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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> djd_debug,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_max_hours,
> days_in_year,
> hours_in_day,
> glob_dump,
> glob_iter,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_hmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_hmin_init,
> glob_disp_incr,
> djd_debug2,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10abserr,
> glob_warned2,
> glob_max_iter,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> glob_smallish_float,
> glob_relerr,
> glob_log10_relerr,
> glob_last_good_h,
> years_in_century,
> min_in_hour,
> sec_in_min,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_max_order,
> glob_clock_start_sec,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_normmax,
> MAX_UNCHANGED,
> glob_hmax,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_dump_analytic,
> glob_look_poles,
> glob_almost_1,
> centuries_in_millinium,
> glob_max_minutes,
> glob_optimal_start,
> glob_log10_abserr,
> glob_large_float,
> glob_h,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_4D0,
> array_const_0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_1st_rel_error,
> array_last_rel_error,
> array_m1,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> array_tmp19,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp20,
> array_tmp21,
> array_x1_init,
> array_pole,
> array_type_pole,
> array_norms,
> array_x2_init,
> array_complex_pole,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_real_pole,
> array_x2_higher,
> array_x1_higher,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_x2(ind_var);
> omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x2[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_x1(ind_var);
> omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGL, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10relerr, glob_small_float, glob_optimal_clock_start_sec,
glob_initial_pass, djd_debug, glob_unchanged_h_cnt, glob_max_trunc_err,
glob_max_hours, days_in_year, hours_in_day, glob_dump, glob_iter,
glob_current_iter, glob_start, glob_warned, glob_hmin, glob_orig_start_sec,
glob_max_sec, glob_hmin_init, glob_disp_incr, djd_debug2, glob_display_flag,
glob_optimal_expect_sec, glob_percent_done, glob_log10abserr, glob_warned2,
glob_max_iter, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
glob_smallish_float, glob_relerr, glob_log10_relerr, glob_last_good_h,
years_in_century, min_in_hour, sec_in_min, glob_curr_iter_when_opt,
glob_no_eqs, glob_max_order, glob_clock_start_sec, glob_max_opt_iter,
glob_log10normmin, glob_normmax, MAX_UNCHANGED, glob_hmax,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_max_rel_trunc_err,
glob_abserr, glob_dump_analytic, glob_look_poles, glob_almost_1,
centuries_in_millinium, glob_max_minutes, glob_optimal_start,
glob_log10_abserr, glob_large_float, glob_h, glob_html_log, array_const_0D0,
array_const_4D0, array_const_0, array_const_1, array_const_2,
array_const_2D0, array_const_3D0, array_1st_rel_error, array_last_rel_error,
array_m1, array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_tmp18, array_tmp19, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp20, array_tmp21, array_x1_init, array_pole,
array_type_pole, array_norms, array_x2_init, array_complex_pole,
array_x2_higher_work2, array_x2_higher_work, array_poles,
array_x1_higher_work2, array_x1_higher_work, array_real_pole,
array_x2_higher, array_x1_higher, glob_last;
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_x2(ind_var);
omniout_float(ALWAYS, "x2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x2[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x2[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_x1(ind_var);
omniout_float(ALWAYS, "x1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x1[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> djd_debug,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_max_hours,
> days_in_year,
> hours_in_day,
> glob_dump,
> glob_iter,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_hmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_hmin_init,
> glob_disp_incr,
> djd_debug2,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10abserr,
> glob_warned2,
> glob_max_iter,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> glob_smallish_float,
> glob_relerr,
> glob_log10_relerr,
> glob_last_good_h,
> years_in_century,
> min_in_hour,
> sec_in_min,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_max_order,
> glob_clock_start_sec,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_normmax,
> MAX_UNCHANGED,
> glob_hmax,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_dump_analytic,
> glob_look_poles,
> glob_almost_1,
> centuries_in_millinium,
> glob_max_minutes,
> glob_optimal_start,
> glob_log10_abserr,
> glob_large_float,
> glob_h,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_4D0,
> array_const_0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_1st_rel_error,
> array_last_rel_error,
> array_m1,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> array_tmp19,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp20,
> array_tmp21,
> array_x1_init,
> array_pole,
> array_type_pole,
> array_norms,
> array_x2_init,
> array_complex_pole,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_real_pole,
> array_x2_higher,
> array_x1_higher,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_t[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGL, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10relerr, glob_small_float, glob_optimal_clock_start_sec,
glob_initial_pass, djd_debug, glob_unchanged_h_cnt, glob_max_trunc_err,
glob_max_hours, days_in_year, hours_in_day, glob_dump, glob_iter,
glob_current_iter, glob_start, glob_warned, glob_hmin, glob_orig_start_sec,
glob_max_sec, glob_hmin_init, glob_disp_incr, djd_debug2, glob_display_flag,
glob_optimal_expect_sec, glob_percent_done, glob_log10abserr, glob_warned2,
glob_max_iter, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
glob_smallish_float, glob_relerr, glob_log10_relerr, glob_last_good_h,
years_in_century, min_in_hour, sec_in_min, glob_curr_iter_when_opt,
glob_no_eqs, glob_max_order, glob_clock_start_sec, glob_max_opt_iter,
glob_log10normmin, glob_normmax, MAX_UNCHANGED, glob_hmax,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_max_rel_trunc_err,
glob_abserr, glob_dump_analytic, glob_look_poles, glob_almost_1,
centuries_in_millinium, glob_max_minutes, glob_optimal_start,
glob_log10_abserr, glob_large_float, glob_h, glob_html_log, array_const_0D0,
array_const_4D0, array_const_0, array_const_1, array_const_2,
array_const_2D0, array_const_3D0, array_1st_rel_error, array_last_rel_error,
array_m1, array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_tmp18, array_tmp19, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp20, array_tmp21, array_x1_init, array_pole,
array_type_pole, array_norms, array_x2_init, array_complex_pole,
array_x2_higher_work2, array_x2_higher_work, array_poles,
array_x1_higher_work2, array_x1_higher_work, array_real_pole,
array_x2_higher, array_x1_higher, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_t[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(t_start,t_end)
> global
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> djd_debug,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_max_hours,
> days_in_year,
> hours_in_day,
> glob_dump,
> glob_iter,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_hmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_hmin_init,
> glob_disp_incr,
> djd_debug2,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10abserr,
> glob_warned2,
> glob_max_iter,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> glob_smallish_float,
> glob_relerr,
> glob_log10_relerr,
> glob_last_good_h,
> years_in_century,
> min_in_hour,
> sec_in_min,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_max_order,
> glob_clock_start_sec,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_normmax,
> MAX_UNCHANGED,
> glob_hmax,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_dump_analytic,
> glob_look_poles,
> glob_almost_1,
> centuries_in_millinium,
> glob_max_minutes,
> glob_optimal_start,
> glob_log10_abserr,
> glob_large_float,
> glob_h,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_4D0,
> array_const_0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_1st_rel_error,
> array_last_rel_error,
> array_m1,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> array_tmp19,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp20,
> array_tmp21,
> array_x1_init,
> array_pole,
> array_type_pole,
> array_norms,
> array_x2_init,
> array_complex_pole,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_real_pole,
> array_x2_higher,
> array_x1_higher,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(t_start, t_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGL, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10relerr, glob_small_float, glob_optimal_clock_start_sec,
glob_initial_pass, djd_debug, glob_unchanged_h_cnt, glob_max_trunc_err,
glob_max_hours, days_in_year, hours_in_day, glob_dump, glob_iter,
glob_current_iter, glob_start, glob_warned, glob_hmin, glob_orig_start_sec,
glob_max_sec, glob_hmin_init, glob_disp_incr, djd_debug2, glob_display_flag,
glob_optimal_expect_sec, glob_percent_done, glob_log10abserr, glob_warned2,
glob_max_iter, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
glob_smallish_float, glob_relerr, glob_log10_relerr, glob_last_good_h,
years_in_century, min_in_hour, sec_in_min, glob_curr_iter_when_opt,
glob_no_eqs, glob_max_order, glob_clock_start_sec, glob_max_opt_iter,
glob_log10normmin, glob_normmax, MAX_UNCHANGED, glob_hmax,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_max_rel_trunc_err,
glob_abserr, glob_dump_analytic, glob_look_poles, glob_almost_1,
centuries_in_millinium, glob_max_minutes, glob_optimal_start,
glob_log10_abserr, glob_large_float, glob_h, glob_html_log, array_const_0D0,
array_const_4D0, array_const_0, array_const_1, array_const_2,
array_const_2D0, array_const_3D0, array_1st_rel_error, array_last_rel_error,
array_m1, array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_tmp18, array_tmp19, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp20, array_tmp21, array_x1_init, array_pole,
array_type_pole, array_norms, array_x2_init, array_complex_pole,
array_x2_higher_work2, array_x2_higher_work, array_poles,
array_x1_higher_work2, array_x1_higher_work, array_real_pole,
array_x2_higher, array_x1_higher, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start),
convfloat(array_t[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),
convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(t_end), convfloat(t_start),
convfloat(array_t[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> djd_debug,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_max_hours,
> days_in_year,
> hours_in_day,
> glob_dump,
> glob_iter,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_hmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_hmin_init,
> glob_disp_incr,
> djd_debug2,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10abserr,
> glob_warned2,
> glob_max_iter,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> glob_smallish_float,
> glob_relerr,
> glob_log10_relerr,
> glob_last_good_h,
> years_in_century,
> min_in_hour,
> sec_in_min,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_max_order,
> glob_clock_start_sec,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_normmax,
> MAX_UNCHANGED,
> glob_hmax,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_dump_analytic,
> glob_look_poles,
> glob_almost_1,
> centuries_in_millinium,
> glob_max_minutes,
> glob_optimal_start,
> glob_log10_abserr,
> glob_large_float,
> glob_h,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_4D0,
> array_const_0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_1st_rel_error,
> array_last_rel_error,
> array_m1,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> array_tmp19,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp20,
> array_tmp21,
> array_x1_init,
> array_pole,
> array_type_pole,
> array_norms,
> array_x2_init,
> array_complex_pole,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_real_pole,
> array_x2_higher,
> array_x1_higher,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 2 - 1;
> while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1];
> rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1];
> rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]);
> rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]);
> rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]);
> rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]);
> rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float)) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]);
> rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]);
> rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]);
> rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]);
> rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4
> ;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3
> ;
> #BOTTOM RADII COMPLEX EQ = 2
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 2
> if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 2
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if array_pole[1] > array_poles[2,1] then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 2
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGL, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10relerr, glob_small_float, glob_optimal_clock_start_sec,
glob_initial_pass, djd_debug, glob_unchanged_h_cnt, glob_max_trunc_err,
glob_max_hours, days_in_year, hours_in_day, glob_dump, glob_iter,
glob_current_iter, glob_start, glob_warned, glob_hmin, glob_orig_start_sec,
glob_max_sec, glob_hmin_init, glob_disp_incr, djd_debug2, glob_display_flag,
glob_optimal_expect_sec, glob_percent_done, glob_log10abserr, glob_warned2,
glob_max_iter, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
glob_smallish_float, glob_relerr, glob_log10_relerr, glob_last_good_h,
years_in_century, min_in_hour, sec_in_min, glob_curr_iter_when_opt,
glob_no_eqs, glob_max_order, glob_clock_start_sec, glob_max_opt_iter,
glob_log10normmin, glob_normmax, MAX_UNCHANGED, glob_hmax,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_max_rel_trunc_err,
glob_abserr, glob_dump_analytic, glob_look_poles, glob_almost_1,
centuries_in_millinium, glob_max_minutes, glob_optimal_start,
glob_log10_abserr, glob_large_float, glob_h, glob_html_log, array_const_0D0,
array_const_4D0, array_const_0, array_const_1, array_const_2,
array_const_2D0, array_const_3D0, array_1st_rel_error, array_last_rel_error,
array_m1, array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_tmp18, array_tmp19, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp20, array_tmp21, array_x1_init, array_pole,
array_type_pole, array_norms, array_x2_init, array_complex_pole,
array_x2_higher_work2, array_x2_higher_work, array_poles,
array_x1_higher_work2, array_x1_higher_work, array_real_pole,
array_x2_higher, array_x1_higher, glob_last;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or
abs(array_x2_higher[1, m - 1]) < glob_small_float or
abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or
abs(array_x1_higher[1, m - 1]) < glob_small_float or
abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_x2_higher[1, m]) or
glob_large_float <= abs(array_x2_higher[1, m - 1]) or
glob_large_float <= abs(array_x2_higher[1, m - 2]) or
glob_large_float <= abs(array_x2_higher[1, m - 3]) or
glob_large_float <= abs(array_x2_higher[1, m - 4]) or
glob_large_float <= abs(array_x2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3];
rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4];
rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= abs(array_x1_higher[1, m]) or
glob_large_float <= abs(array_x1_higher[1, m - 1]) or
glob_large_float <= abs(array_x1_higher[1, m - 2]) or
glob_large_float <= abs(array_x1_higher[1, m - 3]) or
glob_large_float <= abs(array_x1_higher[1, m - 4]) or
glob_large_float <= abs(array_x1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3];
rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4];
rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[2, 1] := rad_c;
array_complex_pole[2, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> djd_debug,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_max_hours,
> days_in_year,
> hours_in_day,
> glob_dump,
> glob_iter,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_hmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_hmin_init,
> glob_disp_incr,
> djd_debug2,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10abserr,
> glob_warned2,
> glob_max_iter,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> glob_smallish_float,
> glob_relerr,
> glob_log10_relerr,
> glob_last_good_h,
> years_in_century,
> min_in_hour,
> sec_in_min,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_max_order,
> glob_clock_start_sec,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_normmax,
> MAX_UNCHANGED,
> glob_hmax,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_dump_analytic,
> glob_look_poles,
> glob_almost_1,
> centuries_in_millinium,
> glob_max_minutes,
> glob_optimal_start,
> glob_log10_abserr,
> glob_large_float,
> glob_h,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_4D0,
> array_const_0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_1st_rel_error,
> array_last_rel_error,
> array_m1,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> array_tmp19,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp20,
> array_tmp21,
> array_x1_init,
> array_pole,
> array_type_pole,
> array_norms,
> array_x2_init,
> array_complex_pole,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_real_pole,
> array_x2_higher,
> array_x1_higher,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 3
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGL, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10relerr, glob_small_float, glob_optimal_clock_start_sec,
glob_initial_pass, djd_debug, glob_unchanged_h_cnt, glob_max_trunc_err,
glob_max_hours, days_in_year, hours_in_day, glob_dump, glob_iter,
glob_current_iter, glob_start, glob_warned, glob_hmin, glob_orig_start_sec,
glob_max_sec, glob_hmin_init, glob_disp_incr, djd_debug2, glob_display_flag,
glob_optimal_expect_sec, glob_percent_done, glob_log10abserr, glob_warned2,
glob_max_iter, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
glob_smallish_float, glob_relerr, glob_log10_relerr, glob_last_good_h,
years_in_century, min_in_hour, sec_in_min, glob_curr_iter_when_opt,
glob_no_eqs, glob_max_order, glob_clock_start_sec, glob_max_opt_iter,
glob_log10normmin, glob_normmax, MAX_UNCHANGED, glob_hmax,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_max_rel_trunc_err,
glob_abserr, glob_dump_analytic, glob_look_poles, glob_almost_1,
centuries_in_millinium, glob_max_minutes, glob_optimal_start,
glob_log10_abserr, glob_large_float, glob_h, glob_html_log, array_const_0D0,
array_const_4D0, array_const_0, array_const_1, array_const_2,
array_const_2D0, array_const_3D0, array_1st_rel_error, array_last_rel_error,
array_m1, array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_tmp18, array_tmp19, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp20, array_tmp21, array_x1_init, array_pole,
array_type_pole, array_norms, array_x2_init, array_complex_pole,
array_x2_higher_work2, array_x2_higher_work, array_poles,
array_x1_higher_work2, array_x1_higher_work, array_real_pole,
array_x2_higher, array_x1_higher, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x2[iii]) then
array_norms[iii] := abs(array_x2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x1[iii]) then
array_norms[iii] := abs(array_x1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> djd_debug,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_max_hours,
> days_in_year,
> hours_in_day,
> glob_dump,
> glob_iter,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_hmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_hmin_init,
> glob_disp_incr,
> djd_debug2,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10abserr,
> glob_warned2,
> glob_max_iter,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> glob_smallish_float,
> glob_relerr,
> glob_log10_relerr,
> glob_last_good_h,
> years_in_century,
> min_in_hour,
> sec_in_min,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_max_order,
> glob_clock_start_sec,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_normmax,
> MAX_UNCHANGED,
> glob_hmax,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_dump_analytic,
> glob_look_poles,
> glob_almost_1,
> centuries_in_millinium,
> glob_max_minutes,
> glob_optimal_start,
> glob_log10_abserr,
> glob_large_float,
> glob_h,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_4D0,
> array_const_0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_1st_rel_error,
> array_last_rel_error,
> array_m1,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> array_tmp19,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp20,
> array_tmp21,
> array_x1_init,
> array_pole,
> array_type_pole,
> array_norms,
> array_x2_init,
> array_complex_pole,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_real_pole,
> array_x2_higher,
> array_x1_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1
> array_tmp1[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre diff $eq_no = 1 i = 1
> array_tmp4[1] := array_x2_higher[1,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp5[1] := (array_const_2D0[1] * (array_tmp4[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp6[1] := (array_tmp3[1] - (array_tmp5[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp7[1] := array_x1_higher[3,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp8[1] := (array_tmp6[1] - (array_tmp7[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp9[1] := array_x1_higher[2,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp10[1] := (array_tmp8[1] - (array_tmp9[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp11[1] := array_x1_higher[1,1];
> #emit pre add $eq_no = 1 i = 1
> array_tmp12[1] := array_tmp10[1] + array_tmp11[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp12[1] * (glob_h ^ (2)) * factorial_3(0,2);
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1
> array_tmp14[1] := array_x2_higher[1,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp15[1] := (array_const_4D0[1] * (array_tmp14[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp16[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp17[1] := (array_const_2D0[1] * (array_tmp16[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp18[1] := (array_tmp15[1] - (array_tmp17[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp19[1] := array_x1_higher[1,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp20[1] := (array_const_2D0[1] * (array_tmp19[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp21[1] := (array_tmp18[1] - (array_tmp20[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp21[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2
> array_tmp1[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
> #emit pre diff $eq_no = 1 i = 2
> array_tmp4[2] := array_x2_higher[1,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp5[2] := ats(2,array_const_2D0,array_tmp4,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp6[2] := (array_tmp3[2] - (array_tmp5[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp7[2] := array_x1_higher[3,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp8[2] := (array_tmp6[2] - (array_tmp7[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp9[2] := array_x1_higher[2,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp10[2] := (array_tmp8[2] - (array_tmp9[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp11[2] := array_x1_higher[1,2];
> #emit pre add $eq_no = 1 i = 2
> array_tmp12[2] := array_tmp10[2] + array_tmp11[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp12[2] * (glob_h ^ (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2
> array_tmp14[2] := array_x2_higher[1,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp15[2] := ats(2,array_const_4D0,array_tmp14,1);
> #emit pre diff $eq_no = 2 i = 2
> array_tmp16[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp17[2] := ats(2,array_const_2D0,array_tmp16,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp18[2] := (array_tmp15[2] - (array_tmp17[2]));
> #emit pre diff $eq_no = 2 i = 2
> array_tmp19[2] := array_x1_higher[1,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp20[2] := ats(2,array_const_2D0,array_tmp19,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp21[2] := (array_tmp18[2] - (array_tmp20[2]));
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp21[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3
> array_tmp1[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
> #emit pre diff $eq_no = 1 i = 3
> array_tmp4[3] := array_x2_higher[1,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp5[3] := ats(3,array_const_2D0,array_tmp4,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp6[3] := (array_tmp3[3] - (array_tmp5[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp7[3] := array_x1_higher[3,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp8[3] := (array_tmp6[3] - (array_tmp7[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp9[3] := array_x1_higher[2,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp10[3] := (array_tmp8[3] - (array_tmp9[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp11[3] := array_x1_higher[1,3];
> #emit pre add $eq_no = 1 i = 3
> array_tmp12[3] := array_tmp10[3] + array_tmp11[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp12[3] * (glob_h ^ (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3
> array_tmp14[3] := array_x2_higher[1,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp15[3] := ats(3,array_const_4D0,array_tmp14,1);
> #emit pre diff $eq_no = 2 i = 3
> array_tmp16[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp17[3] := ats(3,array_const_2D0,array_tmp16,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp18[3] := (array_tmp15[3] - (array_tmp17[3]));
> #emit pre diff $eq_no = 2 i = 3
> array_tmp19[3] := array_x1_higher[1,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp20[3] := ats(3,array_const_2D0,array_tmp19,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp21[3] := (array_tmp18[3] - (array_tmp20[3]));
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp21[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4
> array_tmp1[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
> #emit pre diff $eq_no = 1 i = 4
> array_tmp4[4] := array_x2_higher[1,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp5[4] := ats(4,array_const_2D0,array_tmp4,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp6[4] := (array_tmp3[4] - (array_tmp5[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp7[4] := array_x1_higher[3,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp8[4] := (array_tmp6[4] - (array_tmp7[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp9[4] := array_x1_higher[2,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp10[4] := (array_tmp8[4] - (array_tmp9[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp11[4] := array_x1_higher[1,4];
> #emit pre add $eq_no = 1 i = 4
> array_tmp12[4] := array_tmp10[4] + array_tmp11[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp12[4] * (glob_h ^ (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4
> array_tmp14[4] := array_x2_higher[1,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp15[4] := ats(4,array_const_4D0,array_tmp14,1);
> #emit pre diff $eq_no = 2 i = 4
> array_tmp16[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp17[4] := ats(4,array_const_2D0,array_tmp16,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp18[4] := (array_tmp15[4] - (array_tmp17[4]));
> #emit pre diff $eq_no = 2 i = 4
> array_tmp19[4] := array_x1_higher[1,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp20[4] := ats(4,array_const_2D0,array_tmp19,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp21[4] := (array_tmp18[4] - (array_tmp20[4]));
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp21[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5
> array_tmp1[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
> #emit pre diff $eq_no = 1 i = 5
> array_tmp4[5] := array_x2_higher[1,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp5[5] := ats(5,array_const_2D0,array_tmp4,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp6[5] := (array_tmp3[5] - (array_tmp5[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp7[5] := array_x1_higher[3,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp8[5] := (array_tmp6[5] - (array_tmp7[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp9[5] := array_x1_higher[2,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp10[5] := (array_tmp8[5] - (array_tmp9[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp11[5] := array_x1_higher[1,5];
> #emit pre add $eq_no = 1 i = 5
> array_tmp12[5] := array_tmp10[5] + array_tmp11[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp12[5] * (glob_h ^ (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5
> array_tmp14[5] := array_x2_higher[1,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp15[5] := ats(5,array_const_4D0,array_tmp14,1);
> #emit pre diff $eq_no = 2 i = 5
> array_tmp16[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp17[5] := ats(5,array_const_2D0,array_tmp16,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp18[5] := (array_tmp15[5] - (array_tmp17[5]));
> #emit pre diff $eq_no = 2 i = 5
> array_tmp19[5] := array_x1_higher[1,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp20[5] := ats(5,array_const_2D0,array_tmp19,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp21[5] := (array_tmp18[5] - (array_tmp20[5]));
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp21[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit diff $eq_no = 1
> array_tmp1[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1);
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
> #emit diff $eq_no = 1
> array_tmp4[kkk] := array_x2_higher[1,kkk];
> #emit mult $eq_no = 1
> array_tmp5[kkk] := ats(kkk,array_const_2D0,array_tmp4,1);
> #emit sub $eq_no = 1
> array_tmp6[kkk] := (array_tmp3[kkk] - (array_tmp5[kkk]));
> #emit diff $eq_no = 1
> array_tmp7[kkk] := array_x1_higher[3,kkk];
> #emit sub $eq_no = 1
> array_tmp8[kkk] := (array_tmp6[kkk] - (array_tmp7[kkk]));
> #emit diff $eq_no = 1
> array_tmp9[kkk] := array_x1_higher[2,kkk];
> #emit sub $eq_no = 1
> array_tmp10[kkk] := (array_tmp8[kkk] - (array_tmp9[kkk]));
> #emit diff $eq_no = 1
> array_tmp11[kkk] := array_x1_higher[1,kkk];
> #emit add $eq_no = 1
> array_tmp12[kkk] := array_tmp10[kkk] + array_tmp11[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp12[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x2[kkk + order_d] := temporary;
> array_x2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> #emit diff $eq_no = 2
> array_tmp14[kkk] := array_x2_higher[1,kkk];
> #emit mult $eq_no = 2
> array_tmp15[kkk] := ats(kkk,array_const_4D0,array_tmp14,1);
> #emit diff $eq_no = 2
> array_tmp16[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 2
> array_tmp17[kkk] := ats(kkk,array_const_2D0,array_tmp16,1);
> #emit sub $eq_no = 2
> array_tmp18[kkk] := (array_tmp15[kkk] - (array_tmp17[kkk]));
> #emit diff $eq_no = 2
> array_tmp19[kkk] := array_x1_higher[1,kkk];
> #emit mult $eq_no = 2
> array_tmp20[kkk] := ats(kkk,array_const_2D0,array_tmp19,1);
> #emit sub $eq_no = 2
> array_tmp21[kkk] := (array_tmp18[kkk] - (array_tmp20[kkk]));
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp21[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x1[kkk + order_d] := temporary;
> array_x1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGL, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10relerr, glob_small_float, glob_optimal_clock_start_sec,
glob_initial_pass, djd_debug, glob_unchanged_h_cnt, glob_max_trunc_err,
glob_max_hours, days_in_year, hours_in_day, glob_dump, glob_iter,
glob_current_iter, glob_start, glob_warned, glob_hmin, glob_orig_start_sec,
glob_max_sec, glob_hmin_init, glob_disp_incr, djd_debug2, glob_display_flag,
glob_optimal_expect_sec, glob_percent_done, glob_log10abserr, glob_warned2,
glob_max_iter, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
glob_smallish_float, glob_relerr, glob_log10_relerr, glob_last_good_h,
years_in_century, min_in_hour, sec_in_min, glob_curr_iter_when_opt,
glob_no_eqs, glob_max_order, glob_clock_start_sec, glob_max_opt_iter,
glob_log10normmin, glob_normmax, MAX_UNCHANGED, glob_hmax,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_max_rel_trunc_err,
glob_abserr, glob_dump_analytic, glob_look_poles, glob_almost_1,
centuries_in_millinium, glob_max_minutes, glob_optimal_start,
glob_log10_abserr, glob_large_float, glob_h, glob_html_log, array_const_0D0,
array_const_4D0, array_const_0, array_const_1, array_const_2,
array_const_2D0, array_const_3D0, array_1st_rel_error, array_last_rel_error,
array_m1, array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_tmp18, array_tmp19, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp20, array_tmp21, array_x1_init, array_pole,
array_type_pole, array_norms, array_x2_init, array_complex_pole,
array_x2_higher_work2, array_x2_higher_work, array_poles,
array_x1_higher_work2, array_x1_higher_work, array_real_pole,
array_x2_higher, array_x1_higher, glob_last;
array_tmp1[1] := array_x2_higher[2, 1];
array_tmp2[1] := array_const_3D0[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_x2_higher[1, 1];
array_tmp5[1] := array_const_2D0[1]*array_tmp4[1];
array_tmp6[1] := array_tmp3[1] - array_tmp5[1];
array_tmp7[1] := array_x1_higher[3, 1];
array_tmp8[1] := array_tmp6[1] - array_tmp7[1];
array_tmp9[1] := array_x1_higher[2, 1];
array_tmp10[1] := array_tmp8[1] - array_tmp9[1];
array_tmp11[1] := array_x1_higher[1, 1];
array_tmp12[1] := array_tmp10[1] + array_tmp11[1];
if 1 <= glob_max_terms then
temporary := array_tmp12[1]*glob_h^2*factorial_3(0, 2);
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 1] := temporary
end if;
kkk := 2;
array_tmp14[1] := array_x2_higher[1, 1];
array_tmp15[1] := array_const_4D0[1]*array_tmp14[1];
array_tmp16[1] := array_x2_higher[2, 1];
array_tmp17[1] := array_const_2D0[1]*array_tmp16[1];
array_tmp18[1] := array_tmp15[1] - array_tmp17[1];
array_tmp19[1] := array_x1_higher[1, 1];
array_tmp20[1] := array_const_2D0[1]*array_tmp19[1];
array_tmp21[1] := array_tmp18[1] - array_tmp20[1];
if 1 <= glob_max_terms then
temporary := array_tmp21[1]*glob_h*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 1] := temporary
end if;
kkk := 2;
array_tmp1[2] := array_x2_higher[2, 2];
array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1);
array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
array_tmp4[2] := array_x2_higher[1, 2];
array_tmp5[2] := ats(2, array_const_2D0, array_tmp4, 1);
array_tmp6[2] := array_tmp3[2] - array_tmp5[2];
array_tmp7[2] := array_x1_higher[3, 2];
array_tmp8[2] := array_tmp6[2] - array_tmp7[2];
array_tmp9[2] := array_x1_higher[2, 2];
array_tmp10[2] := array_tmp8[2] - array_tmp9[2];
array_tmp11[2] := array_x1_higher[1, 2];
array_tmp12[2] := array_tmp10[2] + array_tmp11[2];
if 2 <= glob_max_terms then
temporary := array_tmp12[2]*glob_h^2*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 2] := temporary
end if;
kkk := 3;
array_tmp14[2] := array_x2_higher[1, 2];
array_tmp15[2] := ats(2, array_const_4D0, array_tmp14, 1);
array_tmp16[2] := array_x2_higher[2, 2];
array_tmp17[2] := ats(2, array_const_2D0, array_tmp16, 1);
array_tmp18[2] := array_tmp15[2] - array_tmp17[2];
array_tmp19[2] := array_x1_higher[1, 2];
array_tmp20[2] := ats(2, array_const_2D0, array_tmp19, 1);
array_tmp21[2] := array_tmp18[2] - array_tmp20[2];
if 2 <= glob_max_terms then
temporary := array_tmp21[2]*glob_h*factorial_3(1, 2);
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 2] := temporary
end if;
kkk := 3;
array_tmp1[3] := array_x2_higher[2, 3];
array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1);
array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
array_tmp4[3] := array_x2_higher[1, 3];
array_tmp5[3] := ats(3, array_const_2D0, array_tmp4, 1);
array_tmp6[3] := array_tmp3[3] - array_tmp5[3];
array_tmp7[3] := array_x1_higher[3, 3];
array_tmp8[3] := array_tmp6[3] - array_tmp7[3];
array_tmp9[3] := array_x1_higher[2, 3];
array_tmp10[3] := array_tmp8[3] - array_tmp9[3];
array_tmp11[3] := array_x1_higher[1, 3];
array_tmp12[3] := array_tmp10[3] + array_tmp11[3];
if 3 <= glob_max_terms then
temporary := array_tmp12[3]*glob_h^2*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if;
kkk := 4;
array_tmp14[3] := array_x2_higher[1, 3];
array_tmp15[3] := ats(3, array_const_4D0, array_tmp14, 1);
array_tmp16[3] := array_x2_higher[2, 3];
array_tmp17[3] := ats(3, array_const_2D0, array_tmp16, 1);
array_tmp18[3] := array_tmp15[3] - array_tmp17[3];
array_tmp19[3] := array_x1_higher[1, 3];
array_tmp20[3] := ats(3, array_const_2D0, array_tmp19, 1);
array_tmp21[3] := array_tmp18[3] - array_tmp20[3];
if 3 <= glob_max_terms then
temporary := array_tmp21[3]*glob_h*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 3] := temporary
end if;
kkk := 4;
array_tmp1[4] := array_x2_higher[2, 4];
array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1);
array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
array_tmp4[4] := array_x2_higher[1, 4];
array_tmp5[4] := ats(4, array_const_2D0, array_tmp4, 1);
array_tmp6[4] := array_tmp3[4] - array_tmp5[4];
array_tmp7[4] := array_x1_higher[3, 4];
array_tmp8[4] := array_tmp6[4] - array_tmp7[4];
array_tmp9[4] := array_x1_higher[2, 4];
array_tmp10[4] := array_tmp8[4] - array_tmp9[4];
array_tmp11[4] := array_x1_higher[1, 4];
array_tmp12[4] := array_tmp10[4] + array_tmp11[4];
if 4 <= glob_max_terms then
temporary := array_tmp12[4]*glob_h^2*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 4] := temporary
end if;
kkk := 5;
array_tmp14[4] := array_x2_higher[1, 4];
array_tmp15[4] := ats(4, array_const_4D0, array_tmp14, 1);
array_tmp16[4] := array_x2_higher[2, 4];
array_tmp17[4] := ats(4, array_const_2D0, array_tmp16, 1);
array_tmp18[4] := array_tmp15[4] - array_tmp17[4];
array_tmp19[4] := array_x1_higher[1, 4];
array_tmp20[4] := ats(4, array_const_2D0, array_tmp19, 1);
array_tmp21[4] := array_tmp18[4] - array_tmp20[4];
if 4 <= glob_max_terms then
temporary := array_tmp21[4]*glob_h*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 4] := temporary
end if;
kkk := 5;
array_tmp1[5] := array_x2_higher[2, 5];
array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1);
array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
array_tmp4[5] := array_x2_higher[1, 5];
array_tmp5[5] := ats(5, array_const_2D0, array_tmp4, 1);
array_tmp6[5] := array_tmp3[5] - array_tmp5[5];
array_tmp7[5] := array_x1_higher[3, 5];
array_tmp8[5] := array_tmp6[5] - array_tmp7[5];
array_tmp9[5] := array_x1_higher[2, 5];
array_tmp10[5] := array_tmp8[5] - array_tmp9[5];
array_tmp11[5] := array_x1_higher[1, 5];
array_tmp12[5] := array_tmp10[5] + array_tmp11[5];
if 5 <= glob_max_terms then
temporary := array_tmp12[5]*glob_h^2*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 5] := temporary
end if;
kkk := 6;
array_tmp14[5] := array_x2_higher[1, 5];
array_tmp15[5] := ats(5, array_const_4D0, array_tmp14, 1);
array_tmp16[5] := array_x2_higher[2, 5];
array_tmp17[5] := ats(5, array_const_2D0, array_tmp16, 1);
array_tmp18[5] := array_tmp15[5] - array_tmp17[5];
array_tmp19[5] := array_x1_higher[1, 5];
array_tmp20[5] := ats(5, array_const_2D0, array_tmp19, 1);
array_tmp21[5] := array_tmp18[5] - array_tmp20[5];
if 5 <= glob_max_terms then
temporary := array_tmp21[5]*glob_h*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 5] := temporary
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_x2_higher[2, kkk];
array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1);
array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
array_tmp4[kkk] := array_x2_higher[1, kkk];
array_tmp5[kkk] := ats(kkk, array_const_2D0, array_tmp4, 1);
array_tmp6[kkk] := array_tmp3[kkk] - array_tmp5[kkk];
array_tmp7[kkk] := array_x1_higher[3, kkk];
array_tmp8[kkk] := array_tmp6[kkk] - array_tmp7[kkk];
array_tmp9[kkk] := array_x1_higher[2, kkk];
array_tmp10[kkk] := array_tmp8[kkk] - array_tmp9[kkk];
array_tmp11[kkk] := array_x1_higher[1, kkk];
array_tmp12[kkk] := array_tmp10[kkk] + array_tmp11[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp12[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x2[kkk + order_d] := temporary;
array_x2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
array_tmp14[kkk] := array_x2_higher[1, kkk];
array_tmp15[kkk] := ats(kkk, array_const_4D0, array_tmp14, 1);
array_tmp16[kkk] := array_x2_higher[2, kkk];
array_tmp17[kkk] := ats(kkk, array_const_2D0, array_tmp16, 1);
array_tmp18[kkk] := array_tmp15[kkk] - array_tmp17[kkk];
array_tmp19[kkk] := array_x1_higher[1, kkk];
array_tmp20[kkk] := ats(kkk, array_const_2D0, array_tmp19, 1);
array_tmp21[kkk] := array_tmp18[kkk] - array_tmp20[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp21[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x1[kkk + order_d] := temporary;
array_x1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_x1 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c1 + 6.0 * c3 * exp(-t);
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0*c2*exp(2.0*t) - c3*exp(-t)
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> t_start,t_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGL,
> INFO,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> djd_debug,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_max_hours,
> days_in_year,
> hours_in_day,
> glob_dump,
> glob_iter,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_hmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_hmin_init,
> glob_disp_incr,
> djd_debug2,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10abserr,
> glob_warned2,
> glob_max_iter,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> glob_smallish_float,
> glob_relerr,
> glob_log10_relerr,
> glob_last_good_h,
> years_in_century,
> min_in_hour,
> sec_in_min,
> glob_curr_iter_when_opt,
> glob_no_eqs,
> glob_max_order,
> glob_clock_start_sec,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_normmax,
> MAX_UNCHANGED,
> glob_hmax,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_dump_analytic,
> glob_look_poles,
> glob_almost_1,
> centuries_in_millinium,
> glob_max_minutes,
> glob_optimal_start,
> glob_log10_abserr,
> glob_large_float,
> glob_h,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_4D0,
> array_const_0,
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_1st_rel_error,
> array_last_rel_error,
> array_m1,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> array_tmp19,
> array_t,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp20,
> array_tmp21,
> array_x1_init,
> array_pole,
> array_type_pole,
> array_norms,
> array_x2_init,
> array_complex_pole,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_poles,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_real_pole,
> array_x2_higher,
> array_x1_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> INFO := 2;
> ALWAYS := 1;
> glob_iolevel := 5;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> glob_log10relerr := 0.0;
> glob_small_float := 0.1e-50;
> glob_optimal_clock_start_sec := 0.0;
> glob_initial_pass := true;
> djd_debug := true;
> glob_unchanged_h_cnt := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_max_hours := 0.0;
> days_in_year := 365.0;
> hours_in_day := 24.0;
> glob_dump := false;
> glob_iter := 0;
> glob_current_iter := 0;
> glob_start := 0;
> glob_warned := false;
> glob_hmin := 0.00000000001;
> glob_orig_start_sec := 0.0;
> glob_max_sec := 10000.0;
> glob_hmin_init := 0.001;
> glob_disp_incr := 0.1;
> djd_debug2 := true;
> glob_display_flag := true;
> glob_optimal_expect_sec := 0.1;
> glob_percent_done := 0.0;
> glob_log10abserr := 0.0;
> glob_warned2 := false;
> glob_max_iter := 1000;
> glob_optimal_done := false;
> glob_not_yet_finished := true;
> glob_clock_sec := 0.0;
> glob_smallish_float := 0.1e-100;
> glob_relerr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_last_good_h := 0.1;
> years_in_century := 100.0;
> min_in_hour := 60.0;
> sec_in_min := 60.0;
> glob_curr_iter_when_opt := 0;
> glob_no_eqs := 0;
> glob_max_order := 30;
> glob_clock_start_sec := 0.0;
> glob_max_opt_iter := 10;
> glob_log10normmin := 0.1;
> glob_normmax := 0.0;
> MAX_UNCHANGED := 10;
> glob_hmax := 1.0;
> glob_reached_optimal_h := false;
> glob_not_yet_start_msg := true;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_look_poles := false;
> glob_almost_1 := 0.9990;
> centuries_in_millinium := 10.0;
> glob_max_minutes := 0.0;
> glob_optimal_start := 0.0;
> glob_log10_abserr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_h := 0.1;
> glob_html_log := true;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_max_order := 2;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/complicatedrevpostode.ode#################");
> omniout_str(ALWAYS,"diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1 ) + diff ( x1 , t , 0 );");
> omniout_str(ALWAYS,"diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_tmp10:= Array(1..(max_terms + 1),[]);
> array_tmp11:= Array(1..(max_terms + 1),[]);
> array_tmp12:= Array(1..(max_terms + 1),[]);
> array_tmp13:= Array(1..(max_terms + 1),[]);
> array_tmp14:= Array(1..(max_terms + 1),[]);
> array_tmp15:= Array(1..(max_terms + 1),[]);
> array_tmp16:= Array(1..(max_terms + 1),[]);
> array_tmp17:= Array(1..(max_terms + 1),[]);
> array_tmp18:= Array(1..(max_terms + 1),[]);
> array_tmp19:= Array(1..(max_terms + 1),[]);
> array_t:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_tmp5:= Array(1..(max_terms + 1),[]);
> array_tmp6:= Array(1..(max_terms + 1),[]);
> array_tmp7:= Array(1..(max_terms + 1),[]);
> array_tmp8:= Array(1..(max_terms + 1),[]);
> array_tmp9:= Array(1..(max_terms + 1),[]);
> array_tmp20:= Array(1..(max_terms + 1),[]);
> array_tmp21:= Array(1..(max_terms + 1),[]);
> array_x1_init:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> 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_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_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_tmp18[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp19[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_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_tmp20[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp21[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_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_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[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_x1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp19 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp19[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp18 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp18[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp21 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp21[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp20 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp20[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_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_4D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_4D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_4D0[1] := 4.0;
> array_const_0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0[1] := 0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 2;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0[1] := 2.0;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0[1] := 3.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[1] := exact_soln_x1(t_start);
> array_x2_init[1] := exact_soln_x2(t_start);
> array_x2_init[2] := exact_soln_x2p(t_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> if glob_html_log then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_t[1] := t_start;
> array_t[2] := glob_h;
> order_diff := 2;
> #Start Series array_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_x2();
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> start_array_x1();
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> order_diff := 2;
> #Jump Series array_x2
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x2
> order_diff := 2;
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> order_diff := 1;
> #Jump Series array_x1
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x1
> order_diff := 1;
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 3
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 3
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1 ) + diff ( x1 , t , 0 );");
> omniout_str(INFO,"diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if glob_html_log then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-01T22:13:45-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"complicatedrev")
> ;
> logitem_str(html_log_file,"diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1 ) + diff ( x1 , t , 0 );")
> ;
> logitem_float(html_log_file,t_start)
> ;
> logitem_float(html_log_file,t_end)
> ;
> logitem_float(html_log_file,array_t[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 4
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 4
> ;
> log_revs(html_log_file," 075 | ")
> ;
> logitem_str(html_log_file,"complicatedrev diffeq.mxt")
> ;
> logitem_str(html_log_file,"complicatedrev maple results")
> ;
> logitem_str(html_log_file,"only 1 sub iteration - eqs reversed")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4
> ;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then # if number 4
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;# end if 4
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3
> ;
> if glob_html_log then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp;
global DEBUGL, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10relerr, glob_small_float, glob_optimal_clock_start_sec,
glob_initial_pass, djd_debug, glob_unchanged_h_cnt, glob_max_trunc_err,
glob_max_hours, days_in_year, hours_in_day, glob_dump, glob_iter,
glob_current_iter, glob_start, glob_warned, glob_hmin, glob_orig_start_sec,
glob_max_sec, glob_hmin_init, glob_disp_incr, djd_debug2, glob_display_flag,
glob_optimal_expect_sec, glob_percent_done, glob_log10abserr, glob_warned2,
glob_max_iter, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
glob_smallish_float, glob_relerr, glob_log10_relerr, glob_last_good_h,
years_in_century, min_in_hour, sec_in_min, glob_curr_iter_when_opt,
glob_no_eqs, glob_max_order, glob_clock_start_sec, glob_max_opt_iter,
glob_log10normmin, glob_normmax, MAX_UNCHANGED, glob_hmax,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_max_rel_trunc_err,
glob_abserr, glob_dump_analytic, glob_look_poles, glob_almost_1,
centuries_in_millinium, glob_max_minutes, glob_optimal_start,
glob_log10_abserr, glob_large_float, glob_h, glob_html_log, array_const_0D0,
array_const_4D0, array_const_0, array_const_1, array_const_2,
array_const_2D0, array_const_3D0, array_1st_rel_error, array_last_rel_error,
array_m1, array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_tmp18, array_tmp19, array_t, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp20, array_tmp21, array_x1_init, array_pole,
array_type_pole, array_norms, array_x2_init, array_complex_pole,
array_x2_higher_work2, array_x2_higher_work, array_poles,
array_x1_higher_work2, array_x1_higher_work, array_real_pole,
array_x2_higher, array_x1_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
INFO := 2;
ALWAYS := 1;
glob_iolevel := 5;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
glob_log10relerr := 0.;
glob_small_float := 0.1*10^(-50);
glob_optimal_clock_start_sec := 0.;
glob_initial_pass := true;
djd_debug := true;
glob_unchanged_h_cnt := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_max_hours := 0.;
days_in_year := 365.0;
hours_in_day := 24.0;
glob_dump := false;
glob_iter := 0;
glob_current_iter := 0;
glob_start := 0;
glob_warned := false;
glob_hmin := 0.1*10^(-10);
glob_orig_start_sec := 0.;
glob_max_sec := 10000.0;
glob_hmin_init := 0.001;
glob_disp_incr := 0.1;
djd_debug2 := true;
glob_display_flag := true;
glob_optimal_expect_sec := 0.1;
glob_percent_done := 0.;
glob_log10abserr := 0.;
glob_warned2 := false;
glob_max_iter := 1000;
glob_optimal_done := false;
glob_not_yet_finished := true;
glob_clock_sec := 0.;
glob_smallish_float := 0.1*10^(-100);
glob_relerr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_last_good_h := 0.1;
years_in_century := 100.0;
min_in_hour := 60.0;
sec_in_min := 60.0;
glob_curr_iter_when_opt := 0;
glob_no_eqs := 0;
glob_max_order := 30;
glob_clock_start_sec := 0.;
glob_max_opt_iter := 10;
glob_log10normmin := 0.1;
glob_normmax := 0.;
MAX_UNCHANGED := 10;
glob_hmax := 1.0;
glob_reached_optimal_h := false;
glob_not_yet_start_msg := true;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_look_poles := false;
glob_almost_1 := 0.9990;
centuries_in_millinium := 10.0;
glob_max_minutes := 0.;
glob_optimal_start := 0.;
glob_log10_abserr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_h := 0.1;
glob_html_log := true;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_max_order := 2;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/complicatedrevpostode.ode#################");
omniout_str(ALWAYS, "diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - \
2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t ,\
1 ) + diff ( x1 , t , 0 );");
omniout_str(ALWAYS, "diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) \
- 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_x2 := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_tmp10 := Array(1 .. max_terms + 1, []);
array_tmp11 := Array(1 .. max_terms + 1, []);
array_tmp12 := Array(1 .. max_terms + 1, []);
array_tmp13 := Array(1 .. max_terms + 1, []);
array_tmp14 := Array(1 .. max_terms + 1, []);
array_tmp15 := Array(1 .. max_terms + 1, []);
array_tmp16 := Array(1 .. max_terms + 1, []);
array_tmp17 := Array(1 .. max_terms + 1, []);
array_tmp18 := Array(1 .. max_terms + 1, []);
array_tmp19 := Array(1 .. max_terms + 1, []);
array_t := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_tmp5 := Array(1 .. max_terms + 1, []);
array_tmp6 := Array(1 .. max_terms + 1, []);
array_tmp7 := Array(1 .. max_terms + 1, []);
array_tmp8 := Array(1 .. max_terms + 1, []);
array_tmp9 := Array(1 .. max_terms + 1, []);
array_tmp20 := Array(1 .. max_terms + 1, []);
array_tmp21 := Array(1 .. max_terms + 1, []);
array_x1_init := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
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_last_rel_error[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_x2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_tmp18[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp19[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_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_tmp20[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp21[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_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2_init[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_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[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_x1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
end do;
array_x2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1
end do;
array_tmp19 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp19[term] := 0.; term := term + 1
end do;
array_tmp18 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp18[term] := 0.; term := term + 1
end do;
array_tmp17 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp17[term] := 0.; term := term + 1
end do;
array_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[term] := 0.; term := term + 1
end do;
array_tmp15 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp15[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_tmp21 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp21[term] := 0.; term := term + 1
end do;
array_tmp20 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp20[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_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_4D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_4D0[term] := 0.; term := term + 1
end do;
array_const_4D0[1] := 4.0;
array_const_0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0[term] := 0.; term := term + 1
end do;
array_const_0[1] := 0;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x2_higher[r_order, term_no] := array_x2_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x1_higher[r_order, term_no] := array_x1_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_x2();
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_x1();
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_t[1] <= t_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 2;
order_diff := 2;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
order_diff := 1;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x1[term_no] := array_x1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x1_higher[ord, term_no] :=
array_x1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.\
0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1\
) + diff ( x1 , t , 0 );");
omniout_str(INFO, "diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - \
2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-01T22:13:45-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"complicatedrev");
logitem_str(html_log_file, "diff ( x2 , t , 2 ) = 3.0 * diff (x2 \
, t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - \
diff ( x1 , t , 1 ) + diff ( x1 , t , 0 );");
logitem_float(html_log_file, t_start);
logitem_float(html_log_file, t_end);
logitem_float(html_log_file, array_t[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 075 | ");
logitem_str(html_log_file, "complicatedrev diffeq.mxt");
logitem_str(html_log_file, "complicatedrev maple results");
logitem_str(html_log_file, "only 1 sub iteration - eqs reversed");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( x1 , t , 1 ) = 4.0 * diff ( x2\
, t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t\
, 0 );");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/complicatedrevpostode.ode#################
diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1 ) + diff ( x1 , t , 0 );
diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
#END FIRST INPUT BLOCK
!
#BEGIN SECOND INPUT BLOCK
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.0001
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.0001
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.0001
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5001
x2[1] (analytic) = 0.00082570611074256394598966051590164
x2[1] (numeric) = 0.00082570611074256392862454548221734
absolute error = 1.736511503368430e-20
relative error = 2.1030624344135853131076218807314e-15 %
h = 0.0001
x1[1] (analytic) = 0.001291646017422585871235266471237
x1[1] (numeric) = 0.0012916460174230489348636657751324
absolute error = 4.630636283993038954e-16
relative error = 3.5850660486943929424717187876107e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5002
x2[1] (analytic) = 0.0008257966814495432344339416603249
x2[1] (numeric) = 0.00082579669236800470126384940078639
absolute error = 1.091846146682990774046149e-11
relative error = 1.3221730859543340892947130808656e-06 %
h = 0.0001
x1[1] (analytic) = 0.0012915368582788917633066026400632
x1[1] (numeric) = 0.0012915368364478018186438795723478
absolute error = 2.18310899446627230677154e-11
relative error = 1.6903187705966780270467385341009e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5003
x2[1] (analytic) = 0.00082588727573070556349803310856235
x2[1] (numeric) = 0.00082588731940837270413080905562684
absolute error = 4.367766714063277594706449e-11
relative error = 5.2885748968573059738652334992774e-06 %
h = 0.0001
x1[1] (analytic) = 0.0012914277100505662472629969306448
x1[1] (numeric) = 0.0012914276227275971438773832377984
absolute error = 8.73229691033856136928464e-11
relative error = 6.7617388432811664007174460332190e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5004
x2[1] (analytic) = 0.00082597789359022044558440876232671
x2[1] (numeric) = 0.00082597799187802753747060081130297
absolute error = 9.828780709188619204897626e-11
relative error = 1.1899568723887444830708663956891e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012913185727365178408202846139762
x1[1] (numeric) = 0.0012913183762594045481056946858048
absolute error = 1.964771132927145899281714e-10
relative error = 1.5215231736065489939371765467132e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5005
x2[1] (analytic) = 0.00082606853503225828165826201261726
x2[1] (numeric) = 0.00082606870979424301027179618180314
absolute error = 1.7476198472861353416918588e-10
relative error = 2.1155869920864255417119592350920e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012912094463356551708370721480129
x1[1] (numeric) = 0.0012912090970334034653976883097968
absolute error = 3.493022517054393838382161e-10
relative error = 2.7052330874493682756563749252924e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3.8MB, alloc=2.9MB, time=0.18
t[1] = 0.5006
x2[1] (analytic) = 0.00082615920006099036141977864461309
x2[1] (numeric) = 0.00082615947317429792022500039244805
absolute error = 2.7311330755880522174783496e-10
relative error = 3.3058193570760079898665821299455e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012911003308468869733038234462486
x1[1] (numeric) = 0.0012910997850397725668382706853073
absolute error = 5.458071144064655527609413e-10
relative error = 4.2274570098549020243541904274637e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5007
x2[1] (analytic) = 0.00082624988868058886347644474630742
x2[1] (numeric) = 0.00082625028203547697646803160969154
absolute error = 3.9335488811299158686338412e-10
relative error = 4.7607254597168782172128489515070e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012909912262691220933319472376107
x1[1] (numeric) = 0.0012909904402686875783101893012369
absolute error = 7.860004345150217579363738e-10
relative error = 6.0883483831761599575342066787359e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5008
x2[1] (analytic) = 0.00082634060089522685551538962782877
x2[1] (numeric) = 0.00082634113639507080120783381646098
absolute error = 5.3549984394569244418863221e-10
relative error = 6.4803767764230840379549636703195e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012908821326012694851428855175656
x1[1] (numeric) = 0.0012908810627103212803149294535
absolute error = 1.0698909482048279560640656e-09
relative error = 8.2880607081366911087017265985130e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5009
x2[1] (analytic) = 0.00082643133670907829447576375839823
x2[1] (numeric) = 0.00082643203627037593163955910361721
absolute error = 6.9956129763716379534521898e-10
relative error = 8.4648447676594396011602125814044e-05 %
h = 0.0001
x1[1] (analytic) = 0.0012907730498422382120572030903234
x1[1] (numeric) = 0.0012907716523548435070894619262796
absolute error = 1.3974873947049677411640438e-09
relative error = 0.00010826747543851899031951278019646 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = 0.00082652298167869482186615886883847
absolute error = 8.8555237679514500714096661e-10
relative error = 0.00010714200877937633936666773339498 %
h = 0.0001
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = 0.0012906622091924211457229525069884
absolute error = 1.7687985163007607256950467e-09
relative error = 0.00013704562507850362883603805191251 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5011
x2[1] (analytic) = 0.00082661287915112178821202023981947
x2[1] (numeric) = 0.0008266139726373358448185800471113
absolute error = 1.09348621405660655980729183e-09
relative error = 0.00013228516535812344297854422310371 %
h = 0.0001
x1[1] (analytic) = 0.0012905549170462764699083942648711
x1[1] (numeric) = 0.0012905527332132181352732003500145
absolute error = 2.1838330583346351939148566e-09
relative error = 0.00016921659276095166187227232394001 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5012
x2[1] (analytic) = 0.00082670368578766620467820114309252
x2[1] (numeric) = 0.00082670500916361329417656887182416
absolute error = 1.32337594708949836772873164e-09
relative error = 0.00016007863153877354329035949252672 %
h = 0.0001
x1[1] (analytic) = 0.0012904458670071646728838326718726
x1[1] (numeric) = 0.0012904432244073954658827289361978
absolute error = 2.6425997692070011037356748e-09
relative error = 0.00020478191583005233875038680675689 %
h = 0.0001
TOP MAIN SOLVE Loop
Complex estimate of poles used
NO POLE
Radius of convergence = 9.530e-05
Order of pole = 1.45
t[1] = 0.5013
x2[1] (analytic) = 0.00082679451604012879179140950883443
x2[1] (numeric) = 0.0008267960912748473862901135528127
absolute error = 1.57523471859449870404397827e-09
relative error = 0.00019052312128761677434589756366302 %
h = 0.0001
x1[1] (analytic) = 0.0012903368278725115550179667024679
x1[1] (numeric) = 0.0012903336827651111778934432230638
absolute error = 3.1451074003771245234794041e-09
relative error = 0.00024374313221476686027677354855683 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 6.634e-05
Order of pole = 0.2429
t[1] = 0.5014
x2[1] (analytic) = 0.00082688536991268795533779675988916
x2[1] (numeric) = 0.00082688721898836426210195685893159
absolute error = 1.84907567630676416009904243e-09
relative error = 0.00022361934841125690559227174754076 %
h = 0.0001
x1[1] (analytic) = 0.0012902277996412267249633565185424
x1[1] (numeric) = 0.0012902241082765203609452145248564
absolute error = 3.6913647063640181419936860e-09
relative error = 0.0002861017804290432177617867989196 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 9.350e-05
Order of pole = 16.66
t[1] = 0.5015
x2[1] (analytic) = 0.00082697624740952299139053885956424
x2[1] (numeric) = 0.00082697839232149598907676274131251
absolute error = 2.14491197299768622388174827e-09
relative error = 0.00025936802655657345897344272824217 %
h = 0.0001
x1[1] (analytic) = 0.0012901187823122199004062452509559
x1[1] (numeric) = 0.0012901145009317751528827776129225
absolute error = 4.2813804447475234676380334e-09
relative error = 0.00033185939957204594675883325497259 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 0.0003883
Order of pole = 181.3
t[1] = 0.5016
x2[1] (analytic) = 0.00082706714853481408648245956670656
x2[1] (numeric) = 0.00082706961129158056320135100261953
absolute error = 2.46275676647671889143591297e-09
relative error = 0.00029776986921069239297082246258982 %
h = 0.0001
x1[1] (analytic) = 0.001290009775884400908055656176395
x1[1] (numeric) = 0.0012900048607210247366637400349166
absolute error = 4.9151633761713919161414784e-09
relative error = 0.00038101752932854089628186240851647 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.2MB, time=0.40
NO POLE
NO POLE
t[1] = 0.5017
x2[1] (analytic) = 0.00082715807329274231777868876405026
x2[1] (numeric) = 0.00082716087591596191169565573816934
absolute error = 2.80262321959391696697411908e-09
relative error = 0.0003388255897010426787499874370856 %
h = 0.0001
x1[1] (analytic) = 0.0012899007803566796836324909844552
x1[1] (numeric) = 0.0012898951876344153197886255984061
absolute error = 5.5927222643638438653860491e-09
relative error = 0.00043357770997063512599486825749057 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5018
x2[1] (analytic) = 0.00082724902168748965324935586679766
x2[1] (numeric) = 0.00082725218621198990175567607644218
absolute error = 3.16452450024850632020964452e-09
relative error = 0.00038253590119614195101259475039695 %
h = 0.0001
x1[1] (analytic) = 0.0012897917957279662718586291348401
x1[1] (numeric) = 0.0012897854816620899894750044733871
absolute error = 6.3140658762823836246614530e-09
relative error = 0.00048954148236915142930160081310025 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5019
x2[1] (analytic) = 0.00082733999372323895184231831839524
x2[1] (numeric) = 0.00082734354219702039133673227730581
absolute error = 3.54847378143949441395891057e-09
relative error = 0.00042890151671146297167567481942865 %
h = 0.0001
x1[1] (analytic) = 0.0012896828219971708264460283045716
x1[1] (numeric) = 0.0012896757427941878771502327068213
absolute error = 7.0792029829492957955977503e-09
relative error = 0.00054891038805856293115236255893519 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.502
x2[1] (analytic) = 0.0008274309894041739636559251804687
x2[1] (numeric) = 0.00082743494388841551246898978873804
absolute error = 3.95448424154881306460826934e-09
relative error = 0.00047792314914339909131517606252054 %
h = 0.0001
x1[1] (analytic) = 0.0012895738591632036100858259251
x1[1] (numeric) = 0.0012895659710208405033811265466288
absolute error = 7.8881423631067046993784712e-09
relative error = 0.00061168596952060355891041378158254 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 2.209e-05
Order of pole = 14.49
t[1] = 0.5021
x2[1] (analytic) = 0.00082752200873447933011181582388164
x2[1] (numeric) = 0.00082752639130354492543241828831873
absolute error = 4.38256906559532060246443709e-09
relative error = 0.0005296015114205285243750142544157 %
h = 0.0001
x1[1] (analytic) = 0.0012894649072249749944374418092067
x1[1] (numeric) = 0.0012894561663321606930027267178243
absolute error = 8.7408928143014347150913824e-09
relative error = 0.00067786977104421479501276265729749 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 2.336e-05
Order of pole = 24.83
t[1] = 0.5022
x2[1] (analytic) = 0.0008276130517183405841277537278848
x2[1] (numeric) = 0.00082761788445978987123188078318556
absolute error = 4.83274144928710412705530076e-09
relative error = 0.00058393731699289568033027562785931 %
h = 0.0001
x1[1] (analytic) = 0.0012893559661813954601176818675888
x1[1] (numeric) = 0.0012893463287182235643536521852231
absolute error = 9.6374631718957640296823657e-09
relative error = 0.00074746334020064552635066575603971 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 1.142e-05
Order of pole = 2.464
t[1] = 0.5023
x2[1] (analytic) = 0.00082770411835994415029049539432325
x2[1] (numeric) = 0.00082770942337455170474273680961527
absolute error = 5.30501460755445224141529202e-09
relative error = 0.00064093128086230659402971268388008 %
h = 0.0001
x1[1] (analytic) = 0.0012892470360313755966898429150187
x1[1] (numeric) = 0.001289236458169061789896846002069
absolute error = 1.05778623138067929969129497e-08
relative error = 0.00082046822821234441795999944815774 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5024
x2[1] (analytic) = 0.00082779520866347734502869438387111
x2[1] (numeric) = 0.00082780100806526100965541105811862
absolute error = 5.79940178366462671667424751e-09
relative error = 0.00070058412068222673174488652106454 %
h = 0.0001
x1[1] (analytic) = 0.0012891381167738261026528185659675
x1[1] (numeric) = 0.001289126554674694289315711224315
absolute error = 1.15620991318133371073416525e-08
relative error = 0.00089688598772864142225563284804375 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5025
x2[1] (analytic) = 0.00082788632263312837678584048126422
x2[1] (numeric) = 0.00082789263854937950350277480901202
absolute error = 6.31591625112671693432774780e-09
relative error = 0.00076289655698606919930811266105407 %
h = 0.0001
x1[1] (analytic) = 0.0012890292084076577854302062195851
x1[1] (numeric) = 0.001289016618225122710980849110263
absolute error = 1.25901825350744493571093221e-08
relative error = 0.00097671817309920735967983785177981 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5026
x2[1] (analytic) = 0.00082797746027308634619323399650282
x2[1] (numeric) = 0.00082798431484440170240761824825016
absolute error = 6.85457131535621438425174734e-09
relative error = 0.00082786931338631082119917338016759 %
h = 0.0001
x1[1] (analytic) = 0.001288920310931781561359415133927
x1[1] (numeric) = 0.0012889066488104444388821360327438
absolute error = 1.36621213371224772791011832e-08
relative error = 0.0010599663316071035023544937691725 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.3MB, time=0.62
NO POLE
NO POLE
t[1] = 0.5027
x2[1] (analytic) = 0.00082806862158754124624299520899781
x2[1] (numeric) = 0.00082807603696782566029676518087538
absolute error = 7.41538028441405376997187757e-09
relative error = 0.0008955031130388170595198527265201 %
h = 0.0001
x1[1] (analytic) = 0.0012888114243451084556807755893193
x1[1] (numeric) = 0.0012887966464212585140029438101054
absolute error = 1.47779238499416778317792139e-08
relative error = 0.0011466319719699003801639072892386 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5028
x2[1] (analytic) = 0.00082815980658068396246110896163522
x2[1] (numeric) = 0.00082816780493703665083271134182245
absolute error = 7.99835635268837160238018723e-09
relative error = 0.00096579866459736560160947114513032 %
h = 0.0001
x1[1] (analytic) = 0.0012887025486465496025266491407532
x1[1] (numeric) = 0.0012886866110475795289980036670742
absolute error = 1.59375989700735286454736790e-08
relative error = 0.0012367166486022608585355932153182 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5029
x2[1] (analytic) = 0.0008282510152567062730805044117353
x2[1] (numeric) = 0.00082825961876945064870408127408949
absolute error = 8.60351274437562357686235419e-09
relative error = 0.0010387566795446752357349565177608 %
h = 0.0001
x1[1] (analytic) = 0.0012885936838350162449105399591989
x1[1] (numeric) = 0.0012885765426795207305843775027163
absolute error = 1.71411554955143261624564826e-08
relative error = 0.0013302219086236787901504655946559 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.503
x2[1] (analytic) = 0.0008283422476198008492141699458837
x2[1] (numeric) = 0.00082835147848248897478690746621481
absolute error = 9.23086268812557273752033111e-09
relative error = 0.0011143778691295760073915978387653 %
h = 0.0001
x1[1] (analytic) = 0.0012884848299094197347162072617323
x1[1] (numeric) = 0.0012884664413071899642637181374602
absolute error = 1.83886022297704524891242721e-08
relative error = 0.0014271492999310801440322456407399 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5031
x2[1] (analytic) = 0.00082843350367416125502830326561401
x2[1] (numeric) = 0.00082844338409357890758653538165224
absolute error = 9.88041941765255823211603823e-09
relative error = 0.0011926629444405855659386425476656 %
h = 0.0001
x1[1] (analytic) = 0.0012883759868686715326867788303632
x1[1] (numeric) = 0.0012883563069206921107950054325651
absolute error = 1.96799479794218917733977981e-08
relative error = 0.0015275003710099367599319370885459 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5032
x2[1] (analytic) = 0.00082852478342398194791549665092172
x2[1] (numeric) = 0.00082853533562015368491858679822181
absolute error = 1.055219617173700309014730009e-08
relative error = 0.0012736126164058408751560897698433 %
h = 0.0001
x1[1] (analytic) = 0.0012882671547116832084138656194575
x1[1] (numeric) = 0.001288246139510129084351526451179
absolute error = 2.10152015541240623391682785e-08
relative error = 0.0016312766709345552552490474176664 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5033
x2[1] (analytic) = 0.00082861608687345827866795740859187
x2[1] (numeric) = 0.00082862733307965250584258740943162
absolute error = 1.124620619422717463000083975e-08
relative error = 0.0013572275957930604106302941801996 %
h = 0.0001
x1[1] (analytic) = 0.0012881583334373664403266774516441
x1[1] (numeric) = 0.0012881359390655998316318161026519
absolute error = 2.23943717666086948613489922e-08
relative error = 0.0017384797493682919695661938307173 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5034
x2[1] (analytic) = 0.00082870741402678649165076351232339
x2[1] (numeric) = 0.00082871937648952053259611655441075
absolute error = 1.196246273404094535304208736e-08
relative error = 0.0014435085932095063945263519865922 %
h = 0.0001
x1[1] (analytic) = 0.0012880495230446330156811398020981
x1[1] (numeric) = 0.0012880257055772003309700201103553
absolute error = 2.38174674326847111196917428e-08
relative error = 0.0018491111565637680102786646245289 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5035
x2[1] (analytic) = 0.00082879876488816372497515444163463
x2[1] (numeric) = 0.00082881146586720889252956622783508
absolute error = 1.270097904516755441178620045e-08
relative error = 0.0015324563191019470782455471979338 %
h = 0.0001
x1[1] (analytic) = 0.0012879407235323948305490116710912
x1[1] (numeric) = 0.0012879154390350235914459913726606
absolute error = 2.52844973712391030202984306e-08
relative error = 0.0019631724433630843752015321143145 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5036
x2[1] (analytic) = 0.00082889013946178801067185722653652
x2[1] (numeric) = 0.00082890360123017468004150952920641
absolute error = 1.346176838666936965230266989e-08
relative error = 0.0016240714837566190729618589179466 %
h = 0.0001
x1[1] (analytic) = 0.0012878319348995638898070045446997
x1[1] (numeric) = 0.0012878051394291596519951195385197
absolute error = 2.67954704042378118850061800e-08
relative error = 0.0020806651611980371521889855226445 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=15.2MB, alloc=4.3MB, time=0.84
t[1] = 0.5037
x2[1] (analytic) = 0.00082898153775185827486444770496057
x2[1] (numeric) = 0.00082899578259588095851467874007525
absolute error = 1.424484402268365023103511468e-08
relative error = 0.0017183547972991897280350345808097 %
h = 0.0001
x1[1] (analytic) = 0.0012877231571450523071259024435631
x1[1] (numeric) = 0.0012876948067496955805178937178034
absolute error = 2.83503953567266080087257597e-08
relative error = 0.0022015908620903327957928993633133 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5038
x2[1] (analytic) = 0.0008290729597625743379427469999303
x2[1] (numeric) = 0.0008290880099817967622525532178159
absolute error = 1.505021922242430980621788560e-08
relative error = 0.0018153069696947195572977112398627 %
h = 0.0001
x1[1] (analytic) = 0.0012876143902677723049596830595824
x1[1] (numeric) = 0.001287584440986715472989198246897
absolute error = 2.99492810568319704848126854e-08
relative error = 0.0023259510986518034809876332318308 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5039
x2[1] (analytic) = 0.00082916440549813691473625322346704
x2[1] (numeric) = 0.00082918028340539709841655729447657
absolute error = 1.587790726018368030407100953e-08
relative error = 0.0019149287107476247132140315520803 %
h = 0.0001
x1[1] (analytic) = 0.0012875056342666362145346399804511
x1[1] (numeric) = 0.0012874740421303004525673414321379
absolute error = 3.15921363357619672985483132e-08
relative error = 0.0024537474240846225339879046129858 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.504
x2[1] (analytic) = 0.00082925587496274761468760841422102
x2[1] (numeric) = 0.00082927260288416294896386836852671
absolute error = 1.672792141533427625995430569e-08
relative error = 0.0020172207301016395089070918139226 %
h = 0.0001
x1[1] (analytic) = 0.0012873968891405564758385060019091
x1[1] (numeric) = 0.001287363610170528668702817205881
absolute error = 3.32789700278071356887960281e-08
relative error = 0.002584981392181519940185635631824 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5041
x2[1] (analytic) = 0.00082934736816060894202610071582133
x2[1] (numeric) = 0.00082936496843558127258583537309399
absolute error = 1.760027497233055973465727266e-08
relative error = 0.002122183737239778988052024357264 %
h = 0.0001
x1[1] (analytic) = 0.0012872881548884456376095775276106
x1[1] (numeric) = 0.0012872531450974752962467996968618
absolute error = 3.50097909703413627778307488e-08
relative error = 0.0027196545573259979292264856280951 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5042
x2[1] (analytic) = 0.00082943888509592429594120180293885
x2[1] (numeric) = 0.00082945738007714500664700778131176
absolute error = 1.849498122071070580597837291e-08
relative error = 0.0022298184414843015426287227594889 %
h = 0.0001
x1[1] (analytic) = 0.0012871794315092163573258400564985
x1[1] (numeric) = 0.0012871426469012125345593710217109
absolute error = 3.67846080038227664690347876e-08
relative error = 0.0028577684744925466372230751538108 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5043
x2[1] (analytic) = 0.00082953042577289797075613956205843
x2[1] (numeric) = 0.00082954983782635306912477520405914
absolute error = 1.941205345509836863564200071e-08
relative error = 0.0023401255519966715785154976698536 %
h = 0.0001
x1[1] (analytic) = 0.0012870707190017814011940947575749
x1[1] (numeric) = 0.0012870321155718096066174836681574
absolute error = 3.86034299717945766110894175e-08
relative error = 0.002999324699246859846019250084606 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5044
x2[1] (analytic) = 0.00082962199019573515610150603395714
x2[1] (numeric) = 0.00082964234170071036054961725451249
absolute error = 2.035150497520444811122055535e-08
relative error = 0.0024531057777775222288590323526276 %
h = 0.0001
x1[1] (analytic) = 0.00128696201736505364413908613196
x1[1] (numeric) = 0.0012869215510993327581226613774753
absolute error = 4.04662657208860164247544847e-08
relative error = 0.0031443247877460507992225337811047 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5045
x2[1] (analytic) = 0.00082971357836864193708890062488759
x2[1] (numeric) = 0.00082973489171772776594596234848362
absolute error = 2.131334908582885706172359603e-08
relative error = 0.002568759827666618115034857193778 %
h = 0.0001
x1[1] (analytic) = 0.0012868533265979460697926307621308
x1[1] (numeric) = 0.0012868109534738452566084453949839
absolute error = 4.23731241008131841853671469e-08
relative error = 0.0032927702967388680944915970661006 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5046
x2[1] (analytic) = 0.00082980519029582529448460859346626
x2[1] (numeric) = 0.00082982748789492215677365245459503
absolute error = 2.229759909686228904386112877e-08
relative error = 0.0026870884103428181548132639668211 %
h = 0.0001
x1[1] (analytic) = 0.0012867446466993717704827471482299
x1[1] (numeric) = 0.0012867003226854073905475898049374
absolute error = 4.43240139643799351573432925e-08
relative error = 0.0034446627835659116518102143873461 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5047
x2[1] (analytic) = 0.00082989682598149310488331482026843
x2[1] (numeric) = 0.00082992013024981639287001012199873
absolute error = 2.330426832328798669530173030e-08
relative error = 0.002808092234324038417263191403059 %
h = 0.0001
x1[1] (analytic) = 0.0012866359776682439472227866313365
x1[1] (numeric) = 0.0012865896587240764684589930095673
absolute error = 4.63189441674787637936217692e-08
relative error = 0.0036000038061598487587735656421344 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=1.06
NO POLE
NO POLE
t[1] = 0.5048
x2[1] (analytic) = 0.00082998848542985414088185286713247
x2[1] (numeric) = 0.00083001281879993932439250761769153
absolute error = 2.433337008518351065475055906e-08
relative error = 0.0029317720079672150243492161129304 %
h = 0.0001
x1[1] (analytic) = 0.0012865273195034759097005654035915
x1[1] (numeric) = 0.0012864789615799068180143355508173
absolute error = 4.83579235690916862298527742e-08
relative error = 0.0037587949230456301952240254190052 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5049
x2[1] (analytic) = 0.00083008016864511807125298933317795
x2[1] (numeric) = 0.00083010555356282579376204543272023
absolute error = 2.538491770772250905609954228e-08
relative error = 0.0030581284394682671000715579269393 %
h = 0.0001
x1[1] (analytic) = 0.001286418672203981076267497605066
x1[1] (numeric) = 0.001286368231242949785144396372778
absolute error = 5.04409610312911231012322880e-08
relative error = 0.0039210376933407064394274940013801 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.505
x2[1] (analytic) = 0.00083017187563149546111924351454314
x2[1] (numeric) = 0.00083019833455601663760685431864137
absolute error = 2.645892452117648761080409823e-08
relative error = 0.0031871622368620597688296339469833 %
h = 0.0001
x1[1] (analytic) = 0.0012863100357686729739277295072664
x1[1] (numeric) = 0.0012862574677032537331449976136769
absolute error = 5.25680654192407827318935895e-08
relative error = 0.0040867336767552439596938238625315 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5051
x2[1] (analytic) = 0.00083026360639319777212674237484908
x2[1] (numeric) = 0.00083029116179705868870704649857622
absolute error = 2.755540386091658030412372714e-08
relative error = 0.0033188741080223672060712349423769 %
h = 0.0001
x1[1] (analytic) = 0.0012862014101964652383272747831672
x1[1] (numeric) = 0.0012861466709508640417825805831941
absolute error = 5.47392456011965446941999731e-08
relative error = 0.0042558844335923415912605313261996 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5052
x2[1] (analytic) = 0.0008303553609344373626191108333988
x2[1] (numeric) = 0.00083038403530350477793983648502938
absolute error = 2.867436906741532072565163058e-08
relative error = 0.0034532647606618357436589585785271 %
h = 0.0001
x1[1] (analytic) = 0.0012860927954862716137431508636619
x1[1] (numeric) = 0.0012860358409758231063998188299534
absolute error = 5.69545104485073433320337085e-08
relative error = 0.0044284915247482469669042614278428 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5053
x2[1] (analytic) = 0.00083044713925942748781139737812144
x2[1] (numeric) = 0.00083047695509291373622535263791599
absolute error = 2.981583348624841395525979455e-08
relative error = 0.0035903349023319470204260932174079 %
h = 0.0001
x1[1] (analytic) = 0.0012859841916370059530725163803239
x1[1] (numeric) = 0.0012859249777681703370213506669161
absolute error = 5.92138688356160511657134078e-08
relative error = 0.0046045565117125729948818723745003 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5054
x2[1] (analytic) = 0.00083053894137238229996403501027281
x2[1] (numeric) = 0.00083056992118285039647295351469658
absolute error = 3.097981046809650891850442377e-08
relative error = 0.0037300852404229811675498935507763 %
h = 0.0001
x1[1] (analytic) = 0.0012858755986475822178218096943695
x1[1] (numeric) = 0.0012858140813179421574585185548991
absolute error = 6.15173296400603632911394704e-08
relative error = 0.0047840809565685144707289356445912 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5055
x2[1] (analytic) = 0.0008306307672775168485568375279051
x2[1] (numeric) = 0.00083066293359088559552822479653097
absolute error = 3.216631336874697138726862587e-08
relative error = 0.0038725164821639800498893681357217 %
h = 0.0001
x1[1] (analytic) = 0.0012857670165169144780958885117126
x1[1] (numeric) = 0.0012857031516151720044141728150342
absolute error = 6.38649017424736817156966784e-08
relative error = 0.0049670664219930647407255549423311 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5056
x2[1] (analytic) = 0.0008307226169790470804630311551197
x2[1] (numeric) = 0.00083075599233459617612057496164001
absolute error = 3.337535554909565754380652031e-08
relative error = 0.0040176293346227105534052979368389 %
h = 0.0001
x1[1] (analytic) = 0.001285658445243916912587170584005
x1[1] (numeric) = 0.0012855921886498903265871435077849
absolute error = 6.62565940265860000270762201e-08
relative error = 0.0051535144712572324478491276210519 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5057
x2[1] (analytic) = 0.00083081449048118984012332152411889
x2[1] (numeric) = 0.00083084909743156498881144565754335
absolute error = 3.460695037514868812413342446e-08
relative error = 0.0041654245047056279205581448167624 %
h = 0.0001
x1[1] (analytic) = 0.0012855498848275038085647754955507
x1[1] (numeric) = 0.0012854811924121245837764491796253
absolute error = 6.86924153792247883263159254e-08
relative error = 0.0053434266682262583548938149966394 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=1.31
NO POLE
NO POLE
t[1] = 0.5058
x2[1] (analytic) = 0.00083090638778816286971999601707344
x2[1] (numeric) = 0.00083094224889938089394313563080824
absolute error = 3.586111121802422313961373480e-08
relative error = 0.0043159026991578391335206505654334 %
h = 0.0001
x1[1] (analytic) = 0.0012854413352665895618636675359888
x1[1] (numeric) = 0.0012853701628918992459852368804749
absolute error = 7.11723746903158784306555139e-08
relative error = 0.0055368045773598322452128434209214 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5059
x2[1] (analytic) = 0.0008309983089041848093510614748241
x2[1] (numeric) = 0.00083103544675563876358823844884203
absolute error = 3.713785145395423717697401793e-08
relative error = 0.0044690646245630663452076156610187 %
h = 0.0001
x1[1] (analytic) = 0.0012853327965600886768737996586336
x1[1] (numeric) = 0.0012852591000792357925244535522186
absolute error = 7.36964808528843493461064150e-08
relative error = 0.005733649763712309901096804968117 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.506
x2[1] (analytic) = 0.00083109025383347519720441727943742
x2[1] (numeric) = 0.00083112869101793948349969420312806
absolute error = 3.843718446428629527692369064e-08
relative error = 0.0046249109873436103581198866405208 %
h = 0.0001
x1[1] (analytic) = 0.0012852242687069157665292585243653
x1[1] (numeric) = 0.0012851480039641527111162487056995
absolute error = 7.62647427630554130098186658e-08
relative error = 0.0059339637929329301598153591266959 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5061
x2[1] (analytic) = 0.00083118222258025446973206381763632
x2[1] (numeric) = 0.00083122198170388995506145538388347
absolute error = 3.975912363548532939156624715e-08
relative error = 0.0047834424937603141509996259768566 %
h = 0.0001
x1[1] (analytic) = 0.0012851157517059855522974106309618
x1[1] (numeric) = 0.0012850368745366654969971083056297
absolute error = 7.88771693200553003023253321e-08
relative error = 0.0061377482312660320473495841092191 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5062
x2[1] (analytic) = 0.00083127421514874396182434633212867
x2[1] (numeric) = 0.00083131531883110309723976711617516
absolute error = 4.110368235913541542078404649e-08
relative error = 0.0049446598499125264532939202858836 %
h = 0.0001
x1[1] (analytic) = 0.001285007245556212864168049527763
x1[1] (numeric) = 0.0012849257117867866520207197828386
absolute error = 8.15337694262121473297449244e-08
relative error = 0.0063450046455512719898422359115555 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5063
x2[1] (analytic) = 0.00083136623154316590698423416785765
x2[1] (numeric) = 0.00083140870241719784853506194758823
absolute error = 4.247087403194155082777973058e-08
relative error = 0.0051085637617380653674237649484635 %
h = 0.0001
x1[1] (analytic) = 0.0012848987502565126406425441155605
x1[1] (numeric) = 0.0012848145157045256837605680932539
absolute error = 8.42345519869568819760223066e-08
relative error = 0.0065557346032238411027931827121041 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5064
x2[1] (analytic) = 0.00083145827176774343750163542019918
x2[1] (numeric) = 0.00083150213247979916893446937759956
absolute error = 4.386071205573143283395740038e-08
relative error = 0.0052751549350131820388554454066419 %
h = 0.0001
x1[1] (analytic) = 0.0012847902658057999287229880316013
x1[1] (numeric) = 0.0012847032862798891046122627429857
absolute error = 8.69795259108241107252886156e-08
relative error = 0.0067699396723146825580272912510373 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5065
x2[1] (analytic) = 0.00083155033582670058462774699213345
x2[1] (numeric) = 0.00083159560903653804186494031886712
absolute error = 4.527320983745723719332673367e-08
relative error = 0.0054444340753525243739713174987685 %
h = 0.0001
x1[1] (analytic) = 0.0012846817922029898839013501196003
x1[1] (numeric) = 0.0012845920235028804308955956988615
absolute error = 8.97687001094530057544207388e-08
relative error = 0.0069876214214507090284620515273087 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5066
x2[1] (analytic) = 0.00083164242372426227874944006741881
x2[1] (numeric) = 0.00083168913210505147614698668070405
absolute error = 4.670838078919739754661328524e-08
relative error = 0.0056164018882091008057369714343622 %
h = 0.0001
x1[1] (analytic) = 0.0012845733294469977701486259846507
x1[1] (numeric) = 0.0012844807273635001819563301037339
absolute error = 9.26020834975881922958809168e-08
relative error = 0.0072087814198550202107022351900734 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5067
x2[1] (analytic) = 0.00083173453546465434956368100679754
x2[1] (numeric) = 0.00083178270170298250794903626506466
absolute error = 4.816623832815838535525826712e-08
relative error = 0.0057910590788742441071617462072989 %
h = 0.0001
x1[1] (analytic) = 0.001284464877536738959903990632925
x1[1] (numeric) = 0.0012843693978517458792677197158594
absolute error = 9.54796849930806362709170656e-08
relative error = 0.007433421237347120425488892563956 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=26.7MB, alloc=4.4MB, time=1.54
t[1] = 0.5068
x2[1] (analytic) = 0.00083182667105210352625198767426466
x2[1] (numeric) = 0.00083187631784798020274240316542778
absolute error = 4.964679587667649041549116312e-08
relative error = 0.0059684063524775752525495434247558 %
h = 0.0001
x1[1] (analytic) = 0.0012843564364711289340639521960578
x1[1] (numeric) = 0.0012842580349576120455317589916236
absolute error = 9.84015135168885321932044342e-08
relative error = 0.0076615424443431362960300023926761 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5069
x2[1] (analytic) = 0.00083191883049083743765492120043225
x2[1] (numeric) = 0.00083196998055769965725687385902107
absolute error = 5.115006686221960195265858882e-08
relative error = 0.0061484444139869673265368717422114 %
h = 0.0001
x1[1] (analytic) = 0.0012842480062490832819715067401017
x1[1] (numeric) = 0.0012841466386710902037801637308612
absolute error = 1.013675779930781913430092405e-07
relative error = 0.0078931466118560345042400979534833 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.507
x2[1] (analytic) = 0.00083201101378508461244661319002326
x2[1] (numeric) = 0.00083206368984980200143690918288832
absolute error = 5.267606471738899029599286506e-08
relative error = 0.0063311739682085094809150353188218 %
h = 0.0001
x1[1] (analytic) = 0.001284139586869517701405294158948
x1[1] (numeric) = 0.0012840352089821688764750822039982
absolute error = 1.043778873488249302119549498e-07
relative error = 0.0081282353114958396249162023294047 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5071
x2[1] (analytic) = 0.00083210322093907447930932838052986
x2[1] (numeric) = 0.00083215744574195440039846238435992
absolute error = 5.422480287992108913400383006e-08
relative error = 0.0065165957197864709392333619582934 %
h = 0.0001
x1[1] (analytic) = 0.0012840311783313479985687551521049
x1[1] (numeric) = 0.0012839237458808335846095366802168
absolute error = 1.074324505144139592184718881e-07
relative error = 0.0083668101154698520378774152694571 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5072
x2[1] (analytic) = 0.00083219545195703736710806275907346
x2[1] (numeric) = 0.00083225124825183005638641343654516
absolute error = 5.579629479268927835067747170e-08
relative error = 0.006704710373203265049180348775798 %
h = 0.0001
x1[1] (analytic) = 0.0012839227806334900880792892867217
x1[1] (numeric) = 0.0012838122493570668468075952758211
absolute error = 1.105312764232412716940109006e-07
relative error = 0.0086088725965828659180955029574227 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5073
x2[1] (analytic) = 0.00083228770684320450506517714450406
x2[1] (numeric) = 0.00083234509739710821073261980952317
absolute error = 5.739055390370566744266501911e-08
relative error = 0.0068955186327794133827395855599213 %
h = 0.0001
x1[1] (analytic) = 0.0012838143937748599929574141437547
x1[1] (numeric) = 0.0012837007194008481784242740419564
absolute error = 1.136743740118145331401017983e-07
relative error = 0.0088544243282373873038438520162178 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5074
x2[1] (analytic) = 0.00083237998560180802293506624177892
x2[1] (numeric) = 0.00083243899319547414581458388796769
absolute error = 5.900759366612287951764618877e-08
relative error = 0.0070890212026735098841172981447493 %
h = 0.0001
x1[1] (analytic) = 0.0012837060177543738446159255481629
x1[1] (numeric) = 0.0012835891560021540906451692108116
absolute error = 1.168617522197539707563373513e-07
relative error = 0.0091034668844338522428921577757345 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5075
x2[1] (analytic) = 0.0008324722882370809511788631756612
x2[1] (numeric) = 0.00083253293566461918701473722599937
absolute error = 6.064742753823583587405033817e-08
relative error = 0.0072852187868821850654383364760359 %
h = 0.0001
x1[1] (analytic) = 0.0012835976525709478828490588830272
x1[1] (numeric) = 0.0012834775591509580895858195194091
absolute error = 1.200934199897932632393636181e-07
relative error = 0.0093560018397708450167742267034361 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5076
x2[1] (analytic) = 0.00083256461475325722113917951078113
x2[1] (numeric) = 0.00083262692482224070468034183011737
absolute error = 6.231006898348354116231933624e-08
relative error = 0.0074841120892400702502074142275189 %
h = 0.0001
x1[1] (analytic) = 0.0012834892982234984558216514874832
x1[1] (numeric) = 0.0012833659288372306753907985300621
absolute error = 1.233693862677804308529574211e-07
relative error = 0.0096120307694453164431562820078298 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5077
x2[1] (analytic) = 0.00083265696515457166521488076510333
x2[1] (numeric) = 0.00083272096068604211608400866112078
absolute error = 6.399553147045086912789601745e-08
relative error = 0.00768570181341976186453238918583 %
h = 0.0001
x1[1] (analytic) = 0.0012833809547109420200583061383613
x1[1] (numeric) = 0.0012832542650509393413325368665563
absolute error = 1.266896600026787257692718050e-07
relative error = 0.0098715552492528022563331709744368 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5078
x2[1] (analytic) = 0.00083274933944526001703589742384568
x2[1] (numeric) = 0.0008328150432737328873848335459887
absolute error = 6.570382847287034893612214302e-08
relative error = 0.0078899886629317857761063558530422 %
h = 0.0001
x1[1] (analytic) = 0.001283272622032195140432555615423
x1[1] (numeric) = 0.0012831425677820485729098742850867
absolute error = 1.300542501465675226813303363e-07
relative error = 0.010134576855587641565879881756486 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.4MB, time=1.78
NO POLE
NO POLE
t[1] = 0.5079
x2[1] (analytic) = 0.00083284173762955891163807146089618
x2[1] (numeric) = 0.00083290917260302853559015069074624
absolute error = 6.743497346962395207922985006e-08
relative error = 0.0080969733411245616809453040538277 %
h = 0.0001
x1[1] (analytic) = 0.0012831643001861744901560283500877
x1[1] (numeric) = 0.0012830308370205198469463414989586
absolute error = 1.334631656546432096868511291e-07
relative error = 0.010401097165443195393485786936109 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.508
x2[1] (analytic) = 0.00083293415971170588563803837477598
x2[1] (numeric) = 0.00083300334869165063051790398540207
absolute error = 6.918897994474487986561062609e-08
relative error = 0.0083066565511843675378780795884604 %
h = 0.0001
x1[1] (analytic) = 0.0012830559891717968507676151575396
x1[1] (numeric) = 0.0012829190727563116306881716760356
absolute error = 1.369164154852200794434815040e-07
relative error = 0.010671117756412065287999040347269 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5081
x2[1] (analytic) = 0.00083302660569593937740814474619785
x2[1] (numeric) = 0.00083309757155732679675963629210175
absolute error = 7.096586138741935149154590390e-08
relative error = 0.0085190389961353040507853653392782 %
h = 0.0001
x1[1] (analytic) = 0.0012829476889879791121226370521077
x1[1] (numeric) = 0.0012828072749793793809020415278931
absolute error = 1.404140085997312205955242146e-07
relative error = 0.01094464020668631201870856330494 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5082
x2[1] (analytic) = 0.0008331190755864987272514013242712
x2[1] (numeric) = 0.00083319184121779071564409690769947
absolute error = 7.276563129198839269558342827e-08
relative error = 0.0087341213788392591985843834969469 %
h = 0.0001
x1[1] (analytic) = 0.0012828393996336382723820141458102
x1[1] (numeric) = 0.001282695443679675542972541909613
absolute error = 1.439559539627294094722361972e-07
relative error = 0.01122166609505767434689106552661 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5083
x2[1] (analytic) = 0.00083321156938762417757647164840573
x2[1] (numeric) = 0.00083328615769078212720146739200935
absolute error = 7.458830315794962499574360362e-08
relative error = 0.0089519044019958728129560019569198 %
h = 0.0001
x1[1] (analytic) = 0.0012827311211076914380014356299545
x1[1] (numeric) = 0.0012825835788471495499993778491293
absolute error = 1.475422605418880020577808252e-07
relative error = 0.01150219700091778787565055555032 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5084
x2[1] (analytic) = 0.00083330408710355687307269621296731
x2[1] (numeric) = 0.00083338052099404683212820595305604
absolute error = 7.643389048995905550974008873e-08
relative error = 0.0091723887681425012038109102693346 %
h = 0.0001
x1[1] (analytic) = 0.0012826228534090558237205308396847
x1[1] (numeric) = 0.0012824716804717478218942979250117
absolute error = 1.511729373080018262329146730e-07
relative error = 0.011786234504258403978077804771507 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5085
x2[1] (analytic) = 0.00083339662873853886088515218174166
x2[1] (numeric) = 0.00083347493114533669375251058070285
absolute error = 7.830240679783286735839896119e-08
relative error = 0.0093955751796541818324915127988859 %
h = 0.0001
x1[1] (analytic) = 0.0012825145965366487525520414013697
x1[1] (numeric) = 0.0012823597485434137644777529115478
absolute error = 1.548479932349880742884898219e-07
relative error = 0.012073780185671608803757238884557 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5086
x2[1] (analytic) = 0.00083348919429681309078974865926187
x2[1] (numeric) = 0.00083356938816240964000040112009414
absolute error = 8.019386559654921065246083227e-08
relative error = 0.0096214643387435980327061692122381 %
h = 0.0001
x1[1] (analytic) = 0.0012824063504893876557709944627208
x1[1] (numeric) = 0.0012822477830520877685752836099626
absolute error = 1.585674372998871957108527582e-07
relative error = 0.012364835626350042363648739401621 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5087
x2[1] (analytic) = 0.00083358178378262341536835752605775
x2[1] (numeric) = 0.00083366389206302966536242047640746
absolute error = 8.210828040624999406295034971e-08
relative error = 0.0098500569474610437791923947315548 %
h = 0.0001
x1[1] (analytic) = 0.0012822981152661900729038770055334
x1[1] (numeric) = 0.0012821357839877072091136377845877
absolute error = 1.623312784828637902392209457e-07
relative error = 0.012659402408087117693371847925133 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5088
x2[1] (analytic) = 0.00083367439720021459018397984488692
x2[1] (numeric) = 0.00083375844286496683286095514246934
absolute error = 8.404566475224267697529758242e-08
relative error = 0.010081353707694388504105614881871 %
h = 0.0001
x1[1] (analytic) = 0.0012821898908659736517178112409428
x1[1] (numeric) = 0.0012820237513402064442166161227696
absolute error = 1.661395257672075011951181732e-07
relative error = 0.012957482113277240094919874796839 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=34.3MB, alloc=4.4MB, time=2.01
t[1] = 0.5089
x2[1] (analytic) = 0.0008337670345538322739559478450075
x2[1] (numeric) = 0.00083385304058599727601817524084732
absolute error = 8.600603216500206222739583982e-08
relative error = 0.010315355321169041961130052025632 %
h = 0.0001
x1[1] (analytic) = 0.0012820816772876561482097310870861
x1[1] (numeric) = 0.0012819116850995168143006471372813
absolute error = 1.699921881393339090839498048e-07
relative error = 0.013259076324916026456831423380977 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.509
x2[1] (analytic) = 0.00083385969584772302873516249155556
x2[1] (numeric) = 0.0008339476852439032008245942720895
absolute error = 8.798939618017208943178053394e-08
relative error = 0.010552062489447919137308303147845 %
h = 0.0001
x1[1] (analytic) = 0.001281973474530155426595559729063
x1[1] (numeric) = 0.0012817995852555666411700909299772
absolute error = 1.738892745887854254687990858e-07
relative error = 0.013564186626600524652846850705234 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5091
x2[1] (analytic) = 0.00083395238108613432007936664709021
x2[1] (numeric) = 0.00083404237685647288770824876084143
absolute error = 8.999577033856762888211375122e-08
relative error = 0.010791475913931405212586150943462 %
h = 0.0001
x1[1] (analytic) = 0.0012818652825923894592993882610856
x1[1] (numeric) = 0.0012816874517982812271122717354078
absolute error = 1.778307941082321871165256778e-07
relative error = 0.013872814602529433019077194324105 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5092
x2[1] (analytic) = 0.00083404509027331451722845383237174
x2[1] (numeric) = 0.00083413711544150069350449799162887
absolute error = 9.202516818617627604415925713e-08
relative error = 0.011033596295857320567069132536547 %
h = 0.0001
x1[1] (analytic) = 0.0012817571014732763269426554107106
x1[1] (numeric) = 0.0012815752847175828539922391630849
absolute error = 1.818167556934729504162476257e-07
relative error = 0.014184961837503319909713105060053 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5093
x2[1] (analytic) = 0.00083413782341351289327981259343914
x2[1] (numeric) = 0.00083423190101678705342644402615374
absolute error = 9.407760327416014663143271460e-08
relative error = 0.01127842433630088583598737264795 %
h = 0.0001
x1[1] (analytic) = 0.0012816489311717342183333283450442
x1[1] (numeric) = 0.0012814630840033907823472580570643
absolute error = 1.858471683434359860702879799e-07
relative error = 0.014500629916924843331301334408416 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5094
x2[1] (analytic) = 0.00083423058051097962536370648205495
x2[1] (numeric) = 0.00083432673360013848303597219400907
absolute error = 9.615308915885767226571195412e-08
relative error = 0.011525960736174687012365170402015 %
h = 0.0001
x1[1] (analytic) = 0.0012815407716866814304550845588136
x1[1] (numeric) = 0.0012813508496456212504810268914896
absolute error = 1.899220410601799740576673240e-07
relative error = 0.014819820426798970655616335024153 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5095
x2[1] (analytic) = 0.00083432336156996579481868965658664
x2[1] (numeric) = 0.00083442161320936758021541224877771
absolute error = 9.825163940178539672259219107e-08
relative error = 0.011776206196228640597391811442618 %
h = 0.0001
x1[1] (analytic) = 0.0012814326230170363684564948441937
x1[1] (numeric) = 0.0012812385816341874735576246207144
absolute error = 1.940413828488948988702234793e-07
relative error = 0.015142534953733198411154541875315 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5096
x2[1] (analytic) = 0.0008344161665947233873670581103952
x2[1] (numeric) = 0.0008345165398622930271398203815381
absolute error = 1.0037326756963977276227114290e-07
relative error = 0.012029161417049958798490059438482 %
h = 0.0001
x1[1] (analytic) = 0.0012813244851617175456402073422847
x1[1] (numeric) = 0.0012811262799589996426951859025973
absolute error = 1.982052027179029450214396874e-07
relative error = 0.015468775084937772153278911519493 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5097
x2[1] (analytic) = 0.00083450899558950529329033653480331
x2[1] (numeric) = 0.00083461151357673959224988228385934
absolute error = 1.0251798723429895954574905603e-07
relative error = 0.012284827099063114775078763496641 %
h = 0.0001
x1[1] (analytic) = 0.0012812163581196435834521326761291
x1[1] (numeric) = 0.001281013944609964924059304613539
absolute error = 2.024135096786593928280625901e-07
relative error = 0.015798542408225906413041305889533 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5098
x2[1] (analytic) = 0.00083460184855856530760480082371625
x2[1] (numeric) = 0.00083470653437053813222543745242644
absolute error = 1.0468581197282462063662871019e-07
relative error = 0.012543203942529807932026000520327 %
h = 0.0001
x1[1] (analytic) = 0.0012811082418897332114706301651619
x1[1] (numeric) = 0.0012809015755769874579561655738064
absolute error = 2.066663127457535144645913555e-07
relative error = 0.016131838512014004724710316827975 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5099
x2[1] (analytic) = 0.00083469472550615813023703622697089
x2[1] (numeric) = 0.00083480160226152559395962492749542
absolute error = 1.0687675536746372258870052453e-07
relative error = 0.012804292647548929260789153922891 %
h = 0.0001
x1[1] (analytic) = 0.0012810001364709052673956951209852
x1[1] (numeric) = 0.0012807891728499683579254044016649
absolute error = 2.109636209369094702907193203e-07
relative error = 0.016468664985321879732032136794413 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.4MB, time=2.25
NO POLE
NO POLE
t[1] = 0.51
x2[1] (analytic) = 0.00083478762643653936619953115948893
x2[1] (numeric) = 0.00083489671726754501653365065743693
absolute error = 1.0909083100565033411949794800e-07
relative error = 0.013068093914056526728238312678237 %
h = 0.0001
x1[1] (analytic) = 0.0012808920418620786970381472243591
x1[1] (numeric) = 0.0012806767364188057098326954148149
absolute error = 2.153054432729872054518095442e-07
relative error = 0.016809023417772973373252090731818 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1 ) + diff ( x1 , t , 0 );
diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );
Iterations = 100
Total Elapsed Time = 2 Seconds
Elapsed Time(since restart) = 2 Seconds
Expected Time Remaining = 16 Minutes 31 Seconds
Optimized Time Remaining = 16 Minutes 24 Seconds
Time to Timeout = 14 Minutes 57 Seconds
Percent Done = 0.2244 %
> quit
memory used=38.6MB, alloc=4.4MB, time=2.27