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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_h,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_start,
> glob_max_trunc_err,
> glob_max_order,
> glob_log10_abserr,
> glob_large_float,
> sec_in_min,
> glob_html_log,
> glob_orig_start_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_hmin_init,
> glob_hmin,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_clock_sec,
> min_in_hour,
> djd_debug2,
> glob_normmax,
> glob_relerr,
> glob_look_poles,
> days_in_year,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_log10relerr,
> hours_in_day,
> glob_iter,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_abserr,
> glob_last_good_h,
> years_in_century,
> glob_optimal_expect_sec,
> glob_small_float,
> glob_initial_pass,
> djd_debug,
> glob_dump,
> glob_dump_analytic,
> glob_hmax,
> glob_max_opt_iter,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_t,
> array_type_pole,
> array_1st_rel_error,
> 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_pole,
> array_x1_init,
> array_x2,
> array_x1,
> array_norms,
> array_m1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_poles,
> array_x2_higher,
> array_x1_higher,
> array_x2_higher_work,
> array_real_pole,
> array_complex_pole,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x2_higher_work2,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_x2(ind_var);
> omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x2[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_x1(ind_var);
> omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h,
glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order,
glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log,
glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr,
glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr,
glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr,
glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day,
glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr,
glob_last_good_h, years_in_century, glob_optimal_expect_sec,
glob_small_float, glob_initial_pass, djd_debug, glob_dump,
glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin,
array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0,
array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error,
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_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles,
array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole,
array_complex_pole, array_x1_higher_work, array_x1_higher_work2,
array_x2_higher_work2, glob_last;
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_x2(ind_var);
omniout_float(ALWAYS, "x2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x2[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x2[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_x1(ind_var);
omniout_float(ALWAYS, "x1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x1[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_h,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_start,
> glob_max_trunc_err,
> glob_max_order,
> glob_log10_abserr,
> glob_large_float,
> sec_in_min,
> glob_html_log,
> glob_orig_start_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_hmin_init,
> glob_hmin,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_clock_sec,
> min_in_hour,
> djd_debug2,
> glob_normmax,
> glob_relerr,
> glob_look_poles,
> days_in_year,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_log10relerr,
> hours_in_day,
> glob_iter,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_abserr,
> glob_last_good_h,
> years_in_century,
> glob_optimal_expect_sec,
> glob_small_float,
> glob_initial_pass,
> djd_debug,
> glob_dump,
> glob_dump_analytic,
> glob_hmax,
> glob_max_opt_iter,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_t,
> array_type_pole,
> array_1st_rel_error,
> 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_pole,
> array_x1_init,
> array_x2,
> array_x1,
> array_norms,
> array_m1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_poles,
> array_x2_higher,
> array_x1_higher,
> array_x2_higher_work,
> array_real_pole,
> array_complex_pole,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x2_higher_work2,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_t[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h,
glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order,
glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log,
glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr,
glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr,
glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr,
glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day,
glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr,
glob_last_good_h, years_in_century, glob_optimal_expect_sec,
glob_small_float, glob_initial_pass, djd_debug, glob_dump,
glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin,
array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0,
array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error,
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_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles,
array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole,
array_complex_pole, array_x1_higher_work, array_x1_higher_work2,
array_x2_higher_work2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_t[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(t_start,t_end)
> global
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_h,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_start,
> glob_max_trunc_err,
> glob_max_order,
> glob_log10_abserr,
> glob_large_float,
> sec_in_min,
> glob_html_log,
> glob_orig_start_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_hmin_init,
> glob_hmin,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_clock_sec,
> min_in_hour,
> djd_debug2,
> glob_normmax,
> glob_relerr,
> glob_look_poles,
> days_in_year,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_log10relerr,
> hours_in_day,
> glob_iter,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_abserr,
> glob_last_good_h,
> years_in_century,
> glob_optimal_expect_sec,
> glob_small_float,
> glob_initial_pass,
> djd_debug,
> glob_dump,
> glob_dump_analytic,
> glob_hmax,
> glob_max_opt_iter,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_t,
> array_type_pole,
> array_1st_rel_error,
> 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_pole,
> array_x1_init,
> array_x2,
> array_x1,
> array_norms,
> array_m1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_poles,
> array_x2_higher,
> array_x1_higher,
> array_x2_higher_work,
> array_real_pole,
> array_complex_pole,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x2_higher_work2,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(t_start, t_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h,
glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order,
glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log,
glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr,
glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr,
glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr,
glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day,
glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr,
glob_last_good_h, years_in_century, glob_optimal_expect_sec,
glob_small_float, glob_initial_pass, djd_debug, glob_dump,
glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin,
array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0,
array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error,
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_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles,
array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole,
array_complex_pole, array_x1_higher_work, array_x1_higher_work2,
array_x2_higher_work2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start),
convfloat(array_t[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),
convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(t_end), convfloat(t_start),
convfloat(array_t[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_h,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_start,
> glob_max_trunc_err,
> glob_max_order,
> glob_log10_abserr,
> glob_large_float,
> sec_in_min,
> glob_html_log,
> glob_orig_start_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_hmin_init,
> glob_hmin,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_clock_sec,
> min_in_hour,
> djd_debug2,
> glob_normmax,
> glob_relerr,
> glob_look_poles,
> days_in_year,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_log10relerr,
> hours_in_day,
> glob_iter,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_abserr,
> glob_last_good_h,
> years_in_century,
> glob_optimal_expect_sec,
> glob_small_float,
> glob_initial_pass,
> djd_debug,
> glob_dump,
> glob_dump_analytic,
> glob_hmax,
> glob_max_opt_iter,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_t,
> array_type_pole,
> array_1st_rel_error,
> 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_pole,
> array_x1_init,
> array_x2,
> array_x1,
> array_norms,
> array_m1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_poles,
> array_x2_higher,
> array_x1_higher,
> array_x2_higher_work,
> array_real_pole,
> array_complex_pole,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x2_higher_work2,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 2 - 1;
> while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1];
> rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1];
> rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]);
> rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]);
> rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]);
> rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]);
> rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float)) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]);
> rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]);
> rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]);
> rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]);
> rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4
> ;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3
> ;
> #BOTTOM RADII COMPLEX EQ = 2
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 2
> if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 2
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if array_pole[1] > array_poles[2,1] then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 2
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h,
glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order,
glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log,
glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr,
glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr,
glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr,
glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day,
glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr,
glob_last_good_h, years_in_century, glob_optimal_expect_sec,
glob_small_float, glob_initial_pass, djd_debug, glob_dump,
glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin,
array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0,
array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error,
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_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles,
array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole,
array_complex_pole, array_x1_higher_work, array_x1_higher_work2,
array_x2_higher_work2, glob_last;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or
abs(array_x2_higher[1, m - 1]) < glob_small_float or
abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or
abs(array_x1_higher[1, m - 1]) < glob_small_float or
abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_x2_higher[1, m]) or
glob_large_float <= abs(array_x2_higher[1, m - 1]) or
glob_large_float <= abs(array_x2_higher[1, m - 2]) or
glob_large_float <= abs(array_x2_higher[1, m - 3]) or
glob_large_float <= abs(array_x2_higher[1, m - 4]) or
glob_large_float <= abs(array_x2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3];
rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4];
rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= abs(array_x1_higher[1, m]) or
glob_large_float <= abs(array_x1_higher[1, m - 1]) or
glob_large_float <= abs(array_x1_higher[1, m - 2]) or
glob_large_float <= abs(array_x1_higher[1, m - 3]) or
glob_large_float <= abs(array_x1_higher[1, m - 4]) or
glob_large_float <= abs(array_x1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3];
rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4];
rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[2, 1] := rad_c;
array_complex_pole[2, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_h,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_start,
> glob_max_trunc_err,
> glob_max_order,
> glob_log10_abserr,
> glob_large_float,
> sec_in_min,
> glob_html_log,
> glob_orig_start_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_hmin_init,
> glob_hmin,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_clock_sec,
> min_in_hour,
> djd_debug2,
> glob_normmax,
> glob_relerr,
> glob_look_poles,
> days_in_year,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_log10relerr,
> hours_in_day,
> glob_iter,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_abserr,
> glob_last_good_h,
> years_in_century,
> glob_optimal_expect_sec,
> glob_small_float,
> glob_initial_pass,
> djd_debug,
> glob_dump,
> glob_dump_analytic,
> glob_hmax,
> glob_max_opt_iter,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_t,
> array_type_pole,
> array_1st_rel_error,
> 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_pole,
> array_x1_init,
> array_x2,
> array_x1,
> array_norms,
> array_m1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_poles,
> array_x2_higher,
> array_x1_higher,
> array_x2_higher_work,
> array_real_pole,
> array_complex_pole,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x2_higher_work2,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 3
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h,
glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order,
glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log,
glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr,
glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr,
glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr,
glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day,
glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr,
glob_last_good_h, years_in_century, glob_optimal_expect_sec,
glob_small_float, glob_initial_pass, djd_debug, glob_dump,
glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin,
array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0,
array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error,
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_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles,
array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole,
array_complex_pole, array_x1_higher_work, array_x1_higher_work2,
array_x2_higher_work2, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x2[iii]) then
array_norms[iii] := abs(array_x2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x1[iii]) then
array_norms[iii] := abs(array_x1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_h,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_start,
> glob_max_trunc_err,
> glob_max_order,
> glob_log10_abserr,
> glob_large_float,
> sec_in_min,
> glob_html_log,
> glob_orig_start_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_hmin_init,
> glob_hmin,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_clock_sec,
> min_in_hour,
> djd_debug2,
> glob_normmax,
> glob_relerr,
> glob_look_poles,
> days_in_year,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_log10relerr,
> hours_in_day,
> glob_iter,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_abserr,
> glob_last_good_h,
> years_in_century,
> glob_optimal_expect_sec,
> glob_small_float,
> glob_initial_pass,
> djd_debug,
> glob_dump,
> glob_dump_analytic,
> glob_hmax,
> glob_max_opt_iter,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_t,
> array_type_pole,
> array_1st_rel_error,
> 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_pole,
> array_x1_init,
> array_x2,
> array_x1,
> array_norms,
> array_m1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_poles,
> array_x2_higher,
> array_x1_higher,
> array_x2_higher_work,
> array_real_pole,
> array_complex_pole,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x2_higher_work2,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1
> array_tmp1[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp4[1] := (array_const_2D0[1] * (array_x2[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp6[1] := array_x1_higher[3,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp8[1] := array_x1_higher[2,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp10[1] := array_tmp9[1] + array_x1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2);
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> # emit pre mult $eq_no = 2 i = 1
> array_tmp12[1] := (array_const_4D0[1] * (array_x2[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1]));
> # emit pre mult $eq_no = 2 i = 1
> array_tmp16[1] := (array_const_2D0[1] * (array_x1[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2
> array_tmp1[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp4[2] := ats(2,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp6[2] := array_x1_higher[3,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp8[2] := array_x1_higher[2,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2]));
> #emit pre add $eq_no = 1 i = 2
> array_tmp10[2] := array_tmp9[2] + array_x1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> # emit pre mult $eq_no = 2 i = 2
> array_tmp12[2] := ats(2,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2]));
> # emit pre mult $eq_no = 2 i = 2
> array_tmp16[2] := ats(2,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2]));
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3
> array_tmp1[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp4[3] := ats(3,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp6[3] := array_x1_higher[3,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp8[3] := array_x1_higher[2,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3]));
> #emit pre add $eq_no = 1 i = 3
> array_tmp10[3] := array_tmp9[3] + array_x1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> # emit pre mult $eq_no = 2 i = 3
> array_tmp12[3] := ats(3,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3]));
> # emit pre mult $eq_no = 2 i = 3
> array_tmp16[3] := ats(3,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3]));
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4
> array_tmp1[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp4[4] := ats(4,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp6[4] := array_x1_higher[3,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp8[4] := array_x1_higher[2,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4]));
> #emit pre add $eq_no = 1 i = 4
> array_tmp10[4] := array_tmp9[4] + array_x1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> # emit pre mult $eq_no = 2 i = 4
> array_tmp12[4] := ats(4,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4]));
> # emit pre mult $eq_no = 2 i = 4
> array_tmp16[4] := ats(4,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4]));
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5
> array_tmp1[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp4[5] := ats(5,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp6[5] := array_x1_higher[3,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp8[5] := array_x1_higher[2,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5]));
> #emit pre add $eq_no = 1 i = 5
> array_tmp10[5] := array_tmp9[5] + array_x1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> # emit pre mult $eq_no = 2 i = 5
> array_tmp12[5] := ats(5,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5]));
> # emit pre mult $eq_no = 2 i = 5
> array_tmp16[5] := ats(5,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5]));
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit diff $eq_no = 1
> array_tmp1[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1);
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
> #emit mult $eq_no = 1
> array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1);
> #emit sub $eq_no = 1
> array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk]));
> #emit diff $eq_no = 1
> array_tmp6[kkk] := array_x1_higher[3,kkk];
> #emit sub $eq_no = 1
> array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk]));
> #emit diff $eq_no = 1
> array_tmp8[kkk] := array_x1_higher[2,kkk];
> #emit sub $eq_no = 1
> array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk]));
> #emit add $eq_no = 1
> array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x2[kkk + order_d] := temporary;
> array_x2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> #emit mult $eq_no = 2
> array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1);
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 2
> array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1);
> #emit sub $eq_no = 2
> array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk]));
> #emit mult $eq_no = 2
> array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1);
> #emit sub $eq_no = 2
> array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk]));
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x1[kkk + order_d] := temporary;
> array_x1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h,
glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order,
glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log,
glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr,
glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr,
glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr,
glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day,
glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr,
glob_last_good_h, years_in_century, glob_optimal_expect_sec,
glob_small_float, glob_initial_pass, djd_debug, glob_dump,
glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin,
array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0,
array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error,
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_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles,
array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole,
array_complex_pole, array_x1_higher_work, array_x1_higher_work2,
array_x2_higher_work2, glob_last;
array_tmp1[1] := array_x2_higher[2, 1];
array_tmp2[1] := array_const_3D0[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_const_2D0[1]*array_x2[1];
array_tmp5[1] := array_tmp3[1] - array_tmp4[1];
array_tmp6[1] := array_x1_higher[3, 1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
array_tmp8[1] := array_x1_higher[2, 1];
array_tmp9[1] := array_tmp7[1] - array_tmp8[1];
array_tmp10[1] := array_tmp9[1] + array_x1[1];
if 1 <= glob_max_terms then
temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2);
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 1] := temporary
end if;
kkk := 2;
array_tmp12[1] := array_const_4D0[1]*array_x2[1];
array_tmp13[1] := array_x2_higher[2, 1];
array_tmp14[1] := array_const_2D0[1]*array_tmp13[1];
array_tmp15[1] := array_tmp12[1] - array_tmp14[1];
array_tmp16[1] := array_const_2D0[1]*array_x1[1];
array_tmp17[1] := array_tmp15[1] - array_tmp16[1];
if 1 <= glob_max_terms then
temporary := array_tmp17[1]*glob_h*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 1] := temporary
end if;
kkk := 2;
array_tmp1[2] := array_x2_higher[2, 2];
array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1);
array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1);
array_tmp5[2] := array_tmp3[2] - array_tmp4[2];
array_tmp6[2] := array_x1_higher[3, 2];
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
array_tmp8[2] := array_x1_higher[2, 2];
array_tmp9[2] := array_tmp7[2] - array_tmp8[2];
array_tmp10[2] := array_tmp9[2] + array_x1[2];
if 2 <= glob_max_terms then
temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 2] := temporary
end if;
kkk := 3;
array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1);
array_tmp13[2] := array_x2_higher[2, 2];
array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1);
array_tmp15[2] := array_tmp12[2] - array_tmp14[2];
array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1);
array_tmp17[2] := array_tmp15[2] - array_tmp16[2];
if 2 <= glob_max_terms then
temporary := array_tmp17[2]*glob_h*factorial_3(1, 2);
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 2] := temporary
end if;
kkk := 3;
array_tmp1[3] := array_x2_higher[2, 3];
array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1);
array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1);
array_tmp5[3] := array_tmp3[3] - array_tmp4[3];
array_tmp6[3] := array_x1_higher[3, 3];
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
array_tmp8[3] := array_x1_higher[2, 3];
array_tmp9[3] := array_tmp7[3] - array_tmp8[3];
array_tmp10[3] := array_tmp9[3] + array_x1[3];
if 3 <= glob_max_terms then
temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if;
kkk := 4;
array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1);
array_tmp13[3] := array_x2_higher[2, 3];
array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1);
array_tmp15[3] := array_tmp12[3] - array_tmp14[3];
array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1);
array_tmp17[3] := array_tmp15[3] - array_tmp16[3];
if 3 <= glob_max_terms then
temporary := array_tmp17[3]*glob_h*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 3] := temporary
end if;
kkk := 4;
array_tmp1[4] := array_x2_higher[2, 4];
array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1);
array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1);
array_tmp5[4] := array_tmp3[4] - array_tmp4[4];
array_tmp6[4] := array_x1_higher[3, 4];
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
array_tmp8[4] := array_x1_higher[2, 4];
array_tmp9[4] := array_tmp7[4] - array_tmp8[4];
array_tmp10[4] := array_tmp9[4] + array_x1[4];
if 4 <= glob_max_terms then
temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 4] := temporary
end if;
kkk := 5;
array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1);
array_tmp13[4] := array_x2_higher[2, 4];
array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1);
array_tmp15[4] := array_tmp12[4] - array_tmp14[4];
array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1);
array_tmp17[4] := array_tmp15[4] - array_tmp16[4];
if 4 <= glob_max_terms then
temporary := array_tmp17[4]*glob_h*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 4] := temporary
end if;
kkk := 5;
array_tmp1[5] := array_x2_higher[2, 5];
array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1);
array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1);
array_tmp5[5] := array_tmp3[5] - array_tmp4[5];
array_tmp6[5] := array_x1_higher[3, 5];
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
array_tmp8[5] := array_x1_higher[2, 5];
array_tmp9[5] := array_tmp7[5] - array_tmp8[5];
array_tmp10[5] := array_tmp9[5] + array_x1[5];
if 5 <= glob_max_terms then
temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 5] := temporary
end if;
kkk := 6;
array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1);
array_tmp13[5] := array_x2_higher[2, 5];
array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1);
array_tmp15[5] := array_tmp12[5] - array_tmp14[5];
array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1);
array_tmp17[5] := array_tmp15[5] - array_tmp16[5];
if 5 <= glob_max_terms then
temporary := array_tmp17[5]*glob_h*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 5] := temporary
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_x2_higher[2, kkk];
array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1);
array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1);
array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := array_x1_higher[3, kkk];
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
array_tmp8[kkk] := array_x1_higher[2, kkk];
array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk];
array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp10[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x2[kkk + order_d] := temporary;
array_x2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1);
array_tmp13[kkk] := array_x2_higher[2, kkk];
array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1);
array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk];
array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1);
array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp17[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x1[kkk + order_d] := temporary;
array_x1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_x1 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c1 + 6.0 * c3 * exp(-t);
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0*c2*exp(2.0*t) - c3*exp(-t)
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> t_start,t_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGMASSIVE,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_h,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_start,
> glob_max_trunc_err,
> glob_max_order,
> glob_log10_abserr,
> glob_large_float,
> sec_in_min,
> glob_html_log,
> glob_orig_start_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_hmin_init,
> glob_hmin,
> glob_almost_1,
> centuries_in_millinium,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_clock_sec,
> min_in_hour,
> djd_debug2,
> glob_normmax,
> glob_relerr,
> glob_look_poles,
> days_in_year,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_log10relerr,
> hours_in_day,
> glob_iter,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_abserr,
> glob_last_good_h,
> years_in_century,
> glob_optimal_expect_sec,
> glob_small_float,
> glob_initial_pass,
> djd_debug,
> glob_dump,
> glob_dump_analytic,
> glob_hmax,
> glob_max_opt_iter,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> array_const_1,
> array_const_2,
> #END CONST
> array_t,
> array_type_pole,
> array_1st_rel_error,
> 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_pole,
> array_x1_init,
> array_x2,
> array_x1,
> array_norms,
> array_m1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_poles,
> array_x2_higher,
> array_x1_higher,
> array_x2_higher_work,
> array_real_pole,
> array_complex_pole,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x2_higher_work2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> INFO := 2;
> ALWAYS := 1;
> glob_iolevel := 5;
> glob_max_terms := 30;
> DEBUGL := 3;
> glob_max_minutes := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_h := 0.1;
> glob_reached_optimal_h := false;
> glob_current_iter := 0;
> glob_start := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_max_order := 30;
> glob_log10_abserr := 0.1e-10;
> glob_large_float := 9.0e100;
> sec_in_min := 60.0;
> glob_html_log := true;
> glob_orig_start_sec := 0.0;
> glob_no_eqs := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_hmin := 0.00000000001;
> glob_almost_1 := 0.9990;
> centuries_in_millinium := 10.0;
> glob_log10abserr := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_warned2 := false;
> glob_optimal_start := 0.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_done := false;
> glob_clock_start_sec := 0.0;
> glob_clock_sec := 0.0;
> min_in_hour := 60.0;
> djd_debug2 := true;
> glob_normmax := 0.0;
> glob_relerr := 0.1e-10;
> glob_look_poles := false;
> days_in_year := 365.0;
> glob_warned := false;
> glob_max_hours := 0.0;
> glob_disp_incr := 0.1;
> glob_not_yet_finished := true;
> glob_percent_done := 0.0;
> glob_log10relerr := 0.0;
> hours_in_day := 24.0;
> glob_iter := 0;
> glob_max_sec := 10000.0;
> glob_smallish_float := 0.1e-100;
> glob_max_iter := 1000;
> glob_not_yet_start_msg := true;
> glob_display_flag := true;
> MAX_UNCHANGED := 10;
> glob_abserr := 0.1e-10;
> glob_last_good_h := 0.1;
> years_in_century := 100.0;
> glob_optimal_expect_sec := 0.1;
> glob_small_float := 0.1e-50;
> glob_initial_pass := true;
> djd_debug := true;
> glob_dump := false;
> glob_dump_analytic := false;
> glob_hmax := 1.0;
> glob_max_opt_iter := 10;
> glob_log10normmin := 0.1;
> #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/complicatedrev2postode.ode#################");
> omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_t:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= 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_pole:= Array(1..(max_terms + 1),[]);
> array_x1_init:= Array(1..(max_terms + 1),[]);
> array_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_tmp10:= Array(1..(max_terms + 1),[]);
> array_tmp11:= Array(1..(max_terms + 1),[]);
> array_tmp12:= Array(1..(max_terms + 1),[]);
> array_tmp13:= Array(1..(max_terms + 1),[]);
> array_tmp14:= Array(1..(max_terms + 1),[]);
> array_tmp15:= Array(1..(max_terms + 1),[]);
> array_tmp16:= Array(1..(max_terms + 1),[]);
> array_tmp17:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_t[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_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_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_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_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_norms[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_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2_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_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher[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 <=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 <= 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_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_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_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_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_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_x1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0[1] := 2.0;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0[1] := 3.0;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_4D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_4D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_4D0[1] := 4.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[1] := exact_soln_x1(t_start);
> array_x2_init[1] := exact_soln_x2(t_start);
> array_x2_init[2] := exact_soln_x2p(t_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> if glob_html_log then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_t[1] := t_start;
> array_t[2] := glob_h;
> order_diff := 2;
> #Start Series array_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_x2();
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> start_array_x1();
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> sub_iter := 1;
> while sub_iter <= 3 do # do number 3
> atomall()
> ;
> sub_iter := sub_iter + 1;
> od;# end do number 3
> ;
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> order_diff := 2;
> #Jump Series array_x2
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x2
> order_diff := 2;
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> order_diff := 1;
> #Jump Series array_x1
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x1
> order_diff := 1;
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 3
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 3
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if glob_html_log then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-02T01:53:47-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"complicatedrev2")
> ;
> 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,"complicatedrev2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"complicatedrev2 maple results")
> ;
> logitem_str(html_log_file,"sub iter tot order eqs reversed")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4
> ;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then # if number 4
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;# end if 4
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3
> ;
> if glob_html_log then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp;
global DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h,
glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order,
glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log,
glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr,
glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr,
glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr,
glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day,
glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr,
glob_last_good_h, years_in_century, glob_optimal_expect_sec,
glob_small_float, glob_initial_pass, djd_debug, glob_dump,
glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin,
array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0,
array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error,
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_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles,
array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole,
array_complex_pole, array_x1_higher_work, array_x1_higher_work2,
array_x2_higher_work2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
INFO := 2;
ALWAYS := 1;
glob_iolevel := 5;
glob_max_terms := 30;
DEBUGL := 3;
glob_max_minutes := 0.;
glob_unchanged_h_cnt := 0;
glob_h := 0.1;
glob_reached_optimal_h := false;
glob_current_iter := 0;
glob_start := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_max_order := 30;
glob_log10_abserr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
sec_in_min := 60.0;
glob_html_log := true;
glob_orig_start_sec := 0.;
glob_no_eqs := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_hmin := 0.1*10^(-10);
glob_almost_1 := 0.9990;
centuries_in_millinium := 10.0;
glob_log10abserr := 0.;
glob_curr_iter_when_opt := 0;
glob_warned2 := false;
glob_optimal_start := 0.;
glob_optimal_clock_start_sec := 0.;
glob_optimal_done := false;
glob_clock_start_sec := 0.;
glob_clock_sec := 0.;
min_in_hour := 60.0;
djd_debug2 := true;
glob_normmax := 0.;
glob_relerr := 0.1*10^(-10);
glob_look_poles := false;
days_in_year := 365.0;
glob_warned := false;
glob_max_hours := 0.;
glob_disp_incr := 0.1;
glob_not_yet_finished := true;
glob_percent_done := 0.;
glob_log10relerr := 0.;
hours_in_day := 24.0;
glob_iter := 0;
glob_max_sec := 10000.0;
glob_smallish_float := 0.1*10^(-100);
glob_max_iter := 1000;
glob_not_yet_start_msg := true;
glob_display_flag := true;
MAX_UNCHANGED := 10;
glob_abserr := 0.1*10^(-10);
glob_last_good_h := 0.1;
years_in_century := 100.0;
glob_optimal_expect_sec := 0.1;
glob_small_float := 0.1*10^(-50);
glob_initial_pass := true;
djd_debug := true;
glob_dump := false;
glob_dump_analytic := false;
glob_hmax := 1.0;
glob_max_opt_iter := 10;
glob_log10normmin := 0.1;
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/complicatedrev2postode.ode#################");
omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
diff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_t := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_1st_rel_error := 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_pole := Array(1 .. max_terms + 1, []);
array_x1_init := Array(1 .. max_terms + 1, []);
array_x2 := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_tmp10 := Array(1 .. max_terms + 1, []);
array_tmp11 := Array(1 .. max_terms + 1, []);
array_tmp12 := Array(1 .. max_terms + 1, []);
array_tmp13 := Array(1 .. max_terms + 1, []);
array_tmp14 := Array(1 .. max_terms + 1, []);
array_tmp15 := Array(1 .. max_terms + 1, []);
array_tmp16 := Array(1 .. max_terms + 1, []);
array_tmp17 := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_t[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_1st_rel_error[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_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_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_norms[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_tmp10[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp15[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp16[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp17[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2_init[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher[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 <= 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 <= 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_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_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_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_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_x1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
end do;
array_x2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1
end do;
array_tmp17 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp17[term] := 0.; term := term + 1
end do;
array_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[term] := 0.; term := term + 1
end do;
array_tmp15 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp15[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_4D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_4D0[term] := 0.; term := term + 1
end do;
array_const_4D0[1] := 4.0;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x2_higher[r_order, term_no] := array_x2_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x1_higher[r_order, term_no] := array_x1_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_x2();
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_x1();
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_t[1] <= t_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
sub_iter := 1;
while sub_iter <= 3 do atomall(); sub_iter := sub_iter + 1 end do;
if glob_look_poles then check_for_pole() end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 2;
order_diff := 2;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
order_diff := 1;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x1[term_no] := array_x1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x1_higher[ord, term_no] :=
array_x1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
ff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-02T01:53:47-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"complicatedrev2");
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, "complicatedrev2 diffeq.mxt");
logitem_str(html_log_file, "complicatedrev2 maple results");
logitem_str(html_log_file, "sub iter tot order 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/complicatedrev2postode.ode#################
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
#END FIRST INPUT BLOCK
!
#BEGIN SECOND INPUT BLOCK
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.001
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.001
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.001
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = 0.00082652318951926688082885102467593
absolute error = 1.09339294885410769929680407e-09
relative error = 0.0001322884111602750894560937083493 %
h = 0.001
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = 0.0012906617956534023791764003418242
absolute error = 2.1823375350673072778602109e-09
relative error = 0.00016908642158467607169130706620805 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.502
x2[1] (analytic) = 0.0008274309894041739636559251804687
x2[1] (numeric) = 0.00082743568533374563170506053559616
absolute error = 4.69592957166804913535512746e-09
relative error = 0.00056753126626905141469010651621218 %
h = 0.001
x1[1] (analytic) = 0.0012895738591632036100858259251
x1[1] (numeric) = 0.0012895304745981906282540724479938
absolute error = 4.33845650129818317534771062e-08
relative error = 0.0033642559287867236943712535472889 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.503
x2[1] (analytic) = 0.0008283422476198008492141699458837
x2[1] (numeric) = 0.00088459482297093295741378802757285
absolute error = 5.625257535113210819961808168915e-05
relative error = 6.7909822917726351684230091751351 %
h = 0.001
x1[1] (analytic) = 0.0012884848299094197347162072617323
x1[1] (numeric) = -0.0049375841560521641729929436123067
absolute error = 0.006226068985961583907709150874039
relative error = 483.20855949846732016059948848008 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.21
NO POLE
NO POLE
t[1] = 0.504
x2[1] (analytic) = 0.00082925587496274761468760841422102
x2[1] (numeric) = 1.7819047752952228731507051795107
absolute error = 1.7810755194202601255360175710965
relative error = 214779.96999421569217487929557044 %
h = 0.001
x1[1] (analytic) = 0.0012873968891405564758385060019091
x1[1] (numeric) = -197.64342496743666735511188153441
absolute error = 197.64471236432580791158772004041
relative error = 15352275.124438893298867121912277 %
h = 0.001
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] = 0.505
x2[1] (analytic) = 0.00083017187563149546111924351454314
x2[1] (numeric) = 11677.969939701327108178176973385
absolute error = 11677.969109529451476682715854141
relative error = 1406692933.3936119493830013257466 %
h = 0.001
x1[1] (analytic) = 0.0012863100357686729739277295072664
x1[1] (numeric) = -1294945.8027578425187564318752508
absolute error = 1294945.8040441525545251048491785
relative error = 100671359783.82684539822304607948 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.506
x2[1] (analytic) = 0.00083109025383347519720441727943742
x2[1] (numeric) = 15190133.655680629788756958255439
absolute error = 15190133.654849539534923483058235
relative error = 1827735746482.8570691407040050704 %
h = 0.001
x1[1] (analytic) = 0.0012852242687069157665292585243653
x1[1] (numeric) = -1659087026.1911173902717090267217
absolute error = 1659087026.1924026145404159424882
relative error = 129089301111753.51631930131951026 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 2.520e-05
Order of pole = 20.05
t[1] = 0.507
x2[1] (analytic) = 0.00083201101378508461244661319002326
x2[1] (numeric) = 3215149058.4717771689039053206405
absolute error = 3215149058.4709451578901202360281
relative error = 386431069445126.95939080587236139 %
h = 0.001
x1[1] (analytic) = 0.001284139586869517701405294158948
x1[1] (numeric) = -312994174290.25798705079183120614
absolute error = 312994174290.25927119037870072384
relative error = 24373843582945537.100187866500004 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.508
x2[1] (analytic) = 0.00083293415971170588563803837477598
x2[1] (numeric) = 128346839526.98656082162642607918
absolute error = 128346839526.98572788746671437329
relative error = 15409001783695481.178463189885481 %
h = 0.001
x1[1] (analytic) = 0.0012830559891717968507676151575396
x1[1] (numeric) = -5559642573677.7251265512441919115
absolute error = 5559642573677.7264096072333637084
relative error = 433312546030546536.15320769871422 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=0.46
NO POLE
NO POLE
t[1] = 0.509
x2[1] (analytic) = 0.00083385969584772302873516249155556
x2[1] (numeric) = 909476508149.17723083576601216928
absolute error = 909476508149.17639697607016444625
relative error = 109068289626899329.72012517147899 %
h = 0.001
x1[1] (analytic) = 0.001281973474530155426595559729063
x1[1] (numeric) = 61759254276919.802741728478002898
absolute error = 61759254276919.801459755003472743
relative error = 4817514207893781151.6366857226152 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.51
x2[1] (analytic) = 0.00083478762643653936619953115948893
x2[1] (numeric) = -2196897453344137.6268061971997727
absolute error = 2196897453344137.6276409848262092
relative error = 263168425569751299909.84169222196 %
h = 0.001
x1[1] (analytic) = 0.0012808920418620786970381472243591
x1[1] (numeric) = 243216278518670872.10312222635347
absolute error = 243216278518670872.10184133431161
relative error = 18988038848699430259156.093445197 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 4.676e-05
Order of pole = 3.406
t[1] = 0.511
x2[1] (analytic) = 0.00083571795573059504987431312643056
x2[1] (numeric) = -2648710503393110060.2732435025041
absolute error = 2648710503393110060.2740792204598
relative error = 316938326528783785134818.35325885 %
h = 0.001
x1[1] (analytic) = 0.0012798116900861339038992560756415
x1[1] (numeric) = 288665208555132940889.01693243517
absolute error = 288665208555132940889.01565262348
relative error = 22555287687339782860414540.038094 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.512
x2[1] (analytic) = 0.00083665068799138460946718195917937
x2[1] (numeric) = -1148725493627825941390.7844176365
absolute error = 1148725493627825941390.7852542872
relative error = 137300489931546547034197921.18023 %
h = 0.001
x1[1] (analytic) = 0.0012787324181219691812047754809758
x1[1] (numeric) = 120225511498815605700958.09076191
absolute error = 120225511498815605700958.08948318
relative error = 9401928800349546634057085224.7283 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 4.048e-05
Order of pole = 13.91
t[1] = 0.513
x2[1] (analytic) = 0.00083758582748947453871027492802935
x2[1] (numeric) = -210096106696411492766220.73373276
absolute error = 210096106696411492766220.73457035
relative error = 25083531717118464517858851807.898 %
h = 0.001
x1[1] (analytic) = 0.0012776542248903124748506494008434
x1[1] (numeric) = 20099948297333144918671865.063741
absolute error = 20099948297333144918671865.062463
relative error = 1573191549463137398941932217045.3 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=11.4MB, alloc=4.4MB, time=0.72
t[1] = 0.514
x2[1] (analytic) = 0.0008385233785045209172681139251402
x2[1] (numeric) = -25923957869351262233340807.929845
absolute error = 25923957869351262233340807.930684
relative error = 3091620166343578295757211096374.1 %
h = 0.001
x1[1] (analytic) = 0.0012765771093129704633307325147448
x1[1] (numeric) = 2330446577219046110200347818.4663
absolute error = 2330446577219046110200347818.465
relative error = 1.8255431342280985782980557794469e+32 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.515
x2[1] (analytic) = 0.00083946334532528706846451570820467
x2[1] (numeric) = -2554553462863983425926148214.0911
absolute error = 2554553462863983425926148214.0919
relative error = 3.0430792208969042085516096172102e+32 %
h = 0.001
x1[1] (analytic) = 0.0012755010703128274795433788656077
x1[1] (numeric) = 220162432703007731265300266763.32
absolute error = 220162432703007731265300266763.32
relative error = 1.7260858326760245149315535526630e+34 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.516
x2[1] (analytic) = 0.00084040573224966125289966149752755
x2[1] (numeric) = 382905437799974922008629669691.49
absolute error = 382905437799974922008629669691.49
relative error = 4.5561973592800807775907727531295e+34 %
h = 0.001
x1[1] (analytic) = 0.0012744261068138444336756849984992
x1[1] (numeric) = -48890300214412641155527495449107
absolute error = 48890300214412641155527495449107
relative error = 3.8362600980171267683128998828691e+36 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.517
x2[1] (analytic) = 0.0008413505435846743980286389764889
x2[1] (numeric) = 2.8381007123517247585891510895531e+32
absolute error = 2.8381007123517247585891510895531e+32
relative error = 3.3732678180246463901030732139499e+37 %
h = 0.001
x1[1] (analytic) = 0.0012733522177410577371643104777951
x1[1] (numeric) = -3.0319464357000671925991849933332e+34
absolute error = 3.0319464357000671925991849933332e+34
relative error = 2.3810744532873841505443331732903e+39 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.518
x2[1] (analytic) = 0.00084229778364651786377291305301299
x2[1] (numeric) = 8.9157816957575197449331205416986e+34
absolute error = 8.9157816957575197449331205416986e+34
relative error = 1.0585070825140806962302190866050e+40 %
h = 0.001
x1[1] (analytic) = 0.0012722794020205782277317997435378
x1[1] (numeric) = -9.1081973266512989405817711648826e+36
absolute error = 9.1081973266512989405817711648826e+36
relative error = 7.1589599833071731453862167182889e+41 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.519
x2[1] (analytic) = 0.00084324745676056124423632533367627
x2[1] (numeric) = 1.8009848306206213036086093015404e+37
absolute error = 1.8009848306206213036086093015404e+37
relative error = 2.1357726206958582532697140156487e+42 %
h = 0.001
x1[1] (analytic) = 0.0012712076585795900954973303432135
x1[1] (numeric) = -1.7559642038875284665895426053970e+39
absolute error = 1.7559642038875284665895426053970e+39
relative error = 1.3813354506136243877587970009341e+44 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.4MB, time=0.98
NO POLE
NO POLE
t[1] = 0.52
x2[1] (analytic) = 0.00084419956726137020559736614303792
x2[1] (numeric) = 2.9381939395914476076660439601372e+39
absolute error = 2.9381939395914476076660439601372e+39
relative error = 3.4804494737223216476110748347130e+44 %
h = 0.001
x1[1] (analytic) = 0.00127013698634634981016081364961
x1[1] (numeric) = -2.7892033589816468170502798269432e+41
absolute error = 2.7892033589816468170502798269432e+41
relative error = 2.1959862510617948384657702762582e+46 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.521
x2[1] (analytic) = 0.00084515411949272436024960708923766
x2[1] (numeric) = 2.8828164769390235485375509891162e+41
absolute error = 2.8828164769390235485375509891162e+41
relative error = 3.4109950013251289835990483116487e+46 %
h = 0.001
x1[1] (analytic) = 0.0012690673842501850492592752487639
x1[1] (numeric) = -2.4393714556513207592439195132267e+43
absolute error = 2.4393714556513207592439195132267e+43
relative error = 1.9221764627515011025020683649732e+48 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.522
x2[1] (analytic) = 0.00084611111780763517726232663345645
x2[1] (numeric) = -3.0835833708071225386080135199334e+43
absolute error = 3.0835833708071225386080135199334e+43
relative error = 3.6444189254917467461904399926535e+48 %
h = 0.001
x1[1] (analytic) = 0.0012679988512214936274944432542899
x1[1] (numeric) = 4.1253436949404049769512496557223e+45
absolute error = 4.1253436949404049769512496557223e+45
relative error = 3.2534285744552234457829858504083e+50 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.523
x2[1] (analytic) = 0.00084707056656836392923350586605222
x2[1] (numeric) = -2.4179029109238865073572390611867e+46
absolute error = 2.4179029109238865073572390611867e+46
relative error = 2.8544291424494284036261216292873e+51 %
h = 0.001
x1[1] (analytic) = 0.0012669313861917424271304738755899
x1[1] (numeric) = 2.5842606842144773750490515703002e+48
absolute error = 2.5842606842144773750490515703002e+48
relative error = 2.0397795116454436788853390183402e+53 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.524
x2[1] (analytic) = 0.00084803247014643967560751672664236
x2[1] (numeric) = -7.5370057230450261713434077256891e+48
absolute error = 7.5370057230450261713434077256891e+48
relative error = 8.8876381369495478465011152451617e+53 %
h = 0.001
x1[1] (analytic) = 0.0012658649880934663294607446375807
x1[1] (numeric) = 7.6927800284125934656558547695650e+50
absolute error = 7.6927800284125934656558547695650e+50
relative error = 6.0770936085362286931950614293304e+55 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.525
memory used=19.0MB, alloc=4.4MB, time=1.24
x2[1] (analytic) = 0.00084899683292267728252997022968994
x2[1] (numeric) = -1.6630429620249270359034525997113e+51
absolute error = 1.6630429620249270359034525997113e+51
relative error = 1.9588329396941217116064425131979e+56 %
h = 0.001
x1[1] (analytic) = 0.0012647996558602671473426467186411
x1[1] (numeric) = 1.6416074541388392284185299124989e+53
absolute error = 1.6416074541388392284185299124989e+53
relative error = 1.2979189601552209366185063099501e+58 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 0.0001646
Order of pole = 132
t[1] = 0.526
x2[1] (analytic) = 0.00084996365928719547931233787183942
x2[1] (numeric) = -2.8630998538135398916237853552101e+53
absolute error = 2.8630998538135398916237853552101e+53
relative error = 3.3684967851621087282827986521779e+58 %
h = 0.001
x1[1] (analytic) = 0.0012637353884268125587993089414852
x1[1] (numeric) = 2.7376577430826790481709854581064e+55
absolute error = 2.7376577430826790481709854581064e+55
relative error = 2.1663219754340420691398793662625e+60 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.527
x2[1] (analytic) = 0.00085093295363943495157910530292247
x2[1] (numeric) = -2.9880365775222779343038163266641e+55
absolute error = 2.9880365775222779343038163266641e+55
relative error = 3.5114829725919816267282456525505e+60 %
h = 0.001
x1[1] (analytic) = 0.0012626721847288350416871870185942
x1[1] (numeric) = 2.5706771161701424940197997037491e+57
absolute error = 2.5706771161701424940197997037491e+57
relative error = 2.0359022296212281236273554486349e+62 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.528
x2[1] (analytic) = 0.00085190472038817647117036353980059
x2[1] (numeric) = 1.7868398786828264852282109970259e+57
absolute error = 1.7868398786828264852282109970259e+57
relative error = 2.0974644651207474595896184122519e+62 %
h = 0.001
x1[1] (analytic) = 0.0012616100437031308094284527197097
x1[1] (numeric) = -2.7141382543996044438799734441813e+59
absolute error = 2.7141382543996044438799734441813e+59
relative error = 2.1513289846939960936290617329388e+64 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.529
x2[1] (analytic) = 0.00085287896395155906287288949160932
x2[1] (numeric) = 1.9955262286732546922595035794772e+60
absolute error = 1.9955262286732546922595035794772e+60
relative error = 2.3397531338181703901278884762703e+65 %
h = 0.001
x1[1] (analytic) = 0.001260548964287558747807118693686
x1[1] (numeric) = -2.1521239883380276264544158041182e+62
absolute error = 2.1521239883380276264544158041182e+62
relative error = 1.7072910686610037502739798855189e+67 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.53
x2[1] (analytic) = 0.00085385568875709820805291434710783
x2[1] (numeric) = 6.5614045677978813135363625682398e+62
absolute error = 6.5614045677978813135363625682398e+62
relative error = 7.6844420599327365493580244109066e+67 %
h = 0.001
x1[1] (analytic) = 0.0012594889454210393528278357407412
x1[1] (numeric) = -6.7241226907398039841891773599469e+64
absolute error = 6.7241226907398039841891773599469e+64
relative error = 5.3387707094896108197039126570093e+69 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=1.51
NO POLE
NO POLE
t[1] = 0.531
x2[1] (analytic) = 0.00085483489924170408526392545030159
x2[1] (numeric) = 1.5232678875418984436709413809022e+65
absolute error = 1.5232678875418984436709413809022e+65
relative error = 1.7819439623875198247497978244760e+70 %
h = 0.001
x1[1] (analytic) = 0.0012584299860435536696363003938124
x1[1] (numeric) = -1.5126890724578338356993707388052e+67
absolute error = 1.5126890724578338356993707388052e+67
relative error = 1.2020446820515292288412036371000e+72 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 4.471e-05
Order of pole = 16.11
t[1] = 0.532
x2[1] (analytic) = 0.00085581659985169984790299465988337
x2[1] (numeric) = 2.7031305542048032948968587726712e+67
absolute error = 2.7031305542048032948968587726712e+67
relative error = 3.1585395219877894240565682962974e+72 %
h = 0.001
x1[1] (analytic) = 0.001257372085096142232500211729337
x1[1] (numeric) = -2.5950937522616787181116193549241e+69
absolute error = 2.5950937522616787181116193549241e+69
relative error = 2.0639027882213962912884316359254e+74 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.533
x2[1] (analytic) = 0.0008568007950428399389892738519192
x2[1] (numeric) = 3.0917676683037028372394862651691e+69
absolute error = 3.0917676683037028372394862651691e+69
relative error = 3.6085023335548081715159309117171e+74 %
h = 0.001
x1[1] (analytic) = 0.0012563152415209040058497173883259
x1[1] (numeric) = -2.7262425864120028721874692454044e+71
absolute error = 2.7262425864120028721874692454044e+71
relative error = 2.1700306549744589233989780426184e+76 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.534
x2[1] (analytic) = 0.00085778748928032844313844618417794
x2[1] (numeric) = -6.4053877518790548671826806180032e+70
absolute error = 6.4053877518790548671826806180032e+70
relative error = 7.4673364113215086500356853463122e+75 %
h = 0.001
x1[1] (analytic) = 0.0012552594542609953263762898480893
x1[1] (numeric) = 1.4776029553879756872485320604502e+73
absolute error = 1.4776029553879756872485320604502e+73
relative error = 1.1771295172262852239891540744593e+78 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.535
x2[1] (analytic) = 0.00085877668703883747580706999516187
x2[1] (numeric) = -1.6296499950062552754683335399836e+74
absolute error = 1.6296499950062552754683335399836e+74
relative error = 1.8976411674907934273434809597401e+79 %
h = 0.001
x1[1] (analytic) = 0.0012542047222606288461889750434006
x1[1] (numeric) = 1.7782087202786389312292695741353e+76
absolute error = 1.7782087202786389312292695741353e+76
relative error = 1.4177978193811328366492309253926e+81 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.536
x2[1] (analytic) = 0.00085976839280252560988090076182799
x2[1] (numeric) = -5.7198816544976968685684836788736e+76
absolute error = 5.7198816544976968685684836788736e+76
relative error = 6.6528168543774995686085248483473e+81 %
h = 0.001
x1[1] (analytic) = 0.0012531510444650724770269564932605
x1[1] (numeric) = 5.8890705981453487160301290157988e+78
absolute error = 5.8890705981453487160301290157988e+78
relative error = 4.6994100385234826080938635211753e+83 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.4MB, time=1.76
NO POLE
NO POLE
t[1] = 0.537
x2[1] (analytic) = 0.00086076261106505633968142538779503
x2[1] (numeric) = -1.3811599191741633169149401593430e+79
absolute error = 1.3811599191741633169149401593430e+79
relative error = 1.6045770360136790470038428720869e+84 %
h = 0.001
x1[1] (analytic) = 0.0012520984198206483355273791457368
x1[1] (numeric) = 1.3773922897840372633500847906328e+81
absolute error = 1.3773922897840372633500847906328e+81
relative error = 1.1000671097255566623196829994334e+86 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 2.915e-05
Order of pole = 0.8698
t[1] = 0.538
x2[1] (analytic) = 0.0008617593463296165824649922390997
x2[1] (numeric) = -2.5354217358792180589193414722630e+81
absolute error = 2.5354217358792180589193414722630e+81
relative error = 2.9421459096185282092403628724800e+86 %
h = 0.001
x1[1] (analytic) = 0.0012510468472747316895473782086164
x1[1] (numeric) = 2.4456562024293990765632852230001e+83
absolute error = 2.4456562024293990765632852230001e+83
relative error = 1.9548877867819201274284123246376e+88 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.539
x2[1] (analytic) = 0.00086275860310893521748906978789598
x2[1] (numeric) = -3.1512144899275561941372511125483e+83
absolute error = 3.1512144899275561941372511125483e+83
relative error = 3.6524868932888192133632734783326e+88 %
h = 0.001
x1[1] (analytic) = 0.0012499963257757499055392592878095
x1[1] (numeric) = 2.8344150891632112552218853228415e+85
absolute error = 2.8344150891632112552218853228415e+85
relative error = 2.2675387364872199080947802956975e+90 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 8.426e-05
Order of pole = 12.51
t[1] = 0.54
x2[1] (analytic) = 0.0008637603859253016627203164664802
x2[1] (numeric) = -2.8973468742378521291582873570235e+84
absolute error = 2.8973468742378521291582873570235e+84
relative error = 3.3543409971667950795739810691033e+89 %
h = 0.001
x1[1] (analytic) = 0.0012489468542731813969777772086
x1[1] (numeric) = -4.6915647451505550827772955634034e+86
absolute error = 4.6915647451505550827772955634034e+86
relative error = 3.7564166394260135088088623972110e+91 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.541
x2[1] (analytic) = 0.00086476469931058448925929437526969
x2[1] (numeric) = 1.3109067108457221718202132694702e+88
absolute error = 1.3109067108457221718202132694702e+88
relative error = 1.5159114518559962491984230035665e+93 %
h = 0.001
x1[1] (analytic) = 0.0012478984317175545738384619469313
x1[1] (numeric) = -1.4505335378807750092412584872553e+90
absolute error = 1.4505335378807750092412584872553e+90
relative error = 1.1623810888874361781826351735272e+95 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.5MB, time=2.02
NO POLE
NO POLE
t[1] = 0.542
x2[1] (analytic) = 0.00086577154780625007355680982946525
x2[1] (numeric) = 4.9620873081344920758850029649559e+90
absolute error = 4.9620873081344920758850029649559e+90
relative error = 5.7314049193551823181722389315928e+95 %
h = 0.001
x1[1] (analytic) = 0.001246851057060446793125941148968
x1[1] (numeric) = -5.1346054806778018480955532204282e+92
absolute error = 5.1346054806778018480955532204282e+92
relative error = 4.1180584093043588151265370917093e+97 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.543
x2[1] (analytic) = 0.00086678093596338128749701437068642
x2[1] (numeric) = 1.2446130856122418838612558386458e+93
absolute error = 1.2446130856122418838612558386458e+93
relative error = 1.4359026992545931951455850020606e+98 %
h = 0.001
x1[1] (analytic) = 0.0012458047292544833104512097671668
x1[1] (numeric) = -1.2460386419338376224795093569785e+95
absolute error = 1.2460386419338376224795093569785e+95
relative error = 1.0001877603077444492214746155896e+100 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.544
x2[1] (analytic) = 0.00086779286834269622642255081248739
x2[1] (numeric) = 2.3677701091072226257633632203015e+95
absolute error = 2.3677701091072226257633632203015e+95
relative error = 2.7284968515922131903449811568090e+100 %
h = 0.001
x1[1] (analytic) = 0.00124475944725333623265679839004
x1[1] (numeric) = -2.2951946086995204474539512870810e+97
absolute error = 2.2951946086995204474539512870810e+97
relative error = 1.8438860727380342559779410628511e+102 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.545
x2[1] (analytic) = 0.00086880734951456697517718013294248
x2[1] (numeric) = 3.1567592003226709419783231221908e+97
absolute error = 3.1567592003226709419783231221908e+97
relative error = 3.6334397977715803319598945328408e+102 %
h = 0.001
x1[1] (analytic) = 0.0012437152100117234714887928906918
x1[1] (numeric) = -2.8826980634783566466984404195411e+99
absolute error = 2.8826980634783566466984404195411e+99
relative error = 2.3178120202061240720559913973579e+104 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.546
x2[1] (analytic) = 0.00086982438405903841224147657403825
x2[1] (numeric) = 1.0394559714278914022168365891816e+99
absolute error = 1.0394559714278914022168365891816e+99
relative error = 1.1950182019240097837675458929898e+104 %
h = 0.001
x1[1] (analytic) = 0.0012426720164854076983146590660609
x1[1] (numeric) = -3.5440795930613496206992793798774e+100
absolute error = 3.5440795930613496206992793798774e+100
relative error = 2.8519831025767422344893318367091e+105 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.547
x2[1] (analytic) = 0.00087084397656584705203733015703041
x2[1] (numeric) = -1.0336800401868840538674860002611e+102
absolute error = 1.0336800401868840538674860002611e+102
relative error = 1.1869864958625277834792693845628e+107 %
h = 0.001
x1[1] (analytic) = 0.0012416298656311952998858269846059
x1[1] (numeric) = 1.1640364577113484320860326422200e+104
absolute error = 1.1640364577113484320860326422200e+104
relative error = 9.3750681256333870350735344143879e+108 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.5MB, time=2.28
NO POLE
NO POLE
t[1] = 0.548
x2[1] (analytic) = 0.0008718661316344399254771479758239
x2[1] (numeric) = -4.2786480111082964303931894852392e+104
absolute error = 4.2786480111082964303931894852392e+104
relative error = 4.9074598219423297986534585238744e+109 %
h = 0.001
x1[1] (analytic) = 0.0012405887564069353351439908049313
x1[1] (numeric) = 4.4516532312116311948088458634225e+106
absolute error = 4.4516532312116311948088458634225e+106
relative error = 3.5883391722046279703323742247368e+111 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.549
x2[1] (analytic) = 0.00087289085387399349883379808742284
x2[1] (numeric) = -1.1162439060400833274411264756040e+107
absolute error = 1.1162439060400833274411264756040e+107
relative error = 1.2787897834947634286776322150299e+112 %
h = 0.001
x1[1] (analytic) = 0.0012395486877715184930700808715671
x1[1] (numeric) = 1.1218122900984245712270368944498e+109
absolute error = 1.1218122900984245712270368944498e+109
relative error = 9.0501672194517635248696773917288e+113 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.55
x2[1] (analytic) = 0.00087391814790343263100749258018221
x2[1] (numeric) = -2.2005067776163207475233403666272e+109
absolute error = 2.2005067776163207475233403666272e+109
relative error = 2.5179781228887757003432797034187e+114 %
h = 0.001
x1[1] (analytic) = 0.0012385096586848760515748659367868
x1[1] (numeric) = 2.1431805553893224350187082181441e+111
absolute error = 2.1431805553893224350187082181441e+111
relative error = 1.7304512244701266858919527471475e+116 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.551
x2[1] (analytic) = 0.0008749480183514495692659594675856
x2[1] (numeric) = -3.1170281801300013059078417600079e+111
absolute error = 3.1170281801300013059078417600079e+111
relative error = 3.5625295614738472680677707043461e+116 %
h = 0.001
x1[1] (analytic) = 0.0012374716681079788374301443989802
x1[1] (numeric) = 2.8808558122645671707565555799648e+113
absolute error = 2.8808558122645671707565555799648e+113
relative error = 2.3280175914404777610762139153184e+118 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.552
x2[1] (analytic) = 0.00087598046985652298353440642818536
x2[1] (numeric) = -1.6365027091050105676264309846931e+113
absolute error = 1.6365027091050105676264309846931e+113
relative error = 1.8681954283444854356855231685604e+118 %
h = 0.001
x1[1] (analytic) = 0.0012364347150028361872394844886841
x1[1] (numeric) = 1.0215280512870817284279412689250e+115
absolute error = 1.0215280512870817284279412689250e+115
relative error = 8.2618842619987299803058620601827e+119 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.553
x2[1] (analytic) = 0.00087701550706693703931193309178555
x2[1] (numeric) = 7.9417437826979721212764438461717e+115
absolute error = 7.9417437826979721212764438461717e+115
relative error = 9.0554200224555768490502515799165e+120 %
h = 0.001
x1[1] (analytic) = 0.0012353987983324949094474743729255
x1[1] (numeric) = -9.1527953728361935997546199878268e+117
absolute error = 9.1527953728361935997546199878268e+117
relative error = 7.4087779470000849451614746147866e+122 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.5MB, time=2.57
NO POLE
NO POLE
t[1] = 0.554
x2[1] (analytic) = 0.00087805313464080050929120255853851
x2[1] (numeric) = 3.6645166167290946724325100483841e+118
absolute error = 3.6645166167290946724325100483841e+118
relative error = 4.1734565622024664191546045743876e+123 %
h = 0.001
x1[1] (analytic) = 0.0012343639170610382473864441870416
x1[1] (numeric) = -3.8355325698308304158095289245187e+120
absolute error = 3.8355325698308304158095289245187e+120
relative error = 3.1072947911204752007073680062923e+125 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.555
x2[1] (analytic) = 0.00087909335724606592375833713197844
x2[1] (numeric) = 9.9664217254733075966557119725876e+120
absolute error = 9.9664217254733075966557119725876e+120
relative error = 1.1337159635348739119396953800022e+126 %
h = 0.001
x1[1] (analytic) = 0.0012333300701535848433596230406101
x1[1] (numeric) = -1.0055051605594930505268745833023e+123
absolute error = 1.0055051605594930505268745833023e+123
relative error = 8.1527661158401734244749180927461e+127 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.556
x2[1] (analytic) = 0.00088013617956054875985015784974602
x2[1] (numeric) = 2.0349015806649733577525019467788e+123
absolute error = 2.0349015806649733577525019467788e+123
relative error = 2.3120303743007110251995925703477e+128 %
h = 0.001
x1[1] (analytic) = 0.0012322972565762877037596950805625
x1[1] (numeric) = -1.9908053728133400234494710353380e+125
absolute error = 1.9908053728133400234494710353380e+125
relative error = 1.6155236589136197862999057404919e+130 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.557
x2[1] (analytic) = 0.00088118160627194666974604230748542
x2[1] (numeric) = 3.0419166594856722537739586191418e+125
absolute error = 3.0419166594856722537739586191418e+125
relative error = 3.4520882390580544568160687826249e+130 %
h = 0.001
x1[1] (analytic) = 0.0012312654752963331652217197299492
x1[1] (numeric) = -2.8396072241410448439552316261581e+127
absolute error = 2.8396072241410448439552316261581e+127
relative error = 2.3062509922627581087841975403014e+132 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.558
x2[1] (analytic) = 0.00088222964207785874787183049273793
x2[1] (numeric) = 2.1011642309653974303792993030826e+127
absolute error = 2.1011642309653974303792993030826e+127
relative error = 2.3816522714161592029807769241411e+132 %
h = 0.001
x1[1] (analytic) = 0.0012302347252819398618093822551908
x1[1] (numeric) = -1.5518635561074817518517493781388e+129
absolute error = 1.5518635561074817518517493781388e+129
relative error = 1.2614369633826035829986926599933e+134 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=41.9MB, alloc=4.6MB, time=2.85
t[1] = 0.559
x2[1] (analytic) = 0.00088328029168580483719336387723487
x2[1] (numeric) = -5.8864760083894036921995792288383e+129
absolute error = 5.8864760083894036921995792288383e+129
relative error = 6.6643352781647998095723131308019e+134 %
h = 0.001
x1[1] (analytic) = 0.00122920500550235769323354184798
x1[1] (numeric) = 7.0063582995167713224599649802118e+131
absolute error = 7.0063582995167713224599649802118e+131
relative error = 5.6999103226506773954561936142385e+136 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.56
x2[1] (analytic) = 0.00088433355981324487467739885842914
x2[1] (numeric) = -3.1150418412916309484379017667828e+132
absolute error = 3.1150418412916309484379017667828e+132
relative error = 3.5224738524561603137609496909233e+137 %
h = 0.001
x1[1] (analytic) = 0.0012281763149278667941020454402963
x1[1] (numeric) = 3.2820619556199126748136745143039e+134
absolute error = 3.2820619556199126748136745143039e+134
relative error = 2.6723052022157540272931241106321e+139 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.561
x2[1] (analytic) = 0.00088538945118759827599779179502061
x2[1] (numeric) = -8.8585161934434118012299808277280e+134
absolute error = 8.8585161934434118012299808277280e+134
relative error = 1.0005219941982852683813228783520e+140 %
h = 0.001
x1[1] (analytic) = 0.0012271486525297765041997765022611
x1[1] (numeric) = 8.9728370843019973267850755624201e+136
absolute error = 8.9728370843019973267850755624201e+136
relative error = 7.3119398092516532509873580393713e+141 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.562
x2[1] (analytic) = 0.00088644797054626335956500934725191
x2[1] (numeric) = -1.8726427819414007399244281419497e+137
absolute error = 1.8726427819414007399244281419497e+137
relative error = 2.1125241911123178251793611149196e+142 %
h = 0.001
x1[1] (analytic) = 0.0012261220172804243397979091027969
x1[1] (numeric) = 1.8399057373849162928251911630766e+139
absolute error = 1.8399057373849162928251911630766e+139
relative error = 1.5005894286654135605363417501609e+144 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.563
x2[1] (analytic) = 0.00088750912263663680995717461150232
x2[1] (numeric) = -2.9395178941495789436746070558382e+139
absolute error = 2.9395178941495789436746070558382e+139
relative error = 3.3120987933248250417749318243079e+144 %
h = 0.001
x1[1] (analytic) = 0.0012250964081531749659913385422579
x1[1] (numeric) = 2.7674779169372311921723813704946e+141
absolute error = 2.7674779169372311921723813704946e+141
relative error = 2.2589878629300583200250662679777e+146 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.564
x2[1] (analytic) = 0.00088857291221613318083101663081396
x2[1] (numeric) = -2.4512183399346446864644012444757e+141
absolute error = 2.4512183399346446864644012444757e+141
relative error = 2.7586012427738956611579485597826e+146 %
h = 0.001
x1[1] (analytic) = 0.0012240718241224191700632608943781
x1[1] (numeric) = 1.9628765041616965203023004407598e+143
absolute error = 1.9628765041616965203023004407598e+143
relative error = 1.6035631778134855973372754296046e+148 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.6MB, time=3.12
NO POLE
NO POLE
t[1] = 0.565
x2[1] (analytic) = 0.00088963934405220443739124826907637
x2[1] (numeric) = 4.1349561252277888163910844011948e+143
absolute error = 4.1349561252277888163910844011948e+143
relative error = 4.6479015939128111769200036786600e+148 %
h = 0.001
x1[1] (analytic) = 0.00122304826416357283587587482203
x1[1] (numeric) = -5.1656956429018182233333412262481e+145
absolute error = 5.1656956429018182233333412262481e+145
relative error = 4.2236237066527965865814509389766e+150 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.566
x2[1] (analytic) = 0.00089070842292235953849705515730068
x2[1] (numeric) = 2.6256741133277481488811813978577e+146
absolute error = 2.6256741133277481488811813978577e+146
relative error = 2.9478492015524821430040564240975e+151 %
h = 0.001
x1[1] (analytic) = 0.001222025727253075919286180057411
x1[1] (numeric) = -2.7871501762237413458207269548624e+148
absolute error = 2.7871501762237413458207269548624e+148
relative error = 2.2807622737115544677300702103725e+153 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.567
x2[1] (analytic) = 0.00089178015361418405848453645636232
x2[1] (numeric) = 7.8372906747422933163871804716262e+148
absolute error = 7.8372906747422933163871804716262e+148
relative error = 8.7883663288306202269755423316535e+153 %
h = 0.001
x1[1] (analytic) = 0.0012210042123683914245858479623694
x1[1] (numeric) = -7.9710262956275324452157288421030e+150
absolute error = 7.9710262956275324452157288421030e+150
relative error = 6.5282545423541744950989911622369e+155 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.568
x2[1] (analytic) = 0.00089285454092535984878409653241629
x2[1] (numeric) = 1.7152628492274580523953085865779e+151
absolute error = 1.7152628492274580523953085865779e+151
relative error = 1.9210999895344086580784130411093e+156 %
h = 0.001
x1[1] (analytic) = 0.0012199837184880043819641406086574
x1[1] (numeric) = -1.6922048878529728536450440697855e+153
absolute error = 1.6922048878529728536450440697855e+153
relative error = 1.3870716979323455093485261321511e+158 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 2.892e-05
Order of pole = 2.819
t[1] = 0.569
x2[1] (analytic) = 0.00089393158966368473941194530952011
x2[1] (numeric) = 2.8164341883122487568130440727767e+153
absolute error = 2.8164341883122487568130440727767e+153
relative error = 3.1506149026144703408439097857569e+158 %
h = 0.001
x1[1] (analytic) = 0.0012189642445914208259928558409419
x1[1] (numeric) = -2.6713586668953363351519572787877e+155
absolute error = 2.6713586668953363351519572787877e+155
relative error = 2.1914987898523119523882924836857e+160 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.57
x2[1] (analytic) = 0.00089501130464709228041502404947533
x2[1] (numeric) = 2.7030001957150697518182953492705e+155
absolute error = 2.7030001957150697518182953492705e+155
relative error = 3.0200738042977871783098319226694e+160 %
h = 0.001
x1[1] (analytic) = 0.0012179457896591667751322768074366
x1[1] (numeric) = -2.2708764354108825201033201999193e+157
absolute error = 2.2708764354108825201033201999193e+157
relative error = 1.8645135560970826856238613084162e+162 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.6MB, time=3.39
NO POLE
NO POLE
t[1] = 0.571
x2[1] (analytic) = 0.00089609369070367152334883261215016
x2[1] (numeric) = -2.6538851007375019792137286905298e+157
absolute error = 2.6538851007375019792137286905298e+157
relative error = 2.9616156527711933573089614836187e+162 %
h = 0.001
x1[1] (analytic) = 0.0012169283526727872122571054640167
x1[1] (numeric) = 3.5981871445297746493732663902938e+159
absolute error = 3.5981871445297746493732663902938e+159
relative error = 2.9567781345770569498149087675934e+164 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.572
x2[1] (analytic) = 0.00089717875267168684286779387121317
x2[1] (numeric) = -2.1918964291886309942617622092065e+160
absolute error = 2.1918964291886309942617622092065e+160
relative error = 2.4430989060557172036542352122001e+165 %
h = 0.001
x1[1] (analytic) = 0.0012159119326148450662013605776668
x1[1] (numeric) = 2.3466663967973498245221392136330e+162
absolute error = 2.3466663967973498245221392136330e+162
relative error = 1.9299641148769653742853155644113e+167 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.573
x2[1] (analytic) = 0.00089826649539959779850795090092798
x2[1] (numeric) = -6.9003364019415514610655524615401e+162
absolute error = 6.9003364019415514610655524615401e+162
relative error = 7.6818365566133093771297524541791e+167 %
h = 0.001
x1[1] (analytic) = 0.0012148965284689201943212217740738
x1[1] (numeric) = 7.0480849882964382110846393523429e+164
absolute error = 7.0480849882964382110846393523429e+164
relative error = 5.8013870507793982829626987112047e+169 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.574
x2[1] (analytic) = 0.00089935692374607903674195281006981
x2[1] (numeric) = -1.5639852269764528298734051521815e+165
absolute error = 1.5639852269764528298734051521815e+165
relative error = 1.7390039323453547831740155317034e+170 %
h = 0.001
x1[1] (analytic) = 0.0012138821392196083660748021921261
x1[1] (numeric) = 1.5491116635582366716679371800497e+167
absolute error = 1.5491116635582366716679371800497e+167
relative error = 1.2761631574496546454379933787072e+172 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 0.0003571
Order of pole = 314
t[1] = 0.575
x2[1] (analytic) = 0.00090045004258004023338644567976864
x2[1] (numeric) = -2.6782002001458911257312341891187e+167
absolute error = 2.6782002001458911257312341891187e+167
relative error = 2.9742907140879258749288119698960e+172 %
h = 0.001
x1[1] (analytic) = 0.0012128687638525202476178333250037
x1[1] (numeric) = 2.5570352931855616862860262283403e+169
absolute error = 2.5570352931855616862860262283403e+169
relative error = 2.1082538930786467581879319872561e+174 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.576
x2[1] (analytic) = 0.00090154585678064607644214596380192
x2[1] (numeric) = -2.8713355555072083205406238430460e+169
absolute error = 2.8713355555072083205406238430460e+169
relative error = 3.1849023917214109679098760653181e+174 %
h = 0.001
x1[1] (analytic) = 0.0012118564013542803874142466434628
x1[1] (numeric) = 2.4907978629577821573397962173010e+171
absolute error = 2.4907978629577821573397962173010e+171
relative error = 2.0553572685462172906116081806172e+176 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.6MB, time=3.67
NO POLE
NO POLE
t[1] = 0.577
x2[1] (analytic) = 0.00090264437123733628944703493319481
x2[1] (numeric) = 1.4127678586122844730489323127047e+171
absolute error = 1.4127678586122844730489323127047e+171
relative error = 1.5651433760958103307263050730186e+176 %
h = 0.001
x1[1] (analytic) = 0.0012108450507125262028606376118103
x1[1] (numeric) = -2.2739598558636747847222978225459e+173
absolute error = 2.2739598558636747847222978225459e+173
relative error = 1.8779940955496781217593351145454e+178 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.578
x2[1] (analytic) = 0.00090374559084984569542327429258224
x2[1] (numeric) = 1.8092509461861444618720258007312e+174
absolute error = 1.8092509461861444618720258007312e+174
relative error = 2.0019471901210585822973972742013e+179 %
h = 0.001
x1[1] (analytic) = 0.0012098347109159069679235987209479
x1[1] (numeric) = -1.9564689662597984057374685306933e+176
absolute error = 1.9564689662597984057374685306933e+176
relative error = 1.6171374061326534327740329796935e+181 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.579
x2[1] (analytic) = 0.00090484952052822432149860496429206
x2[1] (numeric) = 6.0445820046076656227896265059928e+176
absolute error = 6.0445820046076656227896265059928e+176
relative error = 6.6802068934943103788166796719799e+181 %
h = 0.001
x1[1] (analytic) = 0.0012088253809540828017889091757341
x1[1] (numeric) = -6.2017419422196130223538839343644e+178
absolute error = 6.2017419422196130223538839343644e+178
relative error = 5.1303869358904419100617446987211e+183 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.58
x2[1] (analytic) = 0.00090595616519285754428315322816622
x2[1] (numeric) = 1.4197258370614728926162059243511e+179
absolute error = 1.4197258370614728926162059243511e+179
relative error = 1.5671021309946551597136936817075e+184 %
h = 0.001
x1[1] (analytic) = 0.0012078170598177236585215698857712
x1[1] (numeric) = -1.4117122440387761132198090843311e+181
absolute error = 1.4117122440387761132198090843311e+181
relative error = 1.1688129692851192755413152833199e+186 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 4.543e-05
Order of pole = 16.38
t[1] = 0.581
x2[1] (analytic) = 0.00090706552977448627608273092139788
x2[1] (numeric) = 2.5295011941253122571812011998517e+181
absolute error = 2.5295011941253122571812011998517e+181
relative error = 2.7886642266674981152595006544294e+186 %
h = 0.001
x1[1] (analytic) = 0.0012068097464985083177356734195659
x1[1] (numeric) = -2.4294352403996662732452371324061e+183
absolute error = 2.4294352403996662732452371324061e+183
relative error = 2.0131054190178179729301728345114e+188 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=57.2MB, alloc=4.6MB, time=3.94
t[1] = 0.582
x2[1] (analytic) = 0.00090817761921422719202987924377588
x2[1] (numeric) = 2.9694828921665853778348993531584e+183
absolute error = 2.9694828921665853778348993531584e+183
relative error = 3.2697159997576677789409880436311e+188 %
h = 0.001
x1[1] (analytic) = 0.0012058034399891233762730995918507
x1[1] (numeric) = -2.6360659723035981709490424352775e+185
absolute error = 2.6360659723035981709490424352775e+185
relative error = 2.1861489898613791406356479389839e+190 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.583
x2[1] (analytic) = 0.00090929243846359299821406888034318
x2[1] (numeric) = -3.8366778695190664222424782899994e+184
absolute error = 3.8366778695190664222424782899994e+184
relative error = 4.2194102878517256031573963250417e+189 %
h = 0.001
x1[1] (analytic) = 0.0012047981392832622408900283626774
x1[1] (numeric) = 1.1655761457764713502850485830256e+187
absolute error = 1.1655761457764713502850485830256e+187
relative error = 9.6744517423464468207740085193811e+191 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.584
x2[1] (analytic) = 0.00091040999248451274089263264624774
x2[1] (numeric) = -1.4733987039421769273307992841632e+188
absolute error = 1.4733987039421769273307992841632e+188
relative error = 1.6183903033854731743799274789541e+193 %
h = 0.001
x1[1] (analytic) = 0.0012037938433756241219502627347115
x1[1] (numeric) = 1.6124807536506692665198483295023e+190
absolute error = 1.6124807536506692665198483295023e+190
relative error = 1.3394990865952793366000938922985e+195 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.585
x2[1] (analytic) = 0.00091153028624935215686417067814311
x2[1] (numeric) = -5.2664589954474224991124817367288e+190
absolute error = 5.2664589954474224991124817367288e+190
relative error = 5.7776017702244125284113421428549e+195 %
h = 0.001
x1[1] (analytic) = 0.0012027905512619130281243553419666
x1[1] (numeric) = 5.4291529538277003792731555963132e+192
absolute error = 5.4291529538277003792731555963132e+192
relative error = 4.5137974754887129256537002721267e+197 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.586
x2[1] (analytic) = 0.0009126533247409340650863323435399
x2[1] (numeric) = -1.2831318889292172269235434114965e+193
absolute error = 1.2831318889292172269235434114965e+193
relative error = 1.4059356977562616921285736018315e+198 %
h = 0.001
x1[1] (analytic) = 0.0012017882619388367620935334290215
x1[1] (numeric) = 1.2808088115399740649047412076587e+195
absolute error = 1.2808088115399740649047412076587e+195
relative error = 1.0657524724643707136885686081884e+200 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.587
x2[1] (analytic) = 0.00091377911295255879962004351467114
x2[1] (numeric) = -2.3742916492168930889440382274940e+195
absolute error = 2.3742916492168930889440382274940e+195
relative error = 2.5983212086619018244682270807470e+200 %
h = 0.001
x1[1] (analytic) = 0.0012007869744041059172574179245617
x1[1] (numeric) = 2.2927493987497574454898435346131e+197
absolute error = 2.2927493987497574454898435346131e+197
relative error = 1.9093723096784432614117627729653e+202 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=61.0MB, alloc=4.6MB, time=4.23
t[1] = 0.588
x2[1] (analytic) = 0.00091490765588802468398241265737402
x2[1] (numeric) = -3.0091915857827392239367176414397e+197
absolute error = 3.0091915857827392239367176414397e+197
relative error = 3.2890659143757710768370917202902e+202 %
h = 0.001
x1[1] (analytic) = 0.0011997866876564328754445333168804
x1[1] (numeric) = 2.7186271433845339062407741966360e+199
absolute error = 2.7186271433845339062407741966360e+199
relative error = 2.2659254110369254106675790938986e+204 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 0.0001471
Order of pole = 39.06
t[1] = 0.589
x2[1] (analytic) = 0.00091603895856164854699071431886538
x2[1] (numeric) = -4.5898139861683876751375097944701e+198
absolute error = 4.5898139861683876751375097944701e+198
relative error = 5.0105008561811048538043315377767e+203 %
h = 0.001
x1[1] (analytic) = 0.0011987874006955308056246060417651
x1[1] (numeric) = -2.4783165100148222787352781290296e+200
absolute error = 2.4783165100148222787352781290296e+200
relative error = 2.0673528171691783783340570732511e+205 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.59
x2[1] (analytic) = 0.00091717302599828628018001406175885
x2[1] (numeric) = 1.1801684404947794720107940027144e+202
absolute error = 1.1801684404947794720107940027144e+202
relative error = 1.2867456925155849422106091161703e+207 %
h = 0.001
x1[1] (analytic) = 0.0011977891125221126636216500949856
x1[1] (numeric) = -1.3107493537648024229749383625332e+204
absolute error = 1.3107493537648024229749383625332e+204
relative error = 1.0943072867016098996686990278039e+209 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.591
x2[1] (analytic) = 0.00091830986323335343687716468589885
x2[1] (numeric) = 4.5620276768210643342320348024697e+204
absolute error = 4.5620276768210643342320348024697e+204
relative error = 4.9678522026957680066158500559386e+209 %
h = 0.001
x1[1] (analytic) = 0.0011967918221378901928268395823847
x1[1] (numeric) = -4.7270245616492396206363960899312e+206
absolute error = 4.7270245616492396206363960899312e+206
relative error = 3.9497467096701202936719332178263e+211 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.592
x2[1] (analytic) = 0.00091944947531284587301406970523356
x2[1] (numeric) = 1.1546241315300502182029383014614e+207
absolute error = 1.1546241315300502182029383014614e+207
relative error = 1.2557776827673813753887796796214e+212 %
h = 0.001
x1[1] (analytic) = 0.0011957955285455729259101689203614
x1[1] (numeric) = -1.1569632544000763301742833938770e+209
absolute error = 1.1569632544000763301742833938770e+209
relative error = 9.6752599151066598075759997234429e+213 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.593
x2[1] (analytic) = 0.00092059186729336042976327650467993
x2[1] (numeric) = 2.2158805456087614183084294385969e+209
absolute error = 2.2158805456087614183084294385969e+209
relative error = 2.4070172943453103419516198869611e+214 %
h = 0.001
x1[1] (analytic) = 0.001194800230748867187529902398324
x1[1] (numeric) = -2.1505151539601950370129241070135e+211
absolute error = 2.1505151539601950370129241070135e+211
relative error = 1.7998951612290136651335197835988e+216 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.6MB, time=4.50
NO POLE
NO POLE
t[1] = 0.594
x2[1] (analytic) = 0.00092173704424211565807912839241284
x2[1] (numeric) = 3.0008114069978380073892632354590e+211
absolute error = 3.0008114069978380073892632354590e+211
relative error = 3.2556046496592851976029892119345e+216 %
h = 0.001
x1[1] (analytic) = 0.0011938059277524750980388158124784
x1[1] (numeric) = -2.7490478408081023007321961445957e+213
absolute error = 2.7490478408081023007321961445957e+213
relative error = 2.3027594158320284361799657222464e+218 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.595
x2[1] (analytic) = 0.00092288501123697258522787188690669
x2[1] (numeric) = 1.1385024083145948641889069070784e+213
absolute error = 1.1385024083145948641889069070784e+213
relative error = 1.2336340870772441284659533213559e+218 %
h = 0.001
x1[1] (analytic) = 0.0011928126185620935781862338771108
x1[1] (numeric) = -5.0235883460945186497752823044904e+214
absolute error = 5.0235883460945186497752823044904e+214
relative error = 4.2115486271014901455900635936752e+219 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.596
x2[1] (analytic) = 0.00092403577336645552339028303603533
x2[1] (numeric) = -9.2558760489434365197517798347519e+215
absolute error = 9.2558760489434365197517798347519e+215
relative error = 1.0016794063310281612429230785660e+221 %
h = 0.001
x1[1] (analytic) = 0.0011918203021844133548148681153206
x1[1] (numeric) = 1.0474849429570159560407055964507e+218
absolute error = 1.0474849429570159560407055964507e+218
relative error = 8.7889503227721990475737144936004e+222 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.597
x2[1] (analytic) = 0.00092518933572977292042054435826881
x2[1] (numeric) = -3.9270899892546612945045755317726e+218
absolute error = 3.9270899892546612945045755317726e+218
relative error = 4.2446338685443692886289033802130e+223 %
h = 0.001
x1[1] (analytic) = 0.0011908289776271179675514609259555
x1[1] (numeric) = 4.0917294079122404325505014929161e+220
absolute error = 4.0917294079122404325505014929161e+220
relative error = 3.4360344640466718194587393897644e+225 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.598
x2[1] (analytic) = 0.00092634570343683825284527212416087
x2[1] (numeric) = -1.0344346851258801577952942167435e+221
absolute error = 1.0344346851258801577952942167435e+221
relative error = 1.1166832007618976556021230829249e+226 %
h = 0.001
x1[1] (analytic) = 0.0011898386438988827764902425173134
x1[1] (numeric) = 1.0405361849240302137470330637133e+223
absolute error = 1.0405361849240302137470330637133e+223
relative error = 8.7451873433391285959119138794376e+227 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.599
x2[1] (analytic) = 0.0009275048816082909611867621605716
x2[1] (numeric) = -2.0570055645524882828405890256035e+223
absolute error = 2.0570055645524882828405890256035e+223
relative error = 2.2177840843119296430848455793513e+228 %
h = 0.001
x1[1] (analytic) = 0.001188849300009373970868208390983
x1[1] (numeric) = 2.0056883236338192325676605111160e+225
absolute error = 2.0056883236338192325676605111160e+225
relative error = 1.6870837402335220778062311367829e+230 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.6MB, time=4.78
NO POLE
NO POLE
t[1] = 0.6
x2[1] (analytic) = 0.00092866687537551742769469116109009
x2[1] (numeric) = -2.9534126619800315371630880515661e+225
absolute error = 2.9534126619800315371630880515661e+225
relative error = 3.1802713548771557277829127172104e+230 %
h = 0.001
x1[1] (analytic) = 0.0011878609449692475787312260510186
x1[1] (numeric) = 2.7366286163010312725677402019894e+227
absolute error = 2.7366286163010312725677402019894e+227
relative error = 2.3038291038113721263050781320324e+232 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
Iterations = 100
Total Elapsed Time = 4 Seconds
Elapsed Time(since restart) = 4 Seconds
Expected Time Remaining = 3 Minutes 27 Seconds
Optimized Time Remaining = 3 Minutes 27 Seconds
Time to Timeout = 14 Minutes 55 Seconds
Percent Done = 2.244 %
> quit
memory used=69.2MB, alloc=4.6MB, time=4.82