955064089711286707 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5031
x2[1] (analytic) = 0.00082843350367416125502830326561401
x2[1] (numeric) = 0.00082844371947480244607932056762007
absolute error = 1.021580064119105101730200606e-08
relative error = 0.0012331467276351393000020302583507 %
h = 5e-05
x1[1] (analytic) = 0.0012883759868686715326867788303632
x1[1] (numeric) = 0.0012883556391832915811688271705125
absolute error = 2.03476853799515179516598507e-08
relative error = 0.0015793282075526315658104616814499 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50315
x2[1] (analytic) = 0.0008284791405868768771043381382677
x2[1] (numeric) = 0.00082848969513132266117806198363867
absolute error = 1.055454444578407372384537097e-08
relative error = 0.0012739662266339573157644050531797 %
h = 5e-05
x1[1] (analytic) = 0.0012883215694297754084796858889148
x1[1] (numeric) = 0.0012883005484380081023299314817082
absolute error = 2.10209917673061497544072066e-08
relative error = 0.0016316572093573082387712156319767 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5032
x2[1] (analytic) = 0.00082852478342398194791549665092172
x2[1] (numeric) = 0.00082853568227180779295847182266308
absolute error = 1.089884782584504297517174136e-08
relative error = 0.0013154522404030203816381161520137 %
h = 5e-05
x1[1] (analytic) = 0.0012882671547116832084138656194575
x1[1] (numeric) = 0.0012882454494311513435513996815309
absolute error = 2.17052805318648624659379266e-08
relative error = 0.0016848431206586609044364466911856 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50325
x2[1] (analytic) = 0.00082857043218600091423089597124342
x2[1] (numeric) = 0.00082858168089843893674067928290445
absolute error = 1.124871243802250978331166103e-08
relative error = 0.0013576048578447646483331598249433 %
h = 5e-05
x1[1] (analytic) = 0.0012882127427142588956940591808277
x1[1] (numeric) = 0.0012881903421614824482162308134136
absolute error = 2.24005527764474778283674141e-08
relative error = 0.0017388861353171841954093783256838 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5033
x2[1] (analytic) = 0.00082861608687345827866795740859187
x2[1] (numeric) = 0.00082862769101339756081327817261424
absolute error = 1.160413993928214532076402237e-08
relative error = 0.0014004241678516031717730064354027 %
h = 5e-05
x1[1] (analytic) = 0.0012881583334373664403266774516441
x1[1] (numeric) = 0.0012881352266277623739388798235123
absolute error = 2.31068096040663877976281318e-08
relative error = 0.0017937864472302387276731502710021 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50335
x2[1] (analytic) = 0.0008286617474868785996978214776885
x2[1] (numeric) = 0.00082867371261886550649384525584157
absolute error = 1.196513198690679602377815307e-08
relative error = 0.0014439102593059247336508564205295 %
h = 5e-05
x1[1] (analytic) = 0.0012881039268808698191194609553229
x1[1] (numeric) = 0.0012880801028287518925374015744666
absolute error = 2.38240521179265820593808563e-08
relative error = 0.0018495442503320578317177233996107 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5034
x2[1] (analytic) = 0.00082870741402678649165076351232339
x2[1] (numeric) = 0.00082871974571702498818946813210342
absolute error = 1.233169023849653870461978003e-08
relative error = 0.001488063221080092662734048910417 %
h = 5e-05
x1[1] (analytic) = 0.0012880495230446330156811398020981
x1[1] (numeric) = 0.0012880249707632115900055906821877
absolute error = 2.45522814214256755491199104e-08
relative error = 0.0019061597385937542848719945211174 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=26.7MB, alloc=4.5MB, time=1.52
t[1] = 0.50345
x2[1] (analytic) = 0.00082875308649370662472160982915166
x2[1] (numeric) = 0.00082876579031005859345728265144321
absolute error = 1.270381635196873567282229155e-08
relative error = 0.0015328831420364436569166036625088 %
h = 5e-05
x1[1] (analytic) = 0.0012879951219285200204210936480425
x1[1] (numeric) = 0.0012879698304299018664851171750458
absolute error = 2.52914986181539359764729967e-08
relative error = 0.0019636331060233270448413325114024 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5035
x2[1] (analytic) = 0.00082879876488816372497515444163463
x2[1] (numeric) = 0.00082881184640014928306501986635347
absolute error = 1.308151198555808986542471884e-08
relative error = 0.0015783701110272866060198768854226 %
h = 5e-05
x1[1] (analytic) = 0.0012879407235323948305490116710912
x1[1] (numeric) = 0.001287914681827582936237657974832
absolute error = 2.60417048118943113536962592e-08
relative error = 0.002021964546665667984450747437023 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50355
x2[1] (analytic) = 0.00082884444921068257435157632418004
x2[1] (numeric) = 0.00082885791398948039105156252203858
absolute error = 1.346477879781669998619785854e-08
relative error = 0.0016245242168949014153413115078029 %
h = 5e-05
x1[1] (analytic) = 0.0012878863278561214500745525640661
x1[1] (numeric) = 0.0012878595249550148276170241988667
absolute error = 2.68029011066224575283651994e-08
relative error = 0.0020811542546025686275939043546676 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5036
x2[1] (analytic) = 0.00082889013946178801067185722653652
x2[1] (numeric) = 0.00082890399308023562478751108649386
absolute error = 1.385361844761411565385995734e-08
relative error = 0.0016713455484715378299512622783016 %
h = 5e-05
x1[1] (analytic) = 0.0012878319348995638898070045446997
x1[1] (numeric) = 0.0012878043598109573830412842826292
absolute error = 2.75750886065067657202620705e-08
relative error = 0.0021412024239527268863881932692266 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50365
x2[1] (analytic) = 0.00082893583564200492764320003849618
x2[1] (numeric) = 0.00082895008367459906503575932187736
absolute error = 1.424803259413739255928338118e-08
relative error = 0.0017188341945794142597378761534084 %
h = 5e-05
x1[1] (analytic) = 0.0012877775446625861673549453826583
x1[1] (numeric) = 0.0012877491863941702589648829222811
absolute error = 2.83582684159083900624603772e-08
relative error = 0.0022021092488717537995360670657894 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5037
x2[1] (analytic) = 0.00082898153775185827486444770496057
x2[1] (numeric) = 0.00082899618577475516601207939865101
absolute error = 1.464802289689114763169369044e-08
relative error = 0.0017669902440307166052000082036702 %
h = 5e-05
x1[1] (analytic) = 0.0012877231571450523071259024435631
x1[1] (numeric) = 0.0012876940047034129258507558364565
absolute error = 2.91524416393812751466071066e-08
relative error = 0.0022638749235521802718928591045642 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50375
x2[1] (analytic) = 0.00082902724579187305783150269142413
x2[1] (numeric) = 0.00082904229938288875544571655396807
absolute error = 1.505359101569761421386254394e-08
relative error = 0.0018158137856275970839881533418888 %
h = 5e-05
x1[1] (analytic) = 0.0012876687723468263403260127500097
x1[1] (numeric) = 0.0012876388147374446681424403466929
absolute error = 2.99576093816721835724033168e-08
relative error = 0.002326499642223463815241292282096 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5038
x2[1] (analytic) = 0.0008290729597625743379427469999303
x2[1] (numeric) = 0.00082908842450118503463999329578393
absolute error = 1.546473861069669724629585363e-08
relative error = 0.0018653049081621730581933739664325 %
h = 5e-05
x1[1] (analytic) = 0.0012876143902677723049596830595824
x1[1] (numeric) = 0.001287583616495024584236181775875
absolute error = 3.07737727477207235012837074e-08
relative error = 0.00238998359915199529027289120475 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50385
x2[1] (analytic) = 0.00082911867966448723250446273555416
x2[1] (numeric) = 0.00082913456113182957853292315416763
absolute error = 1.588146734234602846041861347e-08
relative error = 0.0019154637004165258623842037111808 %
h = 5e-05
x1[1] (analytic) = 0.0012875600109077542458292499598661
x1[1] (numeric) = 0.0012875284099749115864530356640648
absolute error = 3.16009328426593762142958013e-08
relative error = 0.0024543269886411056497765095532075 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5039
x2[1] (analytic) = 0.00082916440549813691473625322346704
x2[1] (numeric) = 0.00082918070927700833575783398129162
absolute error = 1.630377887142102158075782458e-08
relative error = 0.0019662902511626996323915072253026 %
h = 5e-05
x1[1] (analytic) = 0.0012875056342666362145346399804511
x1[1] (numeric) = 0.0012874731951758644010109658010907
absolute error = 3.24390907718135236741793604e-08
relative error = 0.0025195300050310726830341842176367 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50395
x2[1] (analytic) = 0.00082921013726404861377646467663714
x2[1] (numeric) = 0.00082922686893890762870400080157761
absolute error = 1.673167485901492753612494047e-08
relative error = 0.0020177846491627001348412760177397 %
h = 5e-05
x1[1] (analytic) = 0.0012874512603442822694730297219339
x1[1] (numeric) = 0.0012874179720966415679969380752684
absolute error = 3.32882476407014760916466655e-08
relative error = 0.0025855928426991277614245284101548 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=30.5MB, alloc=4.5MB, time=1.74
t[1] = 0.504
x2[1] (analytic) = 0.00082925587496274761468760841422102
x2[1] (numeric) = 0.00082927304011971415357728821347647
absolute error = 1.716515696653888967979925545e-08
relative error = 0.0020699469831684935974353402186172 %
h = 5e-05
x1[1] (analytic) = 0.0012873968891405564758385060019091
x1[1] (numeric) = 0.001287362740736001441339010137626
absolute error = 3.41484045550344994958642831e-08
relative error = 0.0026525156960594625852338753999593 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50405
x2[1] (analytic) = 0.00082930161859475925846178363070083
x2[1] (numeric) = 0.00082931922282161498046080234436041
absolute error = 1.760422685572199901871365958e-08
relative error = 0.0021227773419220055399799760441893 %
h = 5e-05
x1[1] (analytic) = 0.0012873425206553229056217260179551
x1[1] (numeric) = 0.0012873075010927021887784168810059
absolute error = 3.50195626207168433091369492e-08
relative error = 0.0027202987595632359316753851202108 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5041
x2[1] (analytic) = 0.00082934736816060894202610071582133
x2[1] (numeric) = 0.00082936541704679755337555236000599
absolute error = 1.804888618861134945164418466e-08
relative error = 0.0021762758141551196061623887924326 %
h = 5e-05
x1[1] (analytic) = 0.0012872881548884456376095775276106
x1[1] (numeric) = 0.0012872522531655017918416517334163
absolute error = 3.59017229438457679257941943e-08
relative error = 0.0027889422276985804041163254665201 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50415
x2[1] (analytic) = 0.00082939312366082211824810512538206
x2[1] (numeric) = 0.00082941162279744969034112153014651
absolute error = 1.849913662757209301640476445e-08
relative error = 0.0022304424885896763960750509414606 %
h = 5e-05
x1[1] (analytic) = 0.0012872337918397887573848390453416
x1[1] (numeric) = 0.0012871969969531580458125437650045
absolute error = 3.67948866307115722952803371e-08
relative error = 0.002858446294990609182513740392183 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5042
x2[1] (analytic) = 0.00082943888509592429594120180293885
x2[1] (numeric) = 0.00082945784007575958343634785157286
absolute error = 1.895497983528749514604863401e-08
relative error = 0.0022852774539374722994878750309954 %
h = 5e-05
x1[1] (analytic) = 0.0012871794315092163573258400564985
x1[1] (numeric) = 0.0012871417324544285597043306080238
absolute error = 3.76990547877976215094484747e-08
relative error = 0.0029288111560014227750587169576382 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50425
x2[1] (analytic) = 0.00082948465246644103987008015246953
x2[1] (numeric) = 0.00082950406888391579886001423026184
absolute error = 1.941641747475898993407779231e-08
relative error = 0.0023407807989002583298682008209635 %
h = 5e-05
x1[1] (analytic) = 0.0012871250738965925366061212482615
x1[1] (numeric) = 0.0012870864596680707562317271891667
absolute error = 3.86142285217803743940590948e-08
relative error = 0.0030000370053301157710294633419651 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5043
x2[1] (analytic) = 0.00082953042577289797075613956205843
x2[1] (numeric) = 0.00082955030922410727699154822401139
absolute error = 1.988345120930623540866195296e-08
relative error = 0.0023969526121697389591485762087669 %
h = 5e-05
x1[1] (analytic) = 0.0012870707190017814011940947575749
x1[1] (numeric) = 0.0012870311785928418717829902736363
absolute error = 3.95404089395294111044839386e-08
relative error = 0.0030721240376127835948534101018352 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50435
x2[1] (analytic) = 0.00082957620501582076528291547865441
x2[1] (numeric) = 0.00082959656109852333245173134706231
absolute error = 2.035608270256716881586840790e-08
relative error = 0.0024537929824275709532423112886725 %
h = 5e-05
x1[1] (analytic) = 0.0012870163668246470638527044360674
x1[1] (numeric) = 0.0012869758892274989563919788203279
absolute error = 4.04775971481074607256157395e-08
relative error = 0.0031450724475225292613785467126817 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5044
x2[1] (analytic) = 0.00082962199019573515610150603395714
x2[1] (numeric) = 0.00082964282450935365416341793818631
absolute error = 2.083431361849806191190422917e-08
relative error = 0.0025113019983453622083067848736265 %
h = 5e-05
x1[1] (analytic) = 0.00128696201736505364413908613196
x1[1] (numeric) = 0.0012869205915707988737102101474927
absolute error = 4.14257942547704288759844673e-08
relative error = 0.003218882429769470132354205813243 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50445
x2[1] (analytic) = 0.00082966778131316693183599922148616
x2[1] (numeric) = 0.00082968909945878830541226359372039
absolute error = 2.131814562137357626437223423e-08
relative error = 0.0025694797485846705877544827451191 %
h = 5e-05
x1[1] (analytic) = 0.0012869076706228652684042279889585
x1[1] (numeric) = 0.0012868652856214983009789119082553
absolute error = 4.23850013669674253160807032e-08
relative error = 0.0032935541791007446741215072618302 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5045
x2[1] (analytic) = 0.00082971357836864193708890062488759
x2[1] (numeric) = 0.0008297353859490177239074631670279
absolute error = 2.180758037578681856254214031e-08
relative error = 0.0026283263217970027600117468010614 %
h = 5e-05
x1[1] (analytic) = 0.0012868533265979460697926307621308
x1[1] (numeric) = 0.0012868099713783537290010698753567
absolute error = 4.33552195923407915608867741e-08
relative error = 0.0033690878903005192165136743903105 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.5MB, time=1.97
NO POLE
NO POLE
t[1] = 0.50455
x2[1] (analytic) = 0.00082975938136268607244656169753319
x2[1] (numeric) = 0.0008297816839822327218424983358667
absolute error = 2.230261954664939593663833351e-08
relative error = 0.0026878418066238130370252142037215 %
h = 5e-05
x1[1] (analytic) = 0.0012867989852901601882419681507683
x1[1] (numeric) = 0.0012867546488401214621134715344945
absolute error = 4.43364500387261284966162738e-08
relative error = 0.0034454837581899947129664348009221 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5046
x2[1] (analytic) = 0.00082980519029582529448460859346626
x2[1] (numeric) = 0.00082982799356062448595589473914524
absolute error = 2.280326479919147128614567898e-08
relative error = 0.0027480262916965022135159256064519 %
h = 5e-05
x1[1] (analytic) = 0.0012867446466993717704827471482299
x1[1] (numeric) = 0.0012866993180055576181587454856319
absolute error = 4.53286938141523240016625980e-08
relative error = 0.0035227419776274135018387180256803 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50465
x2[1] (analytic) = 0.00082985100516858561577337154974936
x2[1] (numeric) = 0.00082987431468638457759198868454745
absolute error = 2.330951779896181861713479809e-08
relative error = 0.0028088798656364164069810813904913 %
h = 5e-05
x1[1] (analytic) = 0.001286690310825444970037968408768
x1[1] (numeric) = 0.0012866439788734181284573966516463
absolute error = 4.63319520268415805717571217e-08
relative error = 0.0036008627435080660689438625292823 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5047
x2[1] (analytic) = 0.00082989682598149310488331482026843
x2[1] (numeric) = 0.00082992064736170493276170342850761
absolute error = 2.382138021182787838860823918e-08
relative error = 0.002870402617054845898443424828277 %
h = 5e-05
x1[1] (analytic) = 0.0012866359776682439472227866313365
x1[1] (numeric) = 0.00128658863144245873777983729369
absolute error = 4.73462257852094429493376465e-08
relative error = 0.0036798462507642978112915444799932 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50475
x2[1] (analytic) = 0.00082994265273507388639046716104801
x2[1] (numeric) = 0.00082996699158877786220333503001671
absolute error = 2.433885370397581286786896870e-08
relative error = 0.0029325946345530239739482310194129 %
h = 5e-05
x1[1] (analytic) = 0.001286581647227632869144170960378
x1[1] (numeric) = 0.001286533275711435004318413832633
absolute error = 4.83715161978648257571277450e-08
relative error = 0.0037596926943655158020406407187338 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5048
x2[1] (analytic) = 0.00082998848542985414088185286713247
x2[1] (numeric) = 0.00083001334736979605144334777974179
absolute error = 2.486193994191056149491260932e-08
relative error = 0.0029954560067221257668078803209419 %
h = 5e-05
x1[1] (analytic) = 0.0012865273195034759097005654035915
x1[1] (numeric) = 0.0012864779116791022996594294759595
absolute error = 4.94078243736100411359276320e-08
relative error = 0.0038404022693181955566632385799424 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50485
x2[1] (analytic) = 0.00083003432406636010496092336108762
x2[1] (numeric) = 0.00083005971470695256085717920594029
absolute error = 2.539064059245589625584485267e-08
relative error = 0.0030589868221432671005939950269432 %
h = 5e-05
x1[1] (analytic) = 0.0012864729944956372495815492666783
x1[1] (numeric) = 0.0012864225393442158087551626494895
absolute error = 5.04551514214408263866171888e-08
relative error = 0.0039219751706658878003200049826118 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5049
x2[1] (analytic) = 0.00083008016864511807125298933317795
x2[1] (numeric) = 0.00083010609360244082573005465865133
absolute error = 2.592495732275447706532547338e-08
relative error = 0.0031231871693875033328771178364244 %
h = 5e-05
x1[1] (analytic) = 0.001286418672203981076267497605066
x1[1] (numeric) = 0.001286367158705530529895881233296
absolute error = 5.15134984505463716163717700e-08
relative error = 0.0040044115934892252364471274798989 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50495
x2[1] (analytic) = 0.00083012601916665438841065343327373
x2[1] (numeric) = 0.00083015248405845465631781147364636
absolute error = 2.646489180026790715804037263e-08
relative error = 0.0031880571370158281997139107372988 %
h = 5e-05
x1[1] (analytic) = 0.0012863643526283715840292416926091
x1[1] (numeric) = 0.0012863117697618012746818526011888
absolute error = 5.25828665703093473890914203e-08
relative error = 0.0040877117329059293165550398371083 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.505
x2[1] (analytic) = 0.00083017187563149546111924351454314
x2[1] (numeric) = 0.00083019888607718823790773271762169
absolute error = 2.701044569277678848920307855e-08
relative error = 0.0032535968135791726608818527326769 %
h = 5e-05
x1[1] (analytic) = 0.0012863100357686729739277295072664
x1[1] (numeric) = 0.0012862563725117826679953494631352
absolute error = 5.36632568903059323800441312e-08
relative error = 0.0041718757840708170112391449234859 %
h = 5e-05
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 = 31 Minutes 43 Seconds
Optimized Time Remaining = 31 Minutes 32 Seconds
Time to Timeout = 14 Minutes 57 Seconds
Percent Done = 0.1122 %
> quit
memory used=37.9MB, alloc=4.5MB, time=2.18