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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_sec,
> glob_max_hours,
> glob_clock_start_sec,
> djd_debug,
> glob_small_float,
> glob_hmax,
> glob_initial_pass,
> glob_not_yet_finished,
> centuries_in_millinium,
> sec_in_minute,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin_init,
> years_in_century,
> glob_max_iter,
> glob_dump_analytic,
> djd_debug2,
> glob_dump,
> glob_good_digits,
> glob_percent_done,
> glob_disp_incr,
> hours_in_day,
> min_in_hour,
> glob_max_opt_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_warned2,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_log10relerr,
> glob_log10abserr,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_max_minutes,
> glob_relerr,
> glob_h,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_almost_1,
> glob_normmax,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_html_log,
> glob_optimal_start,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> array_const_1,
> array_const_2D0,
> #END CONST
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_norms,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_pole,
> array_x1_init,
> array_m1,
> array_1st_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher_work,
> array_x1_higher_work2,
> array_x2_higher,
> array_x1_set_initial,
> array_x1_higher,
> array_fact_2,
> array_x2_set_initial,
> array_x1_higher_work,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
>
>
>
>
>
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_x1(ind_var);
> omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 3
> glob_good_digits := -trunc(log10(relerr/100.0));
> else
> glob_good_digits := Digits;
> fi;# end if 3
> ;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> 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_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_x2(ind_var);
> omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 3
> glob_good_digits := -trunc(log10(relerr/100.0));
> else
> glob_good_digits := Digits;
> fi;# end if 3
> ;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> 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_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> 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, glob_max_terms, INFO, DEBUGL, glob_iolevel, ALWAYS,
glob_max_sec, glob_max_hours, glob_clock_start_sec, djd_debug,
glob_small_float, glob_hmax, glob_initial_pass, glob_not_yet_finished,
centuries_in_millinium, sec_in_minute, glob_curr_iter_when_opt, glob_warned,
glob_max_rel_trunc_err, glob_look_poles, glob_last_good_h, glob_hmin_init,
years_in_century, glob_max_iter, glob_dump_analytic, djd_debug2, glob_dump,
glob_good_digits, glob_percent_done, glob_disp_incr, hours_in_day,
min_in_hour, glob_max_opt_iter, glob_large_float, glob_not_yet_start_msg,
glob_clock_sec, glob_display_flag, glob_log10normmin, glob_start,
glob_warned2, glob_smallish_float, glob_max_trunc_err, glob_log10relerr,
glob_log10abserr, glob_iter, MAX_UNCHANGED, glob_current_iter,
glob_optimal_clock_start_sec, glob_no_eqs, glob_optimal_expect_sec,
glob_subiter_method, glob_max_minutes, glob_relerr, glob_h,
glob_optimal_done, glob_reached_optimal_h, glob_almost_1, glob_normmax,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_hmin, glob_html_log,
glob_optimal_start, glob_abserr, glob_log10_relerr, glob_log10_abserr,
days_in_year, array_const_0D0, array_const_3D0, array_const_2,
array_const_4D0, array_const_1, array_const_2D0, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17, array_norms, array_type_pole, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_t, array_pole, array_x1_init, array_m1,
array_1st_rel_error, array_x2_init, array_x1, array_x2,
array_last_rel_error, array_fact_1, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher_work,
array_x1_higher_work2, array_x2_higher, array_x1_set_initial,
array_x1_higher, array_fact_2, array_x2_set_initial, array_x1_higher_work,
glob_last;
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_x1(ind_var);
omniout_float(ALWAYS, "x1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x1[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then
glob_good_digits := -trunc(log10(relerr/100.0))
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
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_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_x2(ind_var);
omniout_float(ALWAYS, "x2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x2[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x2[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then
glob_good_digits := -trunc(log10(relerr/100.0))
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
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_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_sec,
> glob_max_hours,
> glob_clock_start_sec,
> djd_debug,
> glob_small_float,
> glob_hmax,
> glob_initial_pass,
> glob_not_yet_finished,
> centuries_in_millinium,
> sec_in_minute,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin_init,
> years_in_century,
> glob_max_iter,
> glob_dump_analytic,
> djd_debug2,
> glob_dump,
> glob_good_digits,
> glob_percent_done,
> glob_disp_incr,
> hours_in_day,
> min_in_hour,
> glob_max_opt_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_warned2,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_log10relerr,
> glob_log10abserr,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_max_minutes,
> glob_relerr,
> glob_h,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_almost_1,
> glob_normmax,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_html_log,
> glob_optimal_start,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> array_const_1,
> array_const_2D0,
> #END CONST
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_norms,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_pole,
> array_x1_init,
> array_m1,
> array_1st_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher_work,
> array_x1_higher_work2,
> array_x2_higher,
> array_x1_set_initial,
> array_x1_higher,
> array_fact_2,
> array_x2_set_initial,
> array_x1_higher_work,
> glob_last;
>
> local hnew, sz2, tmp;
>
>
>
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_x1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(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 (omniabs(array_x2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_x2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (omniabs(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");
> 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
> return(hnew);
> #BOTTOM ADJUST FOR POLE
>
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, ALWAYS,
glob_max_sec, glob_max_hours, glob_clock_start_sec, djd_debug,
glob_small_float, glob_hmax, glob_initial_pass, glob_not_yet_finished,
centuries_in_millinium, sec_in_minute, glob_curr_iter_when_opt, glob_warned,
glob_max_rel_trunc_err, glob_look_poles, glob_last_good_h, glob_hmin_init,
years_in_century, glob_max_iter, glob_dump_analytic, djd_debug2, glob_dump,
glob_good_digits, glob_percent_done, glob_disp_incr, hours_in_day,
min_in_hour, glob_max_opt_iter, glob_large_float, glob_not_yet_start_msg,
glob_clock_sec, glob_display_flag, glob_log10normmin, glob_start,
glob_warned2, glob_smallish_float, glob_max_trunc_err, glob_log10relerr,
glob_log10abserr, glob_iter, MAX_UNCHANGED, glob_current_iter,
glob_optimal_clock_start_sec, glob_no_eqs, glob_optimal_expect_sec,
glob_subiter_method, glob_max_minutes, glob_relerr, glob_h,
glob_optimal_done, glob_reached_optimal_h, glob_almost_1, glob_normmax,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_hmin, glob_html_log,
glob_optimal_start, glob_abserr, glob_log10_relerr, glob_log10_abserr,
days_in_year, array_const_0D0, array_const_3D0, array_const_2,
array_const_4D0, array_const_1, array_const_2D0, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17, array_norms, array_type_pole, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_t, array_pole, array_x1_init, array_m1,
array_1st_rel_error, array_x2_init, array_x1, array_x2,
array_last_rel_error, array_fact_1, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher_work,
array_x1_higher_work2, array_x2_higher, array_x1_set_initial,
array_x1_higher, array_fact_2, array_x2_set_initial, array_x1_higher_work,
glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_x1_higher[1, 1]) then
tmp := omniabs(array_x1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_x2_higher[1, 1]) then
tmp := omniabs(array_x2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(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");
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;
return hnew
end proc
> # Begin Function number 5
> prog_report := proc(t_start,t_end)
> global
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_sec,
> glob_max_hours,
> glob_clock_start_sec,
> djd_debug,
> glob_small_float,
> glob_hmax,
> glob_initial_pass,
> glob_not_yet_finished,
> centuries_in_millinium,
> sec_in_minute,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin_init,
> years_in_century,
> glob_max_iter,
> glob_dump_analytic,
> djd_debug2,
> glob_dump,
> glob_good_digits,
> glob_percent_done,
> glob_disp_incr,
> hours_in_day,
> min_in_hour,
> glob_max_opt_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_warned2,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_log10relerr,
> glob_log10abserr,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_max_minutes,
> glob_relerr,
> glob_h,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_almost_1,
> glob_normmax,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_html_log,
> glob_optimal_start,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> array_const_1,
> array_const_2D0,
> #END CONST
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_norms,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_pole,
> array_x1_init,
> array_m1,
> array_1st_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher_work,
> array_x1_higher_work2,
> array_x2_higher,
> array_x1_set_initial,
> array_x1_higher,
> array_fact_2,
> array_x2_set_initial,
> array_x1_higher_work,
> 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, glob_max_terms, INFO, DEBUGL, glob_iolevel, ALWAYS,
glob_max_sec, glob_max_hours, glob_clock_start_sec, djd_debug,
glob_small_float, glob_hmax, glob_initial_pass, glob_not_yet_finished,
centuries_in_millinium, sec_in_minute, glob_curr_iter_when_opt, glob_warned,
glob_max_rel_trunc_err, glob_look_poles, glob_last_good_h, glob_hmin_init,
years_in_century, glob_max_iter, glob_dump_analytic, djd_debug2, glob_dump,
glob_good_digits, glob_percent_done, glob_disp_incr, hours_in_day,
min_in_hour, glob_max_opt_iter, glob_large_float, glob_not_yet_start_msg,
glob_clock_sec, glob_display_flag, glob_log10normmin, glob_start,
glob_warned2, glob_smallish_float, glob_max_trunc_err, glob_log10relerr,
glob_log10abserr, glob_iter, MAX_UNCHANGED, glob_current_iter,
glob_optimal_clock_start_sec, glob_no_eqs, glob_optimal_expect_sec,
glob_subiter_method, glob_max_minutes, glob_relerr, glob_h,
glob_optimal_done, glob_reached_optimal_h, glob_almost_1, glob_normmax,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_hmin, glob_html_log,
glob_optimal_start, glob_abserr, glob_log10_relerr, glob_log10_abserr,
days_in_year, array_const_0D0, array_const_3D0, array_const_2,
array_const_4D0, array_const_1, array_const_2D0, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17, array_norms, array_type_pole, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_t, array_pole, array_x1_init, array_m1,
array_1st_rel_error, array_x2_init, array_x1, array_x2,
array_last_rel_error, array_fact_1, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher_work,
array_x1_higher_work2, array_x2_higher, array_x1_set_initial,
array_x1_higher, array_fact_2, array_x2_set_initial, array_x1_higher_work,
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,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_sec,
> glob_max_hours,
> glob_clock_start_sec,
> djd_debug,
> glob_small_float,
> glob_hmax,
> glob_initial_pass,
> glob_not_yet_finished,
> centuries_in_millinium,
> sec_in_minute,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin_init,
> years_in_century,
> glob_max_iter,
> glob_dump_analytic,
> djd_debug2,
> glob_dump,
> glob_good_digits,
> glob_percent_done,
> glob_disp_incr,
> hours_in_day,
> min_in_hour,
> glob_max_opt_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_warned2,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_log10relerr,
> glob_log10abserr,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_max_minutes,
> glob_relerr,
> glob_h,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_almost_1,
> glob_normmax,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_html_log,
> glob_optimal_start,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> array_const_1,
> array_const_2D0,
> #END CONST
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_norms,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_pole,
> array_x1_init,
> array_m1,
> array_1st_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher_work,
> array_x1_higher_work2,
> array_x2_higher,
> array_x1_set_initial,
> array_x1_higher,
> array_fact_2,
> array_x2_set_initial,
> array_x1_higher_work,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
>
>
>
>
>
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_x1_higher[1,m]) < glob_small_float) or (omniabs(array_x1_higher[1,m-1]) < glob_small_float) or (omniabs(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 (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 2 - 1;
> while ((m >= 10) and ((omniabs(array_x2_higher[1,m]) < glob_small_float) or (omniabs(array_x2_higher[1,m-1]) < glob_small_float) or (omniabs(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 (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_x1_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif ((omniabs(array_x1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-5]) >= (glob_large_float))) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]);
> rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]);
> rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]);
> rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]);
> rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(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 (omniabs(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 (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_x2_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif ((omniabs(array_x2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-5]) >= (glob_large_float))) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]);
> rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]);
> rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]);
> rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]);
> rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(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 (omniabs(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 (omniabs(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, glob_max_terms, INFO, DEBUGL, glob_iolevel, ALWAYS,
glob_max_sec, glob_max_hours, glob_clock_start_sec, djd_debug,
glob_small_float, glob_hmax, glob_initial_pass, glob_not_yet_finished,
centuries_in_millinium, sec_in_minute, glob_curr_iter_when_opt, glob_warned,
glob_max_rel_trunc_err, glob_look_poles, glob_last_good_h, glob_hmin_init,
years_in_century, glob_max_iter, glob_dump_analytic, djd_debug2, glob_dump,
glob_good_digits, glob_percent_done, glob_disp_incr, hours_in_day,
min_in_hour, glob_max_opt_iter, glob_large_float, glob_not_yet_start_msg,
glob_clock_sec, glob_display_flag, glob_log10normmin, glob_start,
glob_warned2, glob_smallish_float, glob_max_trunc_err, glob_log10relerr,
glob_log10abserr, glob_iter, MAX_UNCHANGED, glob_current_iter,
glob_optimal_clock_start_sec, glob_no_eqs, glob_optimal_expect_sec,
glob_subiter_method, glob_max_minutes, glob_relerr, glob_h,
glob_optimal_done, glob_reached_optimal_h, glob_almost_1, glob_normmax,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_hmin, glob_html_log,
glob_optimal_start, glob_abserr, glob_log10_relerr, glob_log10_abserr,
days_in_year, array_const_0D0, array_const_3D0, array_const_2,
array_const_4D0, array_const_1, array_const_2D0, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17, array_norms, array_type_pole, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_t, array_pole, array_x1_init, array_m1,
array_1st_rel_error, array_x2_init, array_x1, array_x2,
array_last_rel_error, array_fact_1, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher_work,
array_x1_higher_work2, array_x2_higher, array_x1_set_initial,
array_x1_higher, array_fact_2, array_x2_set_initial, array_x1_higher_work,
glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_x1_higher[1, m]) < glob_small_float
or omniabs(array_x1_higher[1, m - 1]) < glob_small_float or
omniabs(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 < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (omniabs(array_x2_higher[1, m]) < glob_small_float
or omniabs(array_x2_higher[1, m - 1]) < glob_small_float or
omniabs(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 < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_x1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= omniabs(array_x1_higher[1, m]) or
glob_large_float <= omniabs(array_x1_higher[1, m - 1]) or
glob_large_float <= omniabs(array_x1_higher[1, m - 2]) or
glob_large_float <= omniabs(array_x1_higher[1, m - 3]) or
glob_large_float <= omniabs(array_x1_higher[1, m - 4]) or
glob_large_float <= omniabs(array_x1_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3];
rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4];
rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(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 < omniabs(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 < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_x2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= omniabs(array_x2_higher[1, m]) or
glob_large_float <= omniabs(array_x2_higher[1, m - 1]) or
glob_large_float <= omniabs(array_x2_higher[1, m - 2]) or
glob_large_float <= omniabs(array_x2_higher[1, m - 3]) or
glob_large_float <= omniabs(array_x2_higher[1, m - 4]) or
glob_large_float <= omniabs(array_x2_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3];
rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4];
rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(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 < omniabs(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 < omniabs(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,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_sec,
> glob_max_hours,
> glob_clock_start_sec,
> djd_debug,
> glob_small_float,
> glob_hmax,
> glob_initial_pass,
> glob_not_yet_finished,
> centuries_in_millinium,
> sec_in_minute,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin_init,
> years_in_century,
> glob_max_iter,
> glob_dump_analytic,
> djd_debug2,
> glob_dump,
> glob_good_digits,
> glob_percent_done,
> glob_disp_incr,
> hours_in_day,
> min_in_hour,
> glob_max_opt_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_warned2,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_log10relerr,
> glob_log10abserr,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_max_minutes,
> glob_relerr,
> glob_h,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_almost_1,
> glob_normmax,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_html_log,
> glob_optimal_start,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> array_const_1,
> array_const_2D0,
> #END CONST
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_norms,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_pole,
> array_x1_init,
> array_m1,
> array_1st_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher_work,
> array_x1_higher_work2,
> array_x2_higher,
> array_x1_set_initial,
> array_x1_higher,
> array_fact_2,
> array_x2_set_initial,
> array_x1_higher_work,
> glob_last;
>
> local iii;
>
>
>
> if ( not glob_initial_pass) then # if number 3
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2
> ;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_x1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_x1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_x2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_x2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 3
> ;
>
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, ALWAYS,
glob_max_sec, glob_max_hours, glob_clock_start_sec, djd_debug,
glob_small_float, glob_hmax, glob_initial_pass, glob_not_yet_finished,
centuries_in_millinium, sec_in_minute, glob_curr_iter_when_opt, glob_warned,
glob_max_rel_trunc_err, glob_look_poles, glob_last_good_h, glob_hmin_init,
years_in_century, glob_max_iter, glob_dump_analytic, djd_debug2, glob_dump,
glob_good_digits, glob_percent_done, glob_disp_incr, hours_in_day,
min_in_hour, glob_max_opt_iter, glob_large_float, glob_not_yet_start_msg,
glob_clock_sec, glob_display_flag, glob_log10normmin, glob_start,
glob_warned2, glob_smallish_float, glob_max_trunc_err, glob_log10relerr,
glob_log10abserr, glob_iter, MAX_UNCHANGED, glob_current_iter,
glob_optimal_clock_start_sec, glob_no_eqs, glob_optimal_expect_sec,
glob_subiter_method, glob_max_minutes, glob_relerr, glob_h,
glob_optimal_done, glob_reached_optimal_h, glob_almost_1, glob_normmax,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_hmin, glob_html_log,
glob_optimal_start, glob_abserr, glob_log10_relerr, glob_log10_abserr,
days_in_year, array_const_0D0, array_const_3D0, array_const_2,
array_const_4D0, array_const_1, array_const_2D0, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17, array_norms, array_type_pole, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_t, array_pole, array_x1_init, array_m1,
array_1st_rel_error, array_x2_init, array_x1, array_x2,
array_last_rel_error, array_fact_1, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher_work,
array_x1_higher_work2, array_x2_higher, array_x1_set_initial,
array_x1_higher, array_fact_2, array_x2_set_initial, array_x1_higher_work,
glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_x1[iii]) then
array_norms[iii] := omniabs(array_x1[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_x2[iii]) then
array_norms[iii] := omniabs(array_x2[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_sec,
> glob_max_hours,
> glob_clock_start_sec,
> djd_debug,
> glob_small_float,
> glob_hmax,
> glob_initial_pass,
> glob_not_yet_finished,
> centuries_in_millinium,
> sec_in_minute,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin_init,
> years_in_century,
> glob_max_iter,
> glob_dump_analytic,
> djd_debug2,
> glob_dump,
> glob_good_digits,
> glob_percent_done,
> glob_disp_incr,
> hours_in_day,
> min_in_hour,
> glob_max_opt_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_warned2,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_log10relerr,
> glob_log10abserr,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_max_minutes,
> glob_relerr,
> glob_h,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_almost_1,
> glob_normmax,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_html_log,
> glob_optimal_start,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> array_const_1,
> array_const_2D0,
> #END CONST
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_norms,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_pole,
> array_x1_init,
> array_m1,
> array_1st_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher_work,
> array_x1_higher_work2,
> array_x2_higher,
> array_x1_set_initial,
> array_x1_higher,
> array_fact_2,
> array_x2_set_initial,
> array_x1_higher_work,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
>
>
>
>
>
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp1[1] := array_const_4D0[1] * array_x2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre diff $eq_no = 1 i = 1
> array_tmp3[1] := array_x2_higher[2,1];
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp6[1] := array_const_2D0[1] * array_x1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_x1_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1
> array_tmp9[1] := array_x2_higher[2,1];
> #emit pre mult CONST FULL $eq_no = 2 i = 1
> array_tmp11[1] := array_const_2D0[1] * array_x2[1];
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x1_higher[3,1];
> #emit pre diff $eq_no = 2 i = 1
> array_tmp15[1] := array_x1_higher[2,1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_x2_set_initial[2,3]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[1] * expt(glob_h , (2)) * factorial_3(0,2);
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp1[2] := array_const_4D0[1] * array_x2[2];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre diff $eq_no = 1 i = 2
> array_tmp3[2] := array_x2_higher[2,2];
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp6[2] := array_const_2D0[1] * array_x1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_x1_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2
> array_tmp9[2] := array_x2_higher[2,2];
> #emit pre mult CONST FULL $eq_no = 2 i = 2
> array_tmp11[2] := array_const_2D0[1] * array_x2[2];
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x1_higher[3,2];
> #emit pre diff $eq_no = 2 i = 2
> array_tmp15[2] := array_x1_higher[2,2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_x2_set_initial[2,4]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[2] * expt(glob_h , (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp1[3] := array_const_4D0[1] * array_x2[3];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre diff $eq_no = 1 i = 3
> array_tmp3[3] := array_x2_higher[2,3];
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp6[3] := array_const_2D0[1] * array_x1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_x1_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3
> array_tmp9[3] := array_x2_higher[2,3];
> #emit pre mult CONST FULL $eq_no = 2 i = 3
> array_tmp11[3] := array_const_2D0[1] * array_x2[3];
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x1_higher[3,3];
> #emit pre diff $eq_no = 2 i = 3
> array_tmp15[3] := array_x1_higher[2,3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_x2_set_initial[2,5]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[3] * expt(glob_h , (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp1[4] := array_const_4D0[1] * array_x2[4];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre diff $eq_no = 1 i = 4
> array_tmp3[4] := array_x2_higher[2,4];
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp6[4] := array_const_2D0[1] * array_x1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_x1_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4
> array_tmp9[4] := array_x2_higher[2,4];
> #emit pre mult CONST FULL $eq_no = 2 i = 4
> array_tmp11[4] := array_const_2D0[1] * array_x2[4];
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x1_higher[3,4];
> #emit pre diff $eq_no = 2 i = 4
> array_tmp15[4] := array_x1_higher[2,4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_x2_set_initial[2,6]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[4] * expt(glob_h , (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp1[5] := array_const_4D0[1] * array_x2[5];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre diff $eq_no = 1 i = 5
> array_tmp3[5] := array_x2_higher[2,5];
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp6[5] := array_const_2D0[1] * array_x1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_x1_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5
> array_tmp9[5] := array_x2_higher[2,5];
> #emit pre mult CONST FULL $eq_no = 2 i = 5
> array_tmp11[5] := array_const_2D0[1] * array_x2[5];
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x1_higher[3,5];
> #emit pre diff $eq_no = 2 i = 5
> array_tmp15[5] := array_x1_higher[2,5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_x2_set_initial[2,7]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[5] * expt(glob_h , (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult CONST FULL $eq_no = 1 i = 1
> array_tmp1[kkk] := array_const_4D0[1] * array_x2[kkk];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit diff $eq_no = 1
> array_tmp3[kkk] := array_x2_higher[2,kkk];
> #emit mult CONST FULL $eq_no = 1 i = 1
> array_tmp6[kkk] := array_const_2D0[1] * array_x1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_x1_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp7[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x1[kkk + order_d] := temporary;
> array_x1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> #emit diff $eq_no = 2
> array_tmp9[kkk] := array_x2_higher[2,kkk];
> #emit mult CONST FULL $eq_no = 2 i = 1
> array_tmp11[kkk] := array_const_2D0[1] * array_x2[kkk];
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x1_higher[3,kkk];
> #emit diff $eq_no = 2
> array_tmp15[kkk] := array_x1_higher[2,kkk];
> #emit assign $eq_no = 2
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_x2_set_initial[2,kkk + order_d]) then # if number 2
> temporary := array_tmp17[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x2[kkk + order_d] := temporary;
> array_x2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
>
> #BOTTOM ATOMALL ???
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, ALWAYS,
glob_max_sec, glob_max_hours, glob_clock_start_sec, djd_debug,
glob_small_float, glob_hmax, glob_initial_pass, glob_not_yet_finished,
centuries_in_millinium, sec_in_minute, glob_curr_iter_when_opt, glob_warned,
glob_max_rel_trunc_err, glob_look_poles, glob_last_good_h, glob_hmin_init,
years_in_century, glob_max_iter, glob_dump_analytic, djd_debug2, glob_dump,
glob_good_digits, glob_percent_done, glob_disp_incr, hours_in_day,
min_in_hour, glob_max_opt_iter, glob_large_float, glob_not_yet_start_msg,
glob_clock_sec, glob_display_flag, glob_log10normmin, glob_start,
glob_warned2, glob_smallish_float, glob_max_trunc_err, glob_log10relerr,
glob_log10abserr, glob_iter, MAX_UNCHANGED, glob_current_iter,
glob_optimal_clock_start_sec, glob_no_eqs, glob_optimal_expect_sec,
glob_subiter_method, glob_max_minutes, glob_relerr, glob_h,
glob_optimal_done, glob_reached_optimal_h, glob_almost_1, glob_normmax,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_hmin, glob_html_log,
glob_optimal_start, glob_abserr, glob_log10_relerr, glob_log10_abserr,
days_in_year, array_const_0D0, array_const_3D0, array_const_2,
array_const_4D0, array_const_1, array_const_2D0, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17, array_norms, array_type_pole, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_t, array_pole, array_x1_init, array_m1,
array_1st_rel_error, array_x2_init, array_x1, array_x2,
array_last_rel_error, array_fact_1, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher_work,
array_x1_higher_work2, array_x2_higher, array_x1_set_initial,
array_x1_higher, array_fact_2, array_x2_set_initial, array_x1_higher_work,
glob_last;
array_tmp1[1] := array_const_4D0[1]*array_x2[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_x2_higher[2, 1];
array_tmp6[1] := array_const_2D0[1]*array_x1[1];
if not array_x1_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp7[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp9[1] := array_x2_higher[2, 1];
array_tmp11[1] := array_const_2D0[1]*array_x2[1];
array_tmp13[1] := array_x1_higher[3, 1];
array_tmp15[1] := array_x1_higher[2, 1];
if not array_x2_set_initial[2, 3] then
if 1 <= glob_max_terms then
temporary := array_tmp17[1]*expt(glob_h, 2)*factorial_3(0, 2);
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_4D0[1]*array_x2[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_x2_higher[2, 2];
array_tmp6[2] := array_const_2D0[1]*array_x1[2];
if not array_x1_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp7[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp9[2] := array_x2_higher[2, 2];
array_tmp11[2] := array_const_2D0[1]*array_x2[2];
array_tmp13[2] := array_x1_higher[3, 2];
array_tmp15[2] := array_x1_higher[2, 2];
if not array_x2_set_initial[2, 4] then
if 2 <= glob_max_terms then
temporary := array_tmp17[2]*expt(glob_h, 2)*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_const_4D0[1]*array_x2[3];
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := array_x2_higher[2, 3];
array_tmp6[3] := array_const_2D0[1]*array_x1[3];
if not array_x1_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp7[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp9[3] := array_x2_higher[2, 3];
array_tmp11[3] := array_const_2D0[1]*array_x2[3];
array_tmp13[3] := array_x1_higher[3, 3];
array_tmp15[3] := array_x1_higher[2, 3];
if not array_x2_set_initial[2, 5] then
if 3 <= glob_max_terms then
temporary := array_tmp17[3]*expt(glob_h, 2)*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_const_4D0[1]*array_x2[4];
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := array_x2_higher[2, 4];
array_tmp6[4] := array_const_2D0[1]*array_x1[4];
if not array_x1_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp7[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp9[4] := array_x2_higher[2, 4];
array_tmp11[4] := array_const_2D0[1]*array_x2[4];
array_tmp13[4] := array_x1_higher[3, 4];
array_tmp15[4] := array_x1_higher[2, 4];
if not array_x2_set_initial[2, 6] then
if 4 <= glob_max_terms then
temporary := array_tmp17[4]*expt(glob_h, 2)*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_const_4D0[1]*array_x2[5];
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := array_x2_higher[2, 5];
array_tmp6[5] := array_const_2D0[1]*array_x1[5];
if not array_x1_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp7[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
array_tmp9[5] := array_x2_higher[2, 5];
array_tmp11[5] := array_const_2D0[1]*array_x2[5];
array_tmp13[5] := array_x1_higher[3, 5];
array_tmp15[5] := array_x1_higher[2, 5];
if not array_x2_set_initial[2, 7] then
if 5 <= glob_max_terms then
temporary := array_tmp17[5]*expt(glob_h, 2)*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_const_4D0[1]*array_x2[kkk];
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := array_x2_higher[2, kkk];
array_tmp6[kkk] := array_const_2D0[1]*array_x1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_x1_set_initial[1, kkk + order_d] then
temporary := array_tmp7[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x1[kkk + order_d] := temporary;
array_x1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
array_tmp9[kkk] := array_x2_higher[2, kkk];
array_tmp11[kkk] := array_const_2D0[1]*array_x2[kkk];
array_tmp13[kkk] := array_x1_higher[3, kkk];
array_tmp15[kkk] := array_x1_higher[2, kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
if not array_x2_set_initial[2, kkk + order_d] then
temporary := array_tmp17[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x2[kkk + order_d] := temporary;
array_x2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, 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);
> fprintf(fd,"
");
> if (secs >= 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_minute * 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_minute;
> sec_int := floor(seconds);
> 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_minute, years_in_century;
secs := secs_in;
fprintf(fd, "");
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*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_minute;
sec_int := floor(seconds);
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_minute, 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_minute * 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_minute;
> 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_minute, years_in_century;
secs := convfloat(secs_in);
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*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_minute;
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
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
>
> local good_digits;
>
>
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 11
> if (rel_error <> 0.0) then # if number 12
> good_digits := -trunc(log10(rel_error/100.0));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 12
> ;
> else
> fprintf(file,"Unknown");
> fi;# end if 11
> ;
> fprintf(file," | ");
>
> # End Function number 9
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if rel_error <> 0. then
good_digits := -trunc(log10(rel_error/100.0));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 10
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 10
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 11
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 12
> 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 12
> 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 13
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 13
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 14
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 14
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 15
> 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 15
> 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 16
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
>
>
>
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (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 16
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < 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 17
> 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 (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 17
> 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 < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 18
> factorial_2 := proc(nnn)
> local ret;
>
>
>
> ret := nnn!;
>
> # End Function number 18
> end;
factorial_2 := proc(nnn) local ret; ret := nnn! end proc
> # Begin Function number 19
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
>
>
>
> if (nnn <= glob_max_terms) then # if number 13
> if (array_fact_1[nnn] = 0) then # if number 14
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 19
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 20
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
>
>
>
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13
> if (array_fact_2[mmm,nnn] = 0) then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 20
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 21
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 21
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 22
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 22
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_x1 := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return(2.0 * c1 + 6.0 * c3 * exp(-t));
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x1p := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return( - 6.0 * c3 * exp(-t));
> end;
exact_soln_x1p := proc(t)
local c1, c2, c3;
c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return -6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return 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
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> t_start,t_end
> ,it, log10norm, max_terms, opt_iter, tmp,subiter;
> global
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> DEBUGL,
> glob_iolevel,
> ALWAYS,
> #Top Generate Globals Decl
> glob_max_sec,
> glob_max_hours,
> glob_clock_start_sec,
> djd_debug,
> glob_small_float,
> glob_hmax,
> glob_initial_pass,
> glob_not_yet_finished,
> centuries_in_millinium,
> sec_in_minute,
> glob_curr_iter_when_opt,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin_init,
> years_in_century,
> glob_max_iter,
> glob_dump_analytic,
> djd_debug2,
> glob_dump,
> glob_good_digits,
> glob_percent_done,
> glob_disp_incr,
> hours_in_day,
> min_in_hour,
> glob_max_opt_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_warned2,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_log10relerr,
> glob_log10abserr,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_max_minutes,
> glob_relerr,
> glob_h,
> glob_optimal_done,
> glob_reached_optimal_h,
> glob_almost_1,
> glob_normmax,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_html_log,
> glob_optimal_start,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> days_in_year,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> array_const_1,
> array_const_2D0,
> #END CONST
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_norms,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_t,
> array_pole,
> array_x1_init,
> array_m1,
> array_1st_rel_error,
> array_x2_init,
> array_x1,
> array_x2,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher_work,
> array_x1_higher_work2,
> array_x2_higher,
> array_x1_set_initial,
> array_x1_higher,
> array_fact_2,
> array_x2_set_initial,
> array_x1_higher_work,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> glob_max_terms := 30;
> INFO := 2;
> DEBUGL := 3;
> glob_iolevel := 5;
> ALWAYS := 1;
> glob_max_sec := 10000.0;
> glob_max_hours := 0.0;
> glob_clock_start_sec := 0.0;
> djd_debug := true;
> glob_small_float := 0.1e-50;
> glob_hmax := 1.0;
> glob_initial_pass := true;
> glob_not_yet_finished := true;
> centuries_in_millinium := 10;
> sec_in_minute := 60;
> glob_curr_iter_when_opt := 0;
> glob_warned := false;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_look_poles := false;
> glob_last_good_h := 0.1;
> glob_hmin_init := 0.001;
> years_in_century := 100;
> glob_max_iter := 1000;
> glob_dump_analytic := false;
> djd_debug2 := true;
> glob_dump := false;
> glob_good_digits := 0;
> glob_percent_done := 0.0;
> glob_disp_incr := 0.1;
> hours_in_day := 24;
> min_in_hour := 60;
> glob_max_opt_iter := 10;
> glob_large_float := 9.0e100;
> glob_not_yet_start_msg := true;
> glob_clock_sec := 0.0;
> glob_display_flag := true;
> glob_log10normmin := 0.1;
> glob_start := 0;
> glob_warned2 := false;
> glob_smallish_float := 0.1e-100;
> glob_max_trunc_err := 0.1e-10;
> glob_log10relerr := 0.0;
> glob_log10abserr := 0.0;
> glob_iter := 0;
> MAX_UNCHANGED := 10;
> glob_current_iter := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_no_eqs := 0;
> glob_optimal_expect_sec := 0.1;
> glob_subiter_method := 3;
> glob_max_minutes := 0.0;
> glob_relerr := 0.1e-10;
> glob_h := 0.1;
> glob_optimal_done := false;
> glob_reached_optimal_h := false;
> glob_almost_1 := 0.9990;
> glob_normmax := 0.0;
> glob_orig_start_sec := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_hmin := 0.00000000001;
> glob_html_log := true;
> glob_optimal_start := 0.0;
> glob_abserr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> days_in_year := 365;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest6postode.ode#################");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#");
> omniout_str(ALWAYS,"# was complicated.ode");
> omniout_str(ALWAYS,"#");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x1_init[1 + 1] := exact_soln_x1p(t_start);");
> omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1 + 1] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 1;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return(2.0 * c1 + 6.0 * c3 * exp(-t));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x1p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return( - 6.0 * c3 * exp(-t));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_tmp10:= Array(0..(max_terms + 1),[]);
> array_tmp11:= Array(0..(max_terms + 1),[]);
> array_tmp12:= Array(0..(max_terms + 1),[]);
> array_tmp13:= Array(0..(max_terms + 1),[]);
> array_tmp14:= Array(0..(max_terms + 1),[]);
> array_tmp15:= Array(0..(max_terms + 1),[]);
> array_tmp16:= Array(0..(max_terms + 1),[]);
> array_tmp17:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_tmp6:= Array(0..(max_terms + 1),[]);
> array_tmp7:= Array(0..(max_terms + 1),[]);
> array_tmp8:= Array(0..(max_terms + 1),[]);
> array_tmp9:= Array(0..(max_terms + 1),[]);
> array_t:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_x1_init:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_x2_init:= Array(0..(max_terms + 1),[]);
> array_x1:= Array(0..(max_terms + 1),[]);
> array_x2:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_x2_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_x2_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x2_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_x2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> 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_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_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_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 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_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[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_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_t := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_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_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0[1] := 3.0;
> array_const_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 2;
> array_const_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_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0[1] := 2.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #
> # was complicated.ode
> #
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[0 + 1] := exact_soln_x1(t_start);
> array_x1_init[1 + 1] := exact_soln_x1p(t_start);
> array_x2_init[0 + 1] := exact_soln_x2(t_start);
> array_x2_init[1 + 1] := exact_soln_x2p(t_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 1;
> #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 := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_x1_set_initial[1,1] := true;
> array_x1_set_initial[1,2] := true;
> array_x1_set_initial[1,3] := false;
> array_x1_set_initial[1,4] := false;
> array_x1_set_initial[1,5] := false;
> array_x1_set_initial[1,6] := false;
> array_x1_set_initial[1,7] := false;
> array_x1_set_initial[1,8] := false;
> array_x1_set_initial[1,9] := false;
> array_x1_set_initial[1,10] := false;
> array_x1_set_initial[1,11] := false;
> array_x1_set_initial[1,12] := false;
> array_x1_set_initial[1,13] := false;
> array_x1_set_initial[1,14] := false;
> array_x1_set_initial[1,15] := false;
> array_x1_set_initial[1,16] := false;
> array_x1_set_initial[1,17] := false;
> array_x1_set_initial[1,18] := false;
> array_x1_set_initial[1,19] := false;
> array_x1_set_initial[1,20] := false;
> array_x1_set_initial[1,21] := false;
> array_x1_set_initial[1,22] := false;
> array_x1_set_initial[1,23] := false;
> array_x1_set_initial[1,24] := false;
> array_x1_set_initial[1,25] := false;
> array_x1_set_initial[1,26] := false;
> array_x1_set_initial[1,27] := false;
> array_x1_set_initial[1,28] := false;
> array_x1_set_initial[1,29] := false;
> array_x1_set_initial[1,30] := false;
> array_x2_set_initial[2,1] := true;
> array_x2_set_initial[2,2] := true;
> array_x2_set_initial[2,3] := false;
> array_x2_set_initial[2,4] := false;
> array_x2_set_initial[2,5] := false;
> array_x2_set_initial[2,6] := false;
> array_x2_set_initial[2,7] := false;
> array_x2_set_initial[2,8] := false;
> array_x2_set_initial[2,9] := false;
> array_x2_set_initial[2,10] := false;
> array_x2_set_initial[2,11] := false;
> array_x2_set_initial[2,12] := false;
> array_x2_set_initial[2,13] := false;
> array_x2_set_initial[2,14] := false;
> array_x2_set_initial[2,15] := false;
> array_x2_set_initial[2,16] := false;
> array_x2_set_initial[2,17] := false;
> array_x2_set_initial[2,18] := false;
> array_x2_set_initial[2,19] := false;
> array_x2_set_initial[2,20] := false;
> array_x2_set_initial[2,21] := false;
> array_x2_set_initial[2,22] := false;
> array_x2_set_initial[2,23] := false;
> array_x2_set_initial[2,24] := false;
> array_x2_set_initial[2,25] := false;
> array_x2_set_initial[2,26] := false;
> array_x2_set_initial[2,27] := false;
> array_x2_set_initial[2,28] := false;
> array_x2_set_initial[2,29] := false;
> array_x2_set_initial[2,30] := false;
> if (glob_html_log) then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_t[1] := t_start;
> array_t[2] := glob_h;
> order_diff := 2;
> #Start Series array_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x1[term_no] := array_x1_init[term_no] * expt(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]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 2;
> #Start Series array_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x2[term_no] := array_x2_init[term_no] * expt(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]* expt(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();
> if (omniabs(array_x1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(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)
> ;
> if (omniabs(array_x2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_x2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> if (glob_subiter_method = 1 ) then # if number 3
> atomall();
> elif (glob_subiter_method = 2 ) then # if number 4
> subiter := 1;
> while (subiter <= 3) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while (subiter <= 3 + glob_max_terms) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> fi;# end if 4
> ;
> if (glob_look_poles) then # if number 4
> #left paren 0004C
> check_for_pole();
> fi;# end if 4
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> #Jump Series array_x1
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[3,iii] := array_x1_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_x2
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 4
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 4
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 4
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if (glob_html_log) then # if number 4
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-09-02T21:57:37-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest6")
> ;
> logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
> ;
> logitem_float(html_log_file,t_start)
> ;
> logitem_float(html_log_file,t_end)
> ;
> logitem_float(html_log_file,array_t[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 5
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 5
> ;
> log_revs(html_log_file," 126 | ")
> ;
> logitem_str(html_log_file,"mtest6 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest6 maple results")
> ;
> logitem_str(html_log_file,"c c++ Maple and Maxima")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logditto(html_log_file)
> ;
> if (glob_percent_done < 100.0) then # if number 5
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 5
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 4
> ;
> if (glob_html_log) then # if number 4
> fclose(html_log_file);
> fi;# end if 4
> ;
> ;;
> #END OUTFILEMAIN
>
> # End Function number 8
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter,
tmp, subiter;
global DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, ALWAYS,
glob_max_sec, glob_max_hours, glob_clock_start_sec, djd_debug,
glob_small_float, glob_hmax, glob_initial_pass, glob_not_yet_finished,
centuries_in_millinium, sec_in_minute, glob_curr_iter_when_opt, glob_warned,
glob_max_rel_trunc_err, glob_look_poles, glob_last_good_h, glob_hmin_init,
years_in_century, glob_max_iter, glob_dump_analytic, djd_debug2, glob_dump,
glob_good_digits, glob_percent_done, glob_disp_incr, hours_in_day,
min_in_hour, glob_max_opt_iter, glob_large_float, glob_not_yet_start_msg,
glob_clock_sec, glob_display_flag, glob_log10normmin, glob_start,
glob_warned2, glob_smallish_float, glob_max_trunc_err, glob_log10relerr,
glob_log10abserr, glob_iter, MAX_UNCHANGED, glob_current_iter,
glob_optimal_clock_start_sec, glob_no_eqs, glob_optimal_expect_sec,
glob_subiter_method, glob_max_minutes, glob_relerr, glob_h,
glob_optimal_done, glob_reached_optimal_h, glob_almost_1, glob_normmax,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_hmin, glob_html_log,
glob_optimal_start, glob_abserr, glob_log10_relerr, glob_log10_abserr,
days_in_year, array_const_0D0, array_const_3D0, array_const_2,
array_const_4D0, array_const_1, array_const_2D0, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17, array_norms, array_type_pole, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_t, array_pole, array_x1_init, array_m1,
array_1st_rel_error, array_x2_init, array_x1, array_x2,
array_last_rel_error, array_fact_1, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher_work,
array_x1_higher_work2, array_x2_higher, array_x1_set_initial,
array_x1_higher, array_fact_2, array_x2_set_initial, array_x1_higher_work,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
glob_max_terms := 30;
INFO := 2;
DEBUGL := 3;
glob_iolevel := 5;
ALWAYS := 1;
glob_max_sec := 10000.0;
glob_max_hours := 0.;
glob_clock_start_sec := 0.;
djd_debug := true;
glob_small_float := 0.1*10^(-50);
glob_hmax := 1.0;
glob_initial_pass := true;
glob_not_yet_finished := true;
centuries_in_millinium := 10;
sec_in_minute := 60;
glob_curr_iter_when_opt := 0;
glob_warned := false;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_look_poles := false;
glob_last_good_h := 0.1;
glob_hmin_init := 0.001;
years_in_century := 100;
glob_max_iter := 1000;
glob_dump_analytic := false;
djd_debug2 := true;
glob_dump := false;
glob_good_digits := 0;
glob_percent_done := 0.;
glob_disp_incr := 0.1;
hours_in_day := 24;
min_in_hour := 60;
glob_max_opt_iter := 10;
glob_large_float := 0.90*10^101;
glob_not_yet_start_msg := true;
glob_clock_sec := 0.;
glob_display_flag := true;
glob_log10normmin := 0.1;
glob_start := 0;
glob_warned2 := false;
glob_smallish_float := 0.1*10^(-100);
glob_max_trunc_err := 0.1*10^(-10);
glob_log10relerr := 0.;
glob_log10abserr := 0.;
glob_iter := 0;
MAX_UNCHANGED := 10;
glob_current_iter := 0;
glob_optimal_clock_start_sec := 0.;
glob_no_eqs := 0;
glob_optimal_expect_sec := 0.1;
glob_subiter_method := 3;
glob_max_minutes := 0.;
glob_relerr := 0.1*10^(-10);
glob_h := 0.1;
glob_optimal_done := false;
glob_reached_optimal_h := false;
glob_almost_1 := 0.9990;
glob_normmax := 0.;
glob_orig_start_sec := 0.;
glob_unchanged_h_cnt := 0;
glob_hmin := 0.1*10^(-10);
glob_html_log := true;
glob_optimal_start := 0.;
glob_abserr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
days_in_year := 365;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest6postode.ode#################");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
diff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#");
omniout_str(ALWAYS, "# was complicated.ode");
omniout_str(ALWAYS, "#");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x1_init[1 + 1] := exact_soln_x1p(t_start);")
;
omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[1 + 1] := exact_soln_x2p(t_start);")
;
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 1;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "return(2.0 * c1 + 6.0 * c3 * exp(-t));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x1p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "return( - 6.0 * c3 * exp(-t));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS,
"return( 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_tmp10 := Array(0 .. max_terms + 1, []);
array_tmp11 := Array(0 .. max_terms + 1, []);
array_tmp12 := Array(0 .. max_terms + 1, []);
array_tmp13 := Array(0 .. max_terms + 1, []);
array_tmp14 := Array(0 .. max_terms + 1, []);
array_tmp15 := Array(0 .. max_terms + 1, []);
array_tmp16 := Array(0 .. max_terms + 1, []);
array_tmp17 := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_tmp6 := Array(0 .. max_terms + 1, []);
array_tmp7 := Array(0 .. max_terms + 1, []);
array_tmp8 := Array(0 .. max_terms + 1, []);
array_tmp9 := Array(0 .. max_terms + 1, []);
array_t := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_x1_init := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_x2_init := Array(0 .. max_terms + 1, []);
array_x1 := Array(0 .. max_terms + 1, []);
array_x2 := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 3, 0 .. 4, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_x2_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 3, 0 .. 4, []);
array_x2_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x2_higher := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_higher := Array(0 .. 4, 0 .. max_terms + 1, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_x2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []);
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_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_t[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 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_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[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_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp17 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp17[term] := 0.; term := term + 1
end do;
array_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[term] := 0.; term := term + 1
end do;
array_tmp15 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp15[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_tmp9 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1
end do;
array_x2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1
end do;
array_x1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
end do;
array_const_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_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_const_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_const_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_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x1_init[2] := exact_soln_x1p(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 1;
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 := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
chk_data();
array_x1_set_initial[1, 1] := true;
array_x1_set_initial[1, 2] := true;
array_x1_set_initial[1, 3] := false;
array_x1_set_initial[1, 4] := false;
array_x1_set_initial[1, 5] := false;
array_x1_set_initial[1, 6] := false;
array_x1_set_initial[1, 7] := false;
array_x1_set_initial[1, 8] := false;
array_x1_set_initial[1, 9] := false;
array_x1_set_initial[1, 10] := false;
array_x1_set_initial[1, 11] := false;
array_x1_set_initial[1, 12] := false;
array_x1_set_initial[1, 13] := false;
array_x1_set_initial[1, 14] := false;
array_x1_set_initial[1, 15] := false;
array_x1_set_initial[1, 16] := false;
array_x1_set_initial[1, 17] := false;
array_x1_set_initial[1, 18] := false;
array_x1_set_initial[1, 19] := false;
array_x1_set_initial[1, 20] := false;
array_x1_set_initial[1, 21] := false;
array_x1_set_initial[1, 22] := false;
array_x1_set_initial[1, 23] := false;
array_x1_set_initial[1, 24] := false;
array_x1_set_initial[1, 25] := false;
array_x1_set_initial[1, 26] := false;
array_x1_set_initial[1, 27] := false;
array_x1_set_initial[1, 28] := false;
array_x1_set_initial[1, 29] := false;
array_x1_set_initial[1, 30] := false;
array_x2_set_initial[2, 1] := true;
array_x2_set_initial[2, 2] := true;
array_x2_set_initial[2, 3] := false;
array_x2_set_initial[2, 4] := false;
array_x2_set_initial[2, 5] := false;
array_x2_set_initial[2, 6] := false;
array_x2_set_initial[2, 7] := false;
array_x2_set_initial[2, 8] := false;
array_x2_set_initial[2, 9] := false;
array_x2_set_initial[2, 10] := false;
array_x2_set_initial[2, 11] := false;
array_x2_set_initial[2, 12] := false;
array_x2_set_initial[2, 13] := false;
array_x2_set_initial[2, 14] := false;
array_x2_set_initial[2, 15] := false;
array_x2_set_initial[2, 16] := false;
array_x2_set_initial[2, 17] := false;
array_x2_set_initial[2, 18] := false;
array_x2_set_initial[2, 19] := false;
array_x2_set_initial[2, 20] := false;
array_x2_set_initial[2, 21] := false;
array_x2_set_initial[2, 22] := false;
array_x2_set_initial[2, 23] := false;
array_x2_set_initial[2, 24] := false;
array_x2_set_initial[2, 25] := false;
array_x2_set_initial[2, 26] := false;
array_x2_set_initial[2, 27] := false;
array_x2_set_initial[2, 28] := false;
array_x2_set_initial[2, 29] := false;
array_x2_set_initial[2, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x1[term_no] := array_x1_init[term_no]*
expt(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]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_init[term_no]*
expt(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]*
expt(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();
if glob_small_float < omniabs(array_x1_higher[1, 1]) then
tmp := omniabs(array_x1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
if glob_small_float < omniabs(array_x2_higher[1, 1]) then
tmp := omniabs(array_x2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_t[1] <= t_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 3 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
if glob_look_poles then check_for_pole() end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[3, iii] := array_x1_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
term_no := glob_max_terms;
while 1 <= term_no do
array_x1[term_no] := array_x1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x1_higher[ord, term_no] :=
array_x1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
term_no := glob_max_terms;
while 1 <= term_no do
array_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
ff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-09-02T21:57:37-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest6")
;
logitem_str(html_log_file,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
;
logitem_float(html_log_file, t_start);
logitem_float(html_log_file, t_end);
logitem_float(html_log_file, array_t[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
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, " 126 | ");
logitem_str(html_log_file,
"mtest6 diffeq.mxt");
logitem_str(html_log_file,
"mtest6 maple results");
logitem_str(html_log_file, "c c++ Maple and Maxima");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \
2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_good_digits(html_log_file, array_last_rel_error[2]);
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
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest6postode.ode#################
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
#
# was complicated.ode
#
t_start := 0.5;
t_end := 5.0;
array_x1_init[0 + 1] := exact_soln_x1(t_start);
array_x1_init[1 + 1] := exact_soln_x1p(t_start);
array_x2_init[0 + 1] := exact_soln_x2(t_start);
array_x2_init[1 + 1] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 1;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return(2.0 * c1 + 6.0 * c3 * exp(-t));
end;
exact_soln_x1p := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return( - 6.0 * c3 * exp(-t));
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1] = 0.5
x1[1] (analytic) = 2.001091755187482740162486839163
x1[1] (numeric) = 2.001091755187482740162486839163
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 1e-05
x2[1] (analytic) = 1.0007256155636055990741531973548
x2[1] (numeric) = 1.0007256155636055990741531973548
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 1e-05
t[1] = 0.5
x1[1] (analytic) = 2.001091755187482740162486839163
x1[1] (numeric) = 2.001091755187482740162486839163
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 1e-05
x2[1] (analytic) = 1.0007256155636055990741531973548
x2[1] (numeric) = 1.0007256155636055990741531973548
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50001
x1[1] (analytic) = 2.001091744269985452912500608286
x1[1] (numeric) = 2.0010917442699308653350852142946
absolute error = 5.45875774153939914e-14
relative error = 2.7278897917450548329683800883503e-12 %
Correct digits = 13
h = 1e-05
x2[1] (analytic) = 1.0007256246172587637000202407718
x2[1] (numeric) = 1.0007256246171409337724338679846
absolute error = 1.178299275863727872e-13
relative error = 1.1774448928640001458640220501978e-11 %
Correct digits = 12
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3.8MB, alloc=2.8MB, time=0.49
t[1] = 0.50002
x1[1] (analytic) = 2.0010917333525973400895138324872
x1[1] (numeric) = 2.0010917333523789905076835894262
absolute error = 2.183495818302430610e-13
relative error = 1.0911522854798047464160040082450e-11 %
Correct digits = 12
h = 1e-05
x2[1] (analytic) = 1.000725633671147590959298917551
x2[1] (numeric) = 1.0007256336706762684707145386144
absolute error = 4.713224885843789366e-13
relative error = 4.7098072910887589392878456682749e-11 %
Correct digits = 12
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50003
x1[1] (analytic) = 2.0010917224353184006017877004751
x1[1] (numeric) = 2.0010917224348271156802819645578
absolute error = 4.912849215057359173e-13
relative error = 2.4550844721292669098605182759693e-11 %
Correct digits = 12
h = 1e-05
x2[1] (analytic) = 1.0007256427252720850194141643805
x2[1] (numeric) = 1.0007256427242116031689952092442
absolute error = 1.0604818504189551363e-12
relative error = 1.0597128774785356885351194372910e-10 %
Correct digits = 11
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50004
x1[1] (analytic) = 2.0010917115181486333575943182919
x1[1] (numeric) = 2.0010917115172752408528803396894
absolute error = 8.733925047139786025e-13
relative error = 4.3645800923905205336928653344164e-11 %
Correct digits = 12
h = 1e-05
x2[1] (analytic) = 1.0007256517796322500478797260023
x2[1] (numeric) = 1.000725651777746937867275879874
absolute error = 1.8853121806038461283e-12
relative error = 1.8839450924947478705846212286622e-10 %
Correct digits = 11
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50005
x1[1] (analytic) = 2.001091700601088037265216709204
x1[1] (numeric) = 2.001091700599723366025478714821
absolute error = 1.3646712397379943830e-12
relative error = 6.8196336995854530777617295039262e-11 %
Correct digits = 12
h = 1e-05
x2[1] (analytic) = 1.0007256608342280902122981569334
x2[1] (numeric) = 1.0007256608312822725655565505038
absolute error = 2.9458176467416064296e-12
relative error = 2.9436815323451430301872142913117e-10 %
Correct digits = 11
h = 1e-05
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.9MB, time=1.09
NO POLE
NO POLE
t[1] = 0.50006
x1[1] (analytic) = 2.0010916896841366112329488135932
x1[1] (numeric) = 2.0010916896821714911980770899526
absolute error = 1.9651200348717236406e-12
relative error = 9.8202398470902103654266548941424e-11 %
Correct digits = 12
h = 1e-05
x2[1] (analytic) = 1.0007256698890596096803608231877
x2[1] (numeric) = 1.0007256698848176072638372211336
absolute error = 4.2420024165236020541e-12
relative error = 4.2389263553056155724413569720607e-10 %
Correct digits = 11
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50007
x1[1] (analytic) = 2.0010916787672943541690954888471
x1[1] (numeric) = 2.0010916787646196163706754650842
absolute error = 2.6747377984200237629e-12
relative error = 1.3366393088335196043284721532438e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007256789441268126198479039976
x2[1] (numeric) = 1.0007256789383529419621178917634
absolute error = 5.7738706577300122342e-12
relative error = 5.7696837197403254141910194278508e-10 %
Correct digits = 11
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50008
x1[1] (analytic) = 2.0010916678505612649819725092502
x1[1] (numeric) = 2.0010916678470677415432738402158
absolute error = 3.4935234386986690344e-12
relative error = 1.7458087976805071044395145958886e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007256879994297031986283935353
x2[1] (numeric) = 1.0007256879918882766603985623932
absolute error = 7.5414265382298311421e-12
relative error = 7.5359577841016996804818151711288e-10 %
Correct digits = 11
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50009
x1[1] (analytic) = 2.0010916569339373425799065658746
x1[1] (numeric) = 2.0010916569295158667158722153474
absolute error = 4.4214758640343505272e-12
relative error = 2.2095319066038753049504806843521e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007256970549682855846601026355
x2[1] (numeric) = 1.000725697045423611358679233023
absolute error = 9.5446742259808696125e-12
relative error = 9.5377527069304344024150535329446e-10 %
Correct digits = 11
h = 1e-05
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=3.9MB, time=1.70
NO POLE
NO POLE
t[1] = 0.5001
x1[1] (analytic) = 2.0010916460174225858712352664712
x1[1] (numeric) = 2.001091646011963991888470590479
absolute error = 5.4585939827646759922e-12
relative error = 2.7278080909629415950772240689257e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007257061107425639459896605159
x2[1] (numeric) = 1.0007257060989589460569599036528
absolute error = 1.17836178890297568631e-11
relative error = 1.1775072646855496212802323559987e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50011
x1[1] (analytic) = 2.00109163510101699376430713536
x1[1] (numeric) = 2.0010916350944121170610689656106
absolute error = 6.6048767032381697494e-12
relative error = 3.3006368061224489310993926357765e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007257151667525424507525165002
x2[1] (numeric) = 1.0007257151524942807552405742826
absolute error = 1.42582616955119422176e-11
relative error = 1.4247921762594124044317201054396e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50012
x1[1] (analytic) = 2.001091624184720565167481613321
x1[1] (numeric) = 2.0010916241768602422336673407422
absolute error = 7.8603229338142725788e-12
relative error = 3.9280175074525657825828766892287e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007257242229982252671729417388
x2[1] (numeric) = 1.0007257242060296154535212449124
absolute error = 1.69686098136516968264e-11
relative error = 1.6956304212951830825347559505580e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50013
x1[1] (analytic) = 2.0010916132685332989891290574857
x1[1] (numeric) = 2.0010916132593083674062657158738
absolute error = 9.2249315828633416119e-12
relative error = 4.6099496503288860789020768755177e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.000725733279479616563564030932
x2[1] (numeric) = 1.0007257332595649501518019155422
absolute error = 1.99146664117621153898e-11
relative error = 1.9900224156822405178345004023486e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=3.9MB, time=2.32
NO POLE
NO POLE
t[1] = 0.50014
x1[1] (analytic) = 2.001091602352455194137630741227
x1[1] (numeric) = 2.0010916023417564925788640910054
absolute error = 1.06987015587666502216e-11
relative error = 5.3464326901324291549625919135876e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007257423361967205083277040506
x2[1] (numeric) = 1.000725742313100284850082586172
absolute error = 2.30964356582451178786e-11
relative error = 2.3079685753187913115575126674189e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50015
x1[1] (analytic) = 2.0010915914364862495213788540507
x1[1] (numeric) = 2.001091591424204617751462466137
absolute error = 1.22816317699163879137e-11
relative error = 6.1374660822496396977234533059416e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007257513931495412699547080584
x2[1] (numeric) = 1.0007257513666356195483632568018
absolute error = 2.65139217215914512566e-11
relative error = 2.6494693161118699736765319826937e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50016
x1[1] (analytic) = 2.001091580520626464048776501486
x1[1] (numeric) = 2.0010915805066527429240608412686
absolute error = 1.39737211247156602174e-11
relative error = 6.9830492820723876922196162007132e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007257604503380830170246186347
x2[1] (numeric) = 1.0007257604201709542466439274316
absolute error = 3.01671287703806912031e-11
relative error = 3.0145250539773390926751525294552e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=3.9MB, time=2.96
NO POLE
NO POLE
t[1] = 0.50017
x1[1] (analytic) = 2.0010915696048758366282377049766
x1[1] (numeric) = 2.0010915695891008680966592164002
absolute error = 1.57749685315784885764e-11
relative error = 7.8831817449979683678842699965338e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007257695077623499182058418952
x2[1] (numeric) = 1.0007257694737062889449245980614
absolute error = 3.40560609732812438338e-11
relative error = 3.4031362048398895051525079613637e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50018
x1[1] (analytic) = 2.0010915586892343661681874017715
x1[1] (numeric) = 2.0010915586715489932692575915318
absolute error = 1.76853728989298102397e-11
relative error = 8.8378629264291021447212141687147e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.000725778565422346142255616115
x2[1] (numeric) = 1.0007257785272416236432052686912
absolute error = 3.81807224990503474238e-11
relative error = 3.8153031846330404656376972090057e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50019
x1[1] (analytic) = 2.0010915477737020515770614448153
x1[1] (numeric) = 2.0010915477539971184418559666634
absolute error = 1.97049331352054781519e-11
relative error = 9.8470922817739345792273538589696e-10 %
Correct digits = 11
h = 1e-05
x2[1] (analytic) = 1.0007257876233180758580200134503
x2[1] (numeric) = 1.000725787580776958341485939321
absolute error = 4.25411175165340741293e-11
relative error = 4.2510264092991398162741981322399e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5002
x1[1] (analytic) = 2.0010915368582788917633066026401
x1[1] (numeric) = 2.001091536836445243614454341795
absolute error = 2.18336481488522608451e-11
relative error = 1.0910869266446036311114742475194e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007257966814495432344339416603
x2[1] (numeric) = 1.0007257966343122930397666099508
absolute error = 4.71372501946673317095e-11
relative error = 4.7103062947893641565241602337602e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=3.9MB, time=3.57
NO POLE
NO POLE
t[1] = 0.50021
x1[1] (analytic) = 2.0010915259429648856353805592552
x1[1] (numeric) = 2.0010915259188933687870527169266
absolute error = 2.40715168483278423286e-11
relative error = 1.2029193335864403008933207716202e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.00072580573981675244052114583
x2[1] (numeric) = 1.0007258056878476277380472805806
absolute error = 5.19691247024738652494e-11
relative error = 5.1931432570637190129625256587926e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50022
x1[1] (analytic) = 2.0010915150277600321017519140388
x1[1] (numeric) = 2.0010915150013414939596510920582
absolute error = 2.64185381421008219806e-11
relative error = 1.3202063945453455316692415514133e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007258147984197076453942100915
x2[1] (numeric) = 1.0007258147413829624363279512104
absolute error = 5.70367452090662588811e-11
relative error = 5.6995377120910390089211525401801e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50023
x1[1] (analytic) = 2.0010915041126643300709001816284
x1[1] (numeric) = 2.0010915040837896191322494671898
absolute error = 2.88747109386507144386e-11
relative error = 1.4429480550643038799834271932728e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007258238572584130182545593471
x2[1] (numeric) = 1.0007258237949182971346086218402
absolute error = 6.23401158836459375069e-11
relative error = 6.2294900758489880343127013459283e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50024
x1[1] (analytic) = 2.0010914931976777784513157918119
x1[1] (numeric) = 2.0010914931662377443048478423214
absolute error = 3.14400341464679494905e-11
relative error = 1.5711442606868423891555117548106e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.000725832916332872728392460991
x2[1] (numeric) = 1.00072583284845363183288929247
absolute error = 6.78792408955031685210e-11
relative error = 6.7830007643240594153145163116329e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=3.9MB, time=4.19
NO POLE
NO POLE
t[1] = 0.50025
x1[1] (analytic) = 2.0010914822828003761515000894181
x1[1] (numeric) = 2.001091482248685869477446217453
absolute error = 3.41145066740538719651e-11
relative error = 1.7047949569570305838828068863950e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007258419756430909451870266318
x2[1] (numeric) = 1.0007258419019889665311699630998
absolute error = 7.36541244140170635320e-11
relative error = 7.3600701935115760841323423929656e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50026
x1[1] (analytic) = 2.0010914713680321220799653342081
x1[1] (numeric) = 2.0010914713311339946500445925846
absolute error = 3.68981274299207416235e-11
relative error = 1.8439000894194804648875097671500e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007258510351890718381062138146
x2[1] (numeric) = 1.0007258509555243012294506337296
absolute error = 7.96647706086555800850e-11
relative error = 7.9606987794156907487239647678438e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50027
x1[1] (analytic) = 2.0010914604533730151452347007656
x1[1] (numeric) = 2.0010914604135821198226429677162
absolute error = 3.97908953225917330494e-11
relative error = 1.9884596036193465035089393804411e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007258600949708195767068277438
x2[1] (numeric) = 1.0007258600090596359277313043594
absolute error = 8.59111836489755233844e-11
relative error = 8.5848869380493860625926910998450e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=30.5MB, alloc=3.9MB, time=4.80
t[1] = 0.50028
x1[1] (analytic) = 2.001091449538823054255842278388
x1[1] (numeric) = 2.0010914494960302449952413428478
absolute error = 4.27928092606009355402e-11
relative error = 2.1384734451023256363357493112049e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007258691549883383306345230051
x2[1] (numeric) = 1.0007258690625949706260119749892
absolute error = 9.23933677046225480159e-11
relative error = 9.2326350854344747945007853555794e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50029
x1[1] (analytic) = 2.0010914386243822383203330709772
x1[1] (numeric) = 2.0010914385784783701678397179794
absolute error = 4.59038681524933529978e-11
relative error = 2.2939415594146572598231470648765e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.000725878215241632269623805288
x2[1] (numeric) = 1.000725878116130305324292645619
absolute error = 9.91113269453311596690e-11
relative error = 9.9039436376015999982327588810901e-09 %
Correct digits = 10
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5003
x1[1] (analytic) = 2.0010914277100505662472629969306
x1[1] (numeric) = 2.001091427660926495340438093111
absolute error = 4.91240709068249038196e-11
relative error = 2.4548638921031232249201062719658e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007258872757307055634980331085
x2[1] (numeric) = 1.0007258871696656400225733162488
absolute error = 1.060650655409247168597e-10
relative error = 1.0598813010590235182378540490673e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50031
x1[1] (analytic) = 2.0010914167958280369451988890319
x1[1] (numeric) = 2.0010914167433746205130364682426
absolute error = 5.24534164321624207893e-11
relative error = 2.6212403887150478316865826869170e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007258963364555623821694195314
x2[1] (numeric) = 1.0007258962232009747208539868786
absolute error = 1.132545876613154326528e-10
relative error = 1.1317243620448684480076569084780e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=3.9MB, time=5.40
NO POLE
NO POLE
t[1] = 0.50032
x1[1] (analytic) = 2.0010914058817146493227184943417
x1[1] (numeric) = 2.0010914058258227456856348433742
absolute error = 5.58919036370836509675e-11
relative error = 2.7930709947982978239007339809003e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007259053974162068956390338926
x2[1] (numeric) = 1.0007259052767363094191346575084
absolute error = 1.206798974765043763842e-10
relative error = 1.2059235883234082818756779780111e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50033
x1[1] (analytic) = 2.0010913949677104022884104740887
x1[1] (numeric) = 2.0010913949082708708582332185058
absolute error = 5.94395314301772555829e-11
relative error = 2.9703556559012823836961215121928e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007259144586126432739968035224
x2[1] (numeric) = 1.0007259143302716441174153281382
absolute error = 1.283409991565814753842e-10
relative error = 1.2824790215012396089983411008832e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50034
x1[1] (analytic) = 2.0010913840538152947508744035603
x1[1] (numeric) = 2.0010913839907189960308315936374
absolute error = 6.30962987200428099229e-11
relative error = 3.1530943175729531261689267989922e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007259235200448756874215154673
x2[1] (numeric) = 1.000725923383806978815695998768
absolute error = 1.362378968717255166993e-10
relative error = 1.3613907031858421319147813925587e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50035
x1[1] (analytic) = 2.0010913731400293256187207719937
x1[1] (numeric) = 2.001091373073167121203429968769
absolute error = 6.68622044152908032247e-11
relative error = 3.3412869253628040940101526971580e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.000725932581712908306180818213
x2[1] (numeric) = 1.0007259324373423135139766693978
absolute error = 1.443705947922041488152e-10
relative error = 1.4426586749855786835281068267879e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=3.9MB, time=6.01
NO POLE
NO POLE
t[1] = 0.50036
x1[1] (analytic) = 2.0010913622263524938005709824666
x1[1] (numeric) = 2.0010913621556152463760283439006
absolute error = 7.07372474245426385660e-11
relative error = 3.5349334248208717521178338261259e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007259416436167453006312234074
x2[1] (numeric) = 1.0007259414908776482122573400276
absolute error = 1.527390970883738833798e-10
relative error = 1.5262829785096952440866491707780e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50037
x1[1] (analytic) = 2.001091351312784798205057351788
x1[1] (numeric) = 2.0010913512380633715486267190322
absolute error = 7.47214266564306327558e-11
relative error = 3.7340337614977349822142426078133e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007259507057563908412181075826
x2[1] (numeric) = 1.0007259505444129829105380106574
absolute error = 1.613434079306800969252e-10
relative error = 1.6122636553683209581552115233125e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50038
x1[1] (analytic) = 2.0010913403993262377408231103894
x1[1] (numeric) = 2.0010913403205114967212250941638
absolute error = 7.88147410195980162256e-11
relative error = 3.9385878809445150774830827381501e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007259597681318490984757138783
x2[1] (numeric) = 1.0007259595979483176088186812872
absolute error = 1.701835314896570325911e-10
relative error = 1.7006007471724681516002950456268e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50039
x1[1] (analytic) = 2.0010913294859768113165224022153
x1[1] (numeric) = 2.0010913294029596218938234692954
absolute error = 8.30171894226989329199e-11
relative error = 4.1485957287128757371717000872266e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007259688307431242430271537639
x2[1] (numeric) = 1.000725968651483652307099351917
absolute error = 1.792594719359278018469e-10
relative error = 1.7912942955340323485623244706698e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=3.9MB, time=6.61
NO POLE
NO POLE
t[1] = 0.5004
x1[1] (analytic) = 2.001091318572736517840820284614
x1[1] (numeric) = 2.001091318485407747066421844427
absolute error = 8.73287707743984401870e-11
relative error = 4.3640572503550230612082837586693e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007259778935902204455844087623
x2[1] (numeric) = 1.0007259777050189870053800225468
absolute error = 1.885712334402043862155e-10
relative error = 1.8843443420657922884448506276062e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50041
x1[1] (analytic) = 2.0010913076596053562223927282289
x1[1] (numeric) = 2.0010913075678558722390202195586
absolute error = 9.17494839833725086703e-11
relative error = 4.5849723914237055448440518552865e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007259869566731418769483321718
x2[1] (numeric) = 1.0007259867585543217036606931766
absolute error = 1.981188201732876389952e-10
relative error = 1.9797509283814099428847560966326e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50042
x1[1] (analytic) = 2.0010912967465833253699266168891
x1[1] (numeric) = 2.0010912966503039974116185946902
absolute error = 9.62793279583080221989e-11
relative error = 4.8113410974722140732604546730216e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007259960199918927080086507894
x2[1] (numeric) = 1.0007259958120896564019413638064
absolute error = 2.079022363060672869830e-10
relative error = 2.0775140960954305327364400543898e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=3.9MB, time=7.22
NO POLE
NO POLE
t[1] = 0.50043
x1[1] (analytic) = 2.0010912858336704241921197475003
x1[1] (numeric) = 2.0010912857327521225842169698218
absolute error = 1.009183016079027776785e-10
relative error = 5.0431633140543819161913680546422e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007260050835464771097439666338
x2[1] (numeric) = 1.0007260048656249911002220344362
absolute error = 2.179214860095219321976e-10
relative error = 2.1776338868232825450529946417941e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50044
x1[1] (analytic) = 2.0010912749208666515976808299356
x1[1] (numeric) = 2.0010912748152002477568153449534
absolute error = 1.056664038408654849822e-10
relative error = 5.2804389867245847225402878105693e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007260141473368992532217586681
x2[1] (numeric) = 1.000726013919160325798502705066
absolute error = 2.281765734547190536021e-10
relative error = 2.2801103421812777500643728540501e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50045
x1[1] (analytic) = 2.0010912640081720064953294869263
x1[1] (numeric) = 2.001091263897648372929413720085
absolute error = 1.105236335659157668413e-10
relative error = 5.5231680610377405149975224800159e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.000726023211363163309598384523
x2[1] (numeric) = 1.0007260229726956604967833756958
absolute error = 2.386675028128150088272e-10
relative error = 2.3849435037866112181605421486350e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50046
x1[1] (analytic) = 2.0010912530955864877937962539533
x1[1] (numeric) = 2.0010912529800964981020120952166
absolute error = 1.154899896917841587367e-10
relative error = 5.7713504825493096846873680725976e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007260322756252734501190822198
x2[1] (numeric) = 1.0007260320262309951950640463256
absolute error = 2.493942782550550358942e-10
relative error = 2.4921334132573613368726288490516e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=3.9MB, time=7.83
NO POLE
NO POLE
t[1] = 0.50047
x1[1] (analytic) = 2.0010912421831100944018225791373
x1[1] (numeric) = 2.0010912420625446232746104703482
absolute error = 1.205654711272121087891e-10
relative error = 6.0249861968152949857553138707154e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007260413401232338461179718932
x2[1] (numeric) = 1.0007260410797663298933447169554
absolute error = 2.603569039527732549378e-10
relative error = 2.6016801122124898278520533440493e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50048
x1[1] (analytic) = 2.0010912312707428252281608231299
x1[1] (numeric) = 2.0010912311449927484472088454798
absolute error = 1.257500767809519776501e-10
relative error = 6.2840751493922415300002220320508e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007260504048570486690180575151
x2[1] (numeric) = 1.0007260501333016645916253875852
absolute error = 2.715553840773926699299e-10
relative error = 2.7135836422718417638596473757261e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50049
x1[1] (analytic) = 2.0010912203584846791815742590047
x1[1] (numeric) = 2.0010912202274408736198072206114
absolute error = 1.310438055617670383933e-10
relative error = 6.5486172858372367815065055329928e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007260594698267220903312286167
x2[1] (numeric) = 1.000726059186836999289906058215
absolute error = 2.829897228004251704017e-10
relative error = 2.8278440450561455857377730048416e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5005
x1[1] (analytic) = 2.001091209446335655170837072148
x1[1] (numeric) = 2.001091209309888998792405595743
absolute error = 1.364466563784314764050e-10
relative error = 6.8186125517079105512563153591757e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007260685350322582816582620126
x2[1] (numeric) = 1.0007260682403723339881867288448
absolute error = 2.946599242934715331678e-10
relative error = 2.9444613621870131194024164089365e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=3.9MB, time=8.43
NO POLE
NO POLE
t[1] = 0.50051
x1[1] (analytic) = 2.0010911985342957521047343601496
x1[1] (numeric) = 2.0010911983923371239650039708746
absolute error = 1.419586281397303892750e-10
relative error = 7.0940608925624349917467233098532e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007260776004736614146888235234
x2[1] (numeric) = 1.0007260772939076686864673994746
absolute error = 3.065659927282214240488e-10
relative error = 3.0634356352869395928202819058512e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50052
x1[1] (analytic) = 2.0010911876223649688920621326937
x1[1] (numeric) = 2.0010911874747852491376023460062
absolute error = 1.475797197544597866875e-10
relative error = 7.3749622539595245916119004163320e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007260866661509356612014696992
x2[1] (numeric) = 1.0007260863474430033847480701044
absolute error = 3.187079322764533995948e-10
relative error = 3.1847669059793036529948687897256e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50053
x1[1] (analytic) = 2.0010911767105433044416273114501
x1[1] (numeric) = 2.0010911765572333743102007211378
absolute error = 1.533099301314265903123e-10
relative error = 7.6613165814584361702602855217790e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007260957320640851930636495429
x2[1] (numeric) = 1.0007260954009783380830287407342
absolute error = 3.310857471100349088087e-10
relative error = 3.3084552158883673829505389597418e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=57.2MB, alloc=3.9MB, time=9.04
t[1] = 0.50054
x1[1] (analytic) = 2.0010911657988307576622477299646
x1[1] (numeric) = 2.0010911656396814994827990962694
absolute error = 1.591492581794486336952e-10
relative error = 7.9531238206189688724717740137100e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007261047982131141822317062334
x2[1] (numeric) = 1.000726104454513672781309411364
absolute error = 3.436994414009222948694e-10
relative error = 3.4345006066392763187155746157333e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50055
x1[1] (analytic) = 2.0010911548872273274627521335501
x1[1] (numeric) = 2.001091154722129624655397471401
absolute error = 1.650977028073546621491e-10
relative error = 8.2503839170014641630298858116630e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007261138645980268007508788489
x2[1] (numeric) = 1.0007261135080490074795900819938
absolute error = 3.565490193211607968551e-10
relative error = 3.5629031198580594663062245691206e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50056
x1[1] (analytic) = 2.0010911439757330127519801791777
x1[1] (numeric) = 2.0010911438045777498279958465326
absolute error = 1.711552629239843326451e-10
relative error = 8.5530968161668058213539316960366e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007261229312188272207553040904
x2[1] (numeric) = 1.0007261225615843421778707526236
absolute error = 3.696344850428845514668e-10
relative error = 3.6936627971716293187127384430887e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50057
x1[1] (analytic) = 2.001091133064347812438782435367
x1[1] (numeric) = 2.0010911328870258750005942216642
absolute error = 1.773219374381882137028e-10
relative error = 8.8612624636764199360911997888910e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.000726131998075519614468018005
x2[1] (numeric) = 1.0007261316151196768761514232534
absolute error = 3.829558427383165947516e-10
relative error = 3.8267796802077818728833916638718e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=3.9MB, time=9.66
NO POLE
NO POLE
t[1] = 0.50058
x1[1] (analytic) = 2.0010911221530717254320203820779
x1[1] (numeric) = 2.0010911219694740001731925967958
absolute error = 1.835977252588277852821e-10
relative error = 9.1748808050922748997840994798940e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007261410651681081542009577096
x2[1] (numeric) = 1.0007261406686550115744320938832
absolute error = 3.965130965797688638264e-10
relative error = 3.9622538105951966467124968891599e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50059
x1[1] (analytic) = 2.0010911112419047506405664106003
x1[1] (numeric) = 2.0010911110519221253457909719274
absolute error = 1.899826252947754386729e-10
relative error = 9.4939517859768814034323609467913e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.000726150132496597012354963114
x2[1] (numeric) = 1.000726149722190346272712764513
absolute error = 4.103062507396421986010e-10
relative error = 4.1000852299634366960224091291825e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5006
x1[1] (analytic) = 2.0010911003308468869733038234462
x1[1] (numeric) = 2.001091100134370250518389347059
absolute error = 1.964766364549144763872e-10
relative error = 9.8184753518932924311751675845484e-09 %
Correct digits = 10
h = 1e-05
x2[1] (analytic) = 1.0007261592000609903614197786446
x2[1] (numeric) = 1.0007261587757256809709934351428
absolute error = 4.243353093904263435018e-10
relative error = 4.2402739799429486315515158528290e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50061
x1[1] (analytic) = 2.0010910894198981333391268342398
x1[1] (numeric) = 2.0010910892168183756909877221906
absolute error = 2.030797576481391120492e-10
relative error = 1.0148451448405103254873341302192e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007261682678612923739740549681
x2[1] (numeric) = 1.0007261678292610156692741057726
absolute error = 4.386002767046999491955e-10
relative error = 4.3828201021650626359422164318513e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=3.9MB, time=10.27
NO POLE
NO POLE
t[1] = 0.50062
x1[1] (analytic) = 2.0010910785090584886469405676084
x1[1] (numeric) = 2.0010910782992665008635860973222
absolute error = 2.097919877833544702862e-10
relative error = 1.0483880021076451428731504349704e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007261773358975072226853507149
x2[1] (numeric) = 1.0007261768827963503675547764024
absolute error = 4.531011568551305743125e-10
relative error = 4.5277236382619924807258930996715e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50063
x1[1] (analytic) = 2.0010910675983279518056610590738
x1[1] (numeric) = 2.0010910673817146260361844724538
absolute error = 2.166133257694765866200e-10
relative error = 1.0824761015472016783945225855070e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007261864041696390803101342026
x2[1] (numeric) = 1.0007261859363316850658354470322
absolute error = 4.678379540144746871704e-10
relative error = 4.6749846298668355433088705219200e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50064
x1[1] (analytic) = 2.0010910566877065217242152549427
x1[1] (numeric) = 2.0010910564641627512087828475854
absolute error = 2.235437705154324073573e-10
relative error = 1.1171094377157021423298193964802e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007261954726776921196937851601
x2[1] (numeric) = 1.000726194989867019764116117662
absolute error = 4.828106723555776674981e-10
relative error = 4.8246031186135728239643603498682e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50065
x1[1] (analytic) = 2.001091045777194197311541012198
x1[1] (numeric) = 2.001091045546610876381381222717
absolute error = 2.305833209301597894810e-10
relative error = 1.1522880051697229715804361789625e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007262045414216705137705964508
x2[1] (numeric) = 1.0007262040434023544623967882918
absolute error = 4.980193160513738081590e-10
relative error = 4.9765791461370689628154016411185e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=3.9MB, time=10.87
NO POLE
NO POLE
t[1] = 0.50066
x1[1] (analytic) = 2.0010910348667909774765870983893
x1[1] (numeric) = 2.0010910346290590015539795978486
absolute error = 2.377319759226075005407e-10
relative error = 1.1880117984658948291310113500789e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007262136104015784355637757966
x2[1] (numeric) = 1.0007262130969376891606774589216
absolute error = 5.134638892748863168750e-10
relative error = 5.1309127540730722568257848110136e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50067
x1[1] (analytic) = 2.0010910239564968611283131915239
x1[1] (numeric) = 2.0010910237115071267265779729802
absolute error = 2.449897344017352185437e-10
relative error = 1.2242808121609026035121415136567e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007262226796174200581854475016
x2[1] (numeric) = 1.0007262221504730238589581295514
absolute error = 5.291443961992273179502e-10
relative error = 5.2876039840582146767879670964908e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50068
x1[1] (analytic) = 2.001091013046311847175689879958
x1[1] (numeric) = 2.0010910127939552518991763481118
absolute error = 2.523565952765135318462e-10
relative error = 1.2610950408114854082640958298052e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.000726231749069199554836654176
x2[1] (numeric) = 1.0007262312040083585572388001812
absolute error = 5.450608409975978539948e-10
relative error = 5.4466528777300118843129759036159e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.0MB, time=11.48
NO POLE
NO POLE
t[1] = 0.50069
x1[1] (analytic) = 2.0010910021362359345276986622872
x1[1] (numeric) = 2.0010910018764033770717747232434
absolute error = 2.598325574559239390438e-10
relative error = 1.2984544789744365813970321268847e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007262408187569210988073584597
x2[1] (numeric) = 1.000726240257543693255519470811
absolute error = 5.612132278432878876487e-10
relative error = 5.6080594767268632488173036668150e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5007
x1[1] (analytic) = 2.0010909912262691220933319472376
x1[1] (numeric) = 2.001090990958851502244373098375
absolute error = 2.674176198489588488626e-10
relative error = 1.3363591212066036848542112119454e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007262498886805888634764447463
x2[1] (numeric) = 1.0007262493110790279538001414408
absolute error = 5.776015609096763033055e-10
relative error = 5.7718238226880518645137891395039e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50071
x1[1] (analytic) = 2.0010909803164114087815930535567
x1[1] (numeric) = 2.0010909800412996274169714735066
absolute error = 2.751117813646215800501e-10
relative error = 1.3748089620648885039742115605244e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007262589588402070223117209071
x2[1] (numeric) = 1.0007262583646143626520808120706
absolute error = 5.942258443702309088365e-10
relative error = 5.9379459572537445674024880183637e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50072
x1[1] (analytic) = 2.0010909694066627935014962099043
x1[1] (numeric) = 2.0010909691237477525895698486382
absolute error = 2.829150409119263612661e-10
relative error = 1.4138039961062470469531438405803e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007262680292357797488699200148
x2[1] (numeric) = 1.0007262674181496973503614827004
absolute error = 6.110860823985084373144e-10
relative error = 6.1064259220649919522585350780598e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.0MB, time=12.08
NO POLE
NO POLE
t[1] = 0.50073
x1[1] (analytic) = 2.0010909584970232751620665547431
x1[1] (numeric) = 2.0010909582061958777621682237698
absolute error = 2.908273973998983309733e-10
relative error = 1.4533442178876895443053660883401e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007262770998673112167967020679
x2[1] (numeric) = 1.0007262764716850320486421533302
absolute error = 6.281822791681545487377e-10
relative error = 6.2772637587637283896269905586613e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50074
x1[1] (analytic) = 2.0010909475874928526723401362302
x1[1] (numeric) = 2.0010909472886440029347665989014
absolute error = 2.988488497375735373288e-10
relative error = 1.4934296219662804483286962649462e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007262861707348055998266557139
x2[1] (numeric) = 1.00072628552522036674692282396
absolute error = 6.455144388529038317539e-10
relative error = 6.4504595089927720428056845943238e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50075
x1[1] (analytic) = 2.0010909366780715249413639121076
x1[1] (numeric) = 2.001090936371092128107364974033
absolute error = 3.069793968339989380746e-10
relative error = 1.5340602028991384325646273732031e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007262952418382670717832999745
x2[1] (numeric) = 1.0007262945787557014452034945898
absolute error = 6.630825656265798053847e-10
relative error = 6.6260132143958248848480364589689e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50076
x1[1] (analytic) = 2.001090925768759290878195749593
x1[1] (numeric) = 2.0010909254535402532799633491646
absolute error = 3.152190375982324004284e-10
relative error = 1.5752359552434363912600415906608e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007263043131776998065790859686
x2[1] (numeric) = 1.0007263036322910361434841652196
absolute error = 6.808866636630949207490e-10
relative error = 6.8039249166174727155438791099333e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.0MB, time=12.69
NO POLE
NO POLE
t[1] = 0.50077
x1[1] (analytic) = 2.001090914859556149391904425271
x1[1] (numeric) = 2.0010909145359883784525617242962
absolute error = 3.235677709393427009748e-10
relative error = 1.6169568735564014388309231465139e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007263133847531079782153986368
x2[1] (numeric) = 1.0007263126858263708417648358494
absolute error = 6.989267371364505627874e-10
relative error = 6.9841946573031851784152621764404e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50078
x1[1] (analytic) = 2.001090903950462099391569624984
x1[1] (numeric) = 2.0010909036184365036251600994278
absolute error = 3.320255957664095255562e-10
relative error = 1.6592229523953149093245718504389e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007263224565644957607825584659
x2[1] (numeric) = 1.0007263217393617055400455064792
absolute error = 7.172027902207370519867e-10
relative error = 7.1668224780993157777122442784551e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50079
x1[1] (analytic) = 2.0010908930414771397862819437227
x1[1] (numeric) = 2.0010908927008846287977584745594
absolute error = 3.405925109885234691633e-10
relative error = 1.7020341863175123558798175458893e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007263315286118673284598232125
x2[1] (numeric) = 1.000726330792897040238326177109
absolute error = 7.357148270901336461035e-10
relative error = 7.3518084206531018953996812077403e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5008
x1[1] (analytic) = 2.0010908821326012694851428855176
x1[1] (numeric) = 2.001090881783332753970356849691
absolute error = 3.492685155147860358266e-10
relative error = 1.7453905698803835501922316717701e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007263406008952268555153896278
x2[1] (numeric) = 1.0007263398464323749366068477388
memory used=83.9MB, alloc=4.0MB, time=13.29
absolute error = 7.544628519189085418890e-10
relative error = 7.5391525266126648081559947291608e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50081
x1[1] (analytic) = 2.0010908712238344873972648633294
x1[1] (numeric) = 2.0010908708657808791429552248226
absolute error = 3.580536082543096385068e-10
relative error = 1.7892920976413724819738416566369e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007263496734145785163063951813
x2[1] (numeric) = 1.0007263488999677096348875183686
absolute error = 7.734468688814188768127e-10
relative error = 7.7288548376270097043609386949810e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50082
x1[1] (analytic) = 2.0010908603151767924317711989403
x1[1] (numeric) = 2.0010908599482290043155535999542
absolute error = 3.669477881162175989861e-10
relative error = 1.8337387641579773584173426938853e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007263587461699264852789197854
x2[1] (numeric) = 1.0007263579535030443331681889984
absolute error = 7.926668821521107307870e-10
relative error = 7.9209153953460257010923479557803e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50083
x1[1] (analytic) = 2.0010908494066281834977961228447
x1[1] (numeric) = 2.0010908490306771294881519750858
absolute error = 3.759510540096441477589e-10
relative error = 1.8787305639877506036573109865612e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007263678191612749369679875196
x2[1] (numeric) = 1.0007263670070383790314488596282
absolute error = 8.121228959055191278914e-10
relative error = 8.1153342414204858611188795029263e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.0MB, time=13.91
NO POLE
NO POLE
t[1] = 0.50084
x1[1] (analytic) = 2.00109083849818865950448477414
x1[1] (numeric) = 2.0010908381131252546607503502174
absolute error = 3.850634048437344239226e-10
relative error = 1.9242674916882988582319165537536e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.000726376892388628045997568355
x2[1] (numeric) = 1.000726376060573713729729530258
absolute error = 8.318149143162680380970e-10
relative error = 8.3121114175020472098957407614776e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50085
x1[1] (analytic) = 2.0010908275898582193609932004178
x1[1] (numeric) = 2.001090827195573379833348725349
absolute error = 3.942848395276444750688e-10
relative error = 1.9703495418172829785466347809175e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007263859658519899870805798786
x2[1] (numeric) = 1.0007263851141090484280102008878
absolute error = 8.517429415590703789908e-10
relative error = 8.5112469652432507525584086621973e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50086
x1[1] (analytic) = 2.0010908166816368619764883576547
x1[1] (numeric) = 2.0010908162780215050059471004806
absolute error = 4.036153569705412571741e-10
relative error = 2.0169767089324180363359588946507e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007263950395513649350188890178
x2[1] (numeric) = 1.0007263941676443831262908715176
absolute error = 8.719069818087280175002e-10
relative error = 8.7127409262975214909183365889017e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50087
x1[1] (analytic) = 2.0010908057735245862601481101032
x1[1] (numeric) = 2.0010908053604696301785454756122
absolute error = 4.130549560816026344910e-10
relative error = 2.0641489875914733181256119990884e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007264041134867570647033137646
x2[1] (numeric) = 1.0007264032211797178245715421474
absolute error = 8.923070392401317716172e-10
relative error = 8.9165933423191684404556528299782e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.0MB, time=14.51
NO POLE
NO POLE
t[1] = 0.50088
x1[1] (analytic) = 2.0010907948655213911211612301825
x1[1] (numeric) = 2.0010907944429177553511438507438
absolute error = 4.226036357700173794387e-10
relative error = 2.1118663723522723246942592190370e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007264131876581705511136249004
x2[1] (numeric) = 1.0007264122747150525228522127772
absolute error = 9.129431180282614121232e-10
relative error = 9.1228042549633846473178440008544e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50089
x1[1] (analytic) = 2.0010907839576272754687273983697
x1[1] (numeric) = 2.0010907835253658805237422258754
absolute error = 4.322613949449851724943e-10
relative error = 2.1601288577726927705372185870945e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007264222620656095693185477205
x2[1] (numeric) = 1.000726421328250387221132883407
absolute error = 9.338152223481856643135e-10
relative error = 9.3313737058862472053154299696726e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5009
x1[1] (analytic) = 2.0010907730498422382120572030903
x1[1] (numeric) = 2.001090772607814005696340601007
absolute error = 4.420282325157166020833e-10
relative error = 2.2089364384106665833266736728297e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007264313367090782944757637584
x2[1] (numeric) = 1.0007264303817857219194135540368
absolute error = 9.549233563750622097216e-10
relative error = 9.5423017367447172729156295600280e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50091
x1[1] (analytic) = 2.0010907621421662782603721406097
x1[1] (numeric) = 2.0010907616902621308689389761386
absolute error = 4.519041473914331644711e-10
relative error = 2.2582891088241799033768833206749e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007264404115885809018319125108
x2[1] (numeric) = 1.0007264394353210566176942246666
absolute error = 9.762675242841376878442e-10
relative error = 9.7555883891966400902430104972428e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.0MB, time=15.10
NO POLE
NO POLE
t[1] = 0.50092
x1[1] (analytic) = 2.0010907512345993945229046149236
x1[1] (numeric) = 2.0010907507727102560415373512702
absolute error = 4.618891384813672636534e-10
relative error = 2.3081868635712730831038942200517e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.000726449486704121566722593162
x2[1] (numeric) = 1.0007264484888563913159748952964
absolute error = 9.978477302507476978656e-10
relative error = 9.9712337049007449960741330343063e-08 %
Correct digits = 9
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50093
x1[1] (analytic) = 2.0010907403271415859088979376491
x1[1] (numeric) = 2.0010907398551583812141357264018
absolute error = 4.719832046947622112473e-10
relative error = 2.3586296972100406864887514018657e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007264585620557044645723663084
x2[1] (numeric) = 1.0007264575423917260142555659262
absolute error = 1.0196639784503168003822e-09
relative error = 1.0189237725516645444833182175907e-07 %
Correct digits = 8
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50094
x1[1] (analytic) = 2.0010907294197928513276063279158
x1[1] (numeric) = 2.0010907289376065063867341015334
absolute error = 4.821863449408722263824e-10
relative error = 2.4096176042986314885407085692423e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007264676376433337708947556838
x2[1] (numeric) = 1.000726466595927060712536236556
absolute error = 1.0417162730583585191278e-09
relative error = 1.0409600492704839023595583418477e-07 %
Correct digits = 8
h = 1e-05
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.0MB, time=15.70
NO POLE
NO POLE
t[1] = 0.50095
x1[1] (analytic) = 2.0010907185125531896882949122565
x1[1] (numeric) = 2.001090718020054631559332476665
absolute error = 4.924985581289624355915e-10
relative error = 2.4611505793952484747584393526332e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007264767134670136612922498832
x2[1] (numeric) = 1.0007264756494623954108169071858
absolute error = 1.0640046182504753426974e-09
relative error = 1.0632322048126707469076618702176e-07 %
Correct digits = 8
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50096
x1[1] (analytic) = 2.001090707605422599900239724498
x1[1] (numeric) = 2.0010907071025027567319308517966
absolute error = 5.029198431683088727014e-10
relative error = 2.5132286170581488405917481265776e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007264857895267483114563040888
x2[1] (numeric) = 1.0007264847029977301090975778156
absolute error = 1.0865290182023587262732e-09
relative error = 1.0857402433444516684642015714831e-07 %
Correct digits = 8
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50097
x1[1] (analytic) = 2.0010906966984010808727277056526
x1[1] (numeric) = 2.0010906961849508819045292269282
absolute error = 5.134501989681984787244e-10
relative error = 2.5658517118456439909067787529863e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007264948658225418971673417936
x2[1] (numeric) = 1.0007264937565330648073782484454
absolute error = 1.1092894770897890933482e-09
relative error = 1.1084841690321416757294543940565e-07 %
Correct digits = 8
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50098
x1[1] (analytic) = 2.0010906857914886315150567038084
x1[1] (numeric) = 2.0010906852673990070771276020598
absolute error = 5.240896244379291017486e-10
relative error = 2.6190198583160995394452264290220e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.000726503942354398594294756527
x2[1] (numeric) = 1.0007265028100683995056589190752
absolute error = 1.1322859990886358374518e-09
relative error = 1.1314639860421441974680585511202e-07 %
Correct digits = 8
h = 1e-05
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.0MB, time=16.31
NO POLE
NO POLE
t[1] = 0.50099
x1[1] (analytic) = 2.0010906748846852507365354740205
x1[1] (numeric) = 2.0010906743498471322497259771914
absolute error = 5.348381184868094968291e-10
relative error = 2.6727330510279353082880469164259e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007265130191223225787969135797
x2[1] (numeric) = 1.000726511863603734203939589705
absolute error = 1.1555185883748573238747e-09
relative error = 1.1546796985409510842089700460378e-07 %
Correct digits = 8
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.501
x1[1] (analytic) = 2.001090663977990937446483678202
x1[1] (numeric) = 2.001090663432295257422324352323
absolute error = 5.456956800241593258790e-10
relative error = 2.7269912845396253273181661501566e-08 %
Correct digits = 9
h = 1e-05
x2[1] (analytic) = 1.0007265220961263180267211517279
x2[1] (numeric) = 1.0007265209171390689022202603348
absolute error = 1.1789872491245008913931e-09
relative error = 1.1781313106951426099447186380383e-07 %
Correct digits = 8
h = 1e-05
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
Iterations = 100
Total Elapsed Time = 16 Seconds
Elapsed Time(since restart) = 16 Seconds
Expected Time Remaining = 20 Hours 18 Minutes 53 Seconds
Optimized Time Remaining = 20 Hours 15 Minutes 1 Seconds
Time to Timeout = 43 Seconds
Percent Done = 0.02244 %
> quit
memory used=104.5MB, alloc=4.0MB, time=16.54