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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> reached_interval := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_dump_analytic,
> glob_h,
> glob_optimal_done,
> glob_clock_sec,
> glob_max_minutes,
> hours_in_day,
> glob_subiter_method,
> glob_normmax,
> glob_iter,
> glob_max_sec,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> djd_debug,
> glob_max_opt_iter,
> glob_look_poles,
> glob_hmin,
> glob_html_log,
> glob_start,
> glob_warned2,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin_init,
> glob_reached_optimal_h,
> centuries_in_millinium,
> glob_dump,
> glob_log10normmin,
> glob_smallish_float,
> glob_display_interval,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_optimal_expect_sec,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_log10abserr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_initial_pass,
> min_in_hour,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_max_trunc_err,
> glob_next_display,
> glob_neg_h,
> glob_display_flag,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_almost_1,
> djd_debug2,
> glob_good_digits,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_relerr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> #END CONST
> array_fact_1,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_t,
> array_pole,
> array_1st_rel_error,
> array_x1_init,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_fact_2,
> array_x1_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_x2_set_initial,
> glob_last;
>
>
>
> local ret;
>
> if ((((array_t[1] >= glob_next_display) and not glob_neg_h) or ((array_t[1] <= glob_next_display) and glob_neg_h)) or (glob_next_display = 0.0)) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1
> ;
> return(ret);
>
> # End Function number 3
> end;
reached_interval := proc()
local ret;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done,
glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method,
glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec,
glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug,
glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start,
glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init,
glob_reached_optimal_h, centuries_in_millinium, glob_dump,
glob_log10normmin, glob_smallish_float, glob_display_interval,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_optimal_expect_sec, glob_last_good_h, glob_hmax,
glob_not_yet_start_msg, glob_log10abserr, glob_current_iter,
glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours,
glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done,
MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h,
glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2,
glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr,
array_const_4D0, array_const_2, array_const_1, array_const_2D0,
array_const_3D0, array_const_0D0, array_fact_1, array_type_pole,
array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t,
array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error,
array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2,
array_x1_higher_work, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last
;
if glob_next_display <= array_t[1] and not glob_neg_h or
array_t[1] <= glob_next_display and glob_neg_h or
glob_next_display = 0. then ret := true
else ret := false
end if;
return ret
end proc
> # Begin Function number 4
> display_alot := proc(iter)
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_dump_analytic,
> glob_h,
> glob_optimal_done,
> glob_clock_sec,
> glob_max_minutes,
> hours_in_day,
> glob_subiter_method,
> glob_normmax,
> glob_iter,
> glob_max_sec,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> djd_debug,
> glob_max_opt_iter,
> glob_look_poles,
> glob_hmin,
> glob_html_log,
> glob_start,
> glob_warned2,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin_init,
> glob_reached_optimal_h,
> centuries_in_millinium,
> glob_dump,
> glob_log10normmin,
> glob_smallish_float,
> glob_display_interval,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_optimal_expect_sec,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_log10abserr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_initial_pass,
> min_in_hour,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_max_trunc_err,
> glob_next_display,
> glob_neg_h,
> glob_display_flag,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_almost_1,
> djd_debug2,
> glob_good_digits,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_relerr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> #END CONST
> array_fact_1,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_t,
> array_pole,
> array_1st_rel_error,
> array_x1_init,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_fact_2,
> array_x1_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_x2_set_initial,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
>
>
>
>
>
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 1
> if (iter >= 0) then # if number 2
> ind_var := array_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_x1(ind_var);
> omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 4
> glob_good_digits := -trunc(log10(relerr/100.0));
> else
> glob_good_digits := Digits;
> fi;# end if 4
> ;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3
> ;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_x2(ind_var);
> omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 4
> glob_good_digits := -trunc(log10(relerr/100.0));
> else
> glob_good_digits := Digits;
> fi;# end if 4
> ;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3
> ;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 3
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 2
> ;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
>
> # End Function number 4
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done,
glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method,
glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec,
glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug,
glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start,
glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init,
glob_reached_optimal_h, centuries_in_millinium, glob_dump,
glob_log10normmin, glob_smallish_float, glob_display_interval,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_optimal_expect_sec, glob_last_good_h, glob_hmax,
glob_not_yet_start_msg, glob_log10abserr, glob_current_iter,
glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours,
glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done,
MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h,
glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2,
glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr,
array_const_4D0, array_const_2, array_const_1, array_const_2D0,
array_const_3D0, array_const_0D0, array_fact_1, array_type_pole,
array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t,
array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error,
array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2,
array_x1_higher_work, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last
;
if reached_interval() then
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_x1(ind_var);
omniout_float(ALWAYS, "x1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x1[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then
glob_good_digits := -trunc(log10(relerr/100.0))
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_x2(ind_var);
omniout_float(ALWAYS, "x2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x2[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x2[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then
glob_good_digits := -trunc(log10(relerr/100.0))
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # Begin Function number 5
> adjust_for_pole := proc(h_param)
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_dump_analytic,
> glob_h,
> glob_optimal_done,
> glob_clock_sec,
> glob_max_minutes,
> hours_in_day,
> glob_subiter_method,
> glob_normmax,
> glob_iter,
> glob_max_sec,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> djd_debug,
> glob_max_opt_iter,
> glob_look_poles,
> glob_hmin,
> glob_html_log,
> glob_start,
> glob_warned2,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin_init,
> glob_reached_optimal_h,
> centuries_in_millinium,
> glob_dump,
> glob_log10normmin,
> glob_smallish_float,
> glob_display_interval,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_optimal_expect_sec,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_log10abserr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_initial_pass,
> min_in_hour,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_max_trunc_err,
> glob_next_display,
> glob_neg_h,
> glob_display_flag,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_almost_1,
> djd_debug2,
> glob_good_digits,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_relerr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> #END CONST
> array_fact_1,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_t,
> array_pole,
> array_1st_rel_error,
> array_x1_init,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_fact_2,
> array_x1_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_x2_set_initial,
> glob_last;
>
> local hnew, sz2, tmp;
>
>
>
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_x1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_x1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (omniabs(array_x2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_x2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if ( not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_t[1];
> fi;# end if 1
> ;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
>
> # End Function number 5
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done,
glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method,
glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec,
glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug,
glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start,
glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init,
glob_reached_optimal_h, centuries_in_millinium, glob_dump,
glob_log10normmin, glob_smallish_float, glob_display_interval,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_optimal_expect_sec, glob_last_good_h, glob_hmax,
glob_not_yet_start_msg, glob_log10abserr, glob_current_iter,
glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours,
glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done,
MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h,
glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2,
glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr,
array_const_4D0, array_const_2, array_const_1, array_const_2D0,
array_const_3D0, array_const_0D0, array_fact_1, array_type_pole,
array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t,
array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error,
array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2,
array_x1_higher_work, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last
;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_x1_higher[1, 1]) then
tmp := omniabs(array_x1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_x2_higher[1, 1]) then
tmp := omniabs(array_x2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_t[1]
end if;
hnew := sz2;
return hnew
end proc
> # Begin Function number 6
> prog_report := proc(t_start,t_end)
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_dump_analytic,
> glob_h,
> glob_optimal_done,
> glob_clock_sec,
> glob_max_minutes,
> hours_in_day,
> glob_subiter_method,
> glob_normmax,
> glob_iter,
> glob_max_sec,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> djd_debug,
> glob_max_opt_iter,
> glob_look_poles,
> glob_hmin,
> glob_html_log,
> glob_start,
> glob_warned2,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin_init,
> glob_reached_optimal_h,
> centuries_in_millinium,
> glob_dump,
> glob_log10normmin,
> glob_smallish_float,
> glob_display_interval,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_optimal_expect_sec,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_log10abserr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_initial_pass,
> min_in_hour,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_max_trunc_err,
> glob_next_display,
> glob_neg_h,
> glob_display_flag,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_almost_1,
> djd_debug2,
> glob_good_digits,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_relerr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> #END CONST
> array_fact_1,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_t,
> array_pole,
> array_1st_rel_error,
> array_x1_init,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_fact_2,
> array_x1_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_x2_set_initial,
> 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 6
> end;
prog_report := proc(t_start, t_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done,
glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method,
glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec,
glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug,
glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start,
glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init,
glob_reached_optimal_h, centuries_in_millinium, glob_dump,
glob_log10normmin, glob_smallish_float, glob_display_interval,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_optimal_expect_sec, glob_last_good_h, glob_hmax,
glob_not_yet_start_msg, glob_log10abserr, glob_current_iter,
glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours,
glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done,
MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h,
glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2,
glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr,
array_const_4D0, array_const_2, array_const_1, array_const_2D0,
array_const_3D0, array_const_0D0, array_fact_1, array_type_pole,
array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t,
array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error,
array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2,
array_x1_higher_work, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, 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 7
> check_for_pole := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_dump_analytic,
> glob_h,
> glob_optimal_done,
> glob_clock_sec,
> glob_max_minutes,
> hours_in_day,
> glob_subiter_method,
> glob_normmax,
> glob_iter,
> glob_max_sec,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> djd_debug,
> glob_max_opt_iter,
> glob_look_poles,
> glob_hmin,
> glob_html_log,
> glob_start,
> glob_warned2,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin_init,
> glob_reached_optimal_h,
> centuries_in_millinium,
> glob_dump,
> glob_log10normmin,
> glob_smallish_float,
> glob_display_interval,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_optimal_expect_sec,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_log10abserr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_initial_pass,
> min_in_hour,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_max_trunc_err,
> glob_next_display,
> glob_neg_h,
> glob_display_flag,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_almost_1,
> djd_debug2,
> glob_good_digits,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_relerr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> #END CONST
> array_fact_1,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_t,
> array_pole,
> array_1st_rel_error,
> array_x1_init,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_fact_2,
> array_x1_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_x2_set_initial,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
>
>
>
>
>
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_x1_higher[1,m]) < glob_small_float) or (omniabs(array_x1_higher[1,m-1]) < glob_small_float) or (omniabs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1];
> rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 2 - 1;
> while ((m >= 10) and ((omniabs(array_x2_higher[1,m]) < glob_small_float) or (omniabs(array_x2_higher[1,m-1]) < glob_small_float) or (omniabs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1];
> rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_x1_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif ((omniabs(array_x1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-5]) >= (glob_large_float))) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]);
> rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]);
> rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]);
> rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]);
> rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_x2_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif ((omniabs(array_x2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-5]) >= (glob_large_float))) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]);
> rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]);
> rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]);
> rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]);
> rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * omniabs(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 (reached_interval()) 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 (reached_interval()) 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 (reached_interval()) 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 (reached_interval()) 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
> if (reached_interval()) then # if number 3
> display_pole();
> fi;# end if 3
>
> # End Function number 7
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done,
glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method,
glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec,
glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug,
glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start,
glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init,
glob_reached_optimal_h, centuries_in_millinium, glob_dump,
glob_log10normmin, glob_smallish_float, glob_display_interval,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_optimal_expect_sec, glob_last_good_h, glob_hmax,
glob_not_yet_start_msg, glob_log10abserr, glob_current_iter,
glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours,
glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done,
MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h,
glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2,
glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr,
array_const_4D0, array_const_2, array_const_1, array_const_2D0,
array_const_3D0, array_const_0D0, array_fact_1, array_type_pole,
array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t,
array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error,
array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2,
array_x1_higher_work, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last
;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_x1_higher[1, m]) < glob_small_float
or omniabs(array_x1_higher[1, m - 1]) < glob_small_float or
omniabs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (omniabs(array_x2_higher[1, m]) < glob_small_float
or omniabs(array_x2_higher[1, m - 1]) < glob_small_float or
omniabs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_x1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= omniabs(array_x1_higher[1, m]) or
glob_large_float <= omniabs(array_x1_higher[1, m - 1]) or
glob_large_float <= omniabs(array_x1_higher[1, m - 2]) or
glob_large_float <= omniabs(array_x1_higher[1, m - 3]) or
glob_large_float <= omniabs(array_x1_higher[1, m - 4]) or
glob_large_float <= omniabs(array_x1_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3];
rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4];
rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_x2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= omniabs(array_x2_higher[1, m]) or
glob_large_float <= omniabs(array_x2_higher[1, m - 1]) or
glob_large_float <= omniabs(array_x2_higher[1, m - 2]) or
glob_large_float <= omniabs(array_x2_higher[1, m - 3]) or
glob_large_float <= omniabs(array_x2_higher[1, m - 4]) or
glob_large_float <= omniabs(array_x2_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3];
rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4];
rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(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 reached_interval() 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 reached_interval() 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 reached_interval() 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 reached_interval() 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;
if reached_interval() then display_pole() end if
end proc
> # Begin Function number 8
> get_norms := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_dump_analytic,
> glob_h,
> glob_optimal_done,
> glob_clock_sec,
> glob_max_minutes,
> hours_in_day,
> glob_subiter_method,
> glob_normmax,
> glob_iter,
> glob_max_sec,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> djd_debug,
> glob_max_opt_iter,
> glob_look_poles,
> glob_hmin,
> glob_html_log,
> glob_start,
> glob_warned2,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin_init,
> glob_reached_optimal_h,
> centuries_in_millinium,
> glob_dump,
> glob_log10normmin,
> glob_smallish_float,
> glob_display_interval,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_optimal_expect_sec,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_log10abserr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_initial_pass,
> min_in_hour,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_max_trunc_err,
> glob_next_display,
> glob_neg_h,
> glob_display_flag,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_almost_1,
> djd_debug2,
> glob_good_digits,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_relerr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> #END CONST
> array_fact_1,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_t,
> array_pole,
> array_1st_rel_error,
> array_x1_init,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_fact_2,
> array_x1_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_x2_set_initial,
> glob_last;
>
> local iii;
>
>
>
> if ( not glob_initial_pass) then # if number 3
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2
> ;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_x1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_x1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_x2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_x2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 3
> ;
>
> # End Function number 8
> end;
get_norms := proc()
local iii;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done,
glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method,
glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec,
glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug,
glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start,
glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init,
glob_reached_optimal_h, centuries_in_millinium, glob_dump,
glob_log10normmin, glob_smallish_float, glob_display_interval,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_optimal_expect_sec, glob_last_good_h, glob_hmax,
glob_not_yet_start_msg, glob_log10abserr, glob_current_iter,
glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours,
glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done,
MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h,
glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2,
glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr,
array_const_4D0, array_const_2, array_const_1, array_const_2D0,
array_const_3D0, array_const_0D0, array_fact_1, array_type_pole,
array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t,
array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error,
array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2,
array_x1_higher_work, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last
;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_x1[iii]) then
array_norms[iii] := omniabs(array_x1[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_x2[iii]) then
array_norms[iii] := omniabs(array_x2[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 9
> atomall := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_dump_analytic,
> glob_h,
> glob_optimal_done,
> glob_clock_sec,
> glob_max_minutes,
> hours_in_day,
> glob_subiter_method,
> glob_normmax,
> glob_iter,
> glob_max_sec,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> djd_debug,
> glob_max_opt_iter,
> glob_look_poles,
> glob_hmin,
> glob_html_log,
> glob_start,
> glob_warned2,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin_init,
> glob_reached_optimal_h,
> centuries_in_millinium,
> glob_dump,
> glob_log10normmin,
> glob_smallish_float,
> glob_display_interval,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_optimal_expect_sec,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_log10abserr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_initial_pass,
> min_in_hour,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_max_trunc_err,
> glob_next_display,
> glob_neg_h,
> glob_display_flag,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_almost_1,
> djd_debug2,
> glob_good_digits,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_relerr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> #END CONST
> array_fact_1,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_t,
> array_pole,
> array_1st_rel_error,
> array_x1_init,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_fact_2,
> array_x1_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_x2_set_initial,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
>
>
>
>
>
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp1[1] := array_const_4D0[1] * array_x2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre diff $eq_no = 1 i = 1
> array_tmp3[1] := array_x2_higher[2,1];
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp6[1] := array_const_2D0[1] * array_x1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_x1_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1
> array_tmp9[1] := array_x2_higher[2,1];
> #emit pre mult CONST FULL $eq_no = 2 i = 1
> array_tmp11[1] := array_const_2D0[1] * array_x2[1];
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x1_higher[3,1];
> #emit pre diff $eq_no = 2 i = 1
> array_tmp15[1] := array_x1_higher[2,1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_x2_set_initial[2,3]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[1] * expt(glob_h , (2)) * factorial_3(0,2);
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp1[2] := array_const_4D0[1] * array_x2[2];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre diff $eq_no = 1 i = 2
> array_tmp3[2] := array_x2_higher[2,2];
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp6[2] := array_const_2D0[1] * array_x1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_x1_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2
> array_tmp9[2] := array_x2_higher[2,2];
> #emit pre mult CONST FULL $eq_no = 2 i = 2
> array_tmp11[2] := array_const_2D0[1] * array_x2[2];
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x1_higher[3,2];
> #emit pre diff $eq_no = 2 i = 2
> array_tmp15[2] := array_x1_higher[2,2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_x2_set_initial[2,4]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[2] * expt(glob_h , (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp1[3] := array_const_4D0[1] * array_x2[3];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre diff $eq_no = 1 i = 3
> array_tmp3[3] := array_x2_higher[2,3];
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp6[3] := array_const_2D0[1] * array_x1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_x1_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3
> array_tmp9[3] := array_x2_higher[2,3];
> #emit pre mult CONST FULL $eq_no = 2 i = 3
> array_tmp11[3] := array_const_2D0[1] * array_x2[3];
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x1_higher[3,3];
> #emit pre diff $eq_no = 2 i = 3
> array_tmp15[3] := array_x1_higher[2,3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_x2_set_initial[2,5]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[3] * expt(glob_h , (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp1[4] := array_const_4D0[1] * array_x2[4];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre diff $eq_no = 1 i = 4
> array_tmp3[4] := array_x2_higher[2,4];
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp6[4] := array_const_2D0[1] * array_x1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_x1_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4
> array_tmp9[4] := array_x2_higher[2,4];
> #emit pre mult CONST FULL $eq_no = 2 i = 4
> array_tmp11[4] := array_const_2D0[1] * array_x2[4];
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x1_higher[3,4];
> #emit pre diff $eq_no = 2 i = 4
> array_tmp15[4] := array_x1_higher[2,4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_x2_set_initial[2,6]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[4] * expt(glob_h , (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp1[5] := array_const_4D0[1] * array_x2[5];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre diff $eq_no = 1 i = 5
> array_tmp3[5] := array_x2_higher[2,5];
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp6[5] := array_const_2D0[1] * array_x1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_x1_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp7[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5
> array_tmp9[5] := array_x2_higher[2,5];
> #emit pre mult CONST FULL $eq_no = 2 i = 5
> array_tmp11[5] := array_const_2D0[1] * array_x2[5];
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x1_higher[3,5];
> #emit pre diff $eq_no = 2 i = 5
> array_tmp15[5] := array_x1_higher[2,5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_x2_set_initial[2,7]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[5] * expt(glob_h , (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult CONST FULL $eq_no = 1 i = 1
> array_tmp1[kkk] := array_const_4D0[1] * array_x2[kkk];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit diff $eq_no = 1
> array_tmp3[kkk] := array_x2_higher[2,kkk];
> #emit mult CONST FULL $eq_no = 1 i = 1
> array_tmp6[kkk] := array_const_2D0[1] * array_x1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_x1_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp7[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x1[kkk + order_d] := temporary;
> array_x1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> #emit diff $eq_no = 2
> array_tmp9[kkk] := array_x2_higher[2,kkk];
> #emit mult CONST FULL $eq_no = 2 i = 1
> array_tmp11[kkk] := array_const_2D0[1] * array_x2[kkk];
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x1_higher[3,kkk];
> #emit diff $eq_no = 2
> array_tmp15[kkk] := array_x1_higher[2,kkk];
> #emit assign $eq_no = 2
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_x2_set_initial[2,kkk + order_d]) then # if number 2
> temporary := array_tmp17[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x2[kkk + order_d] := temporary;
> array_x2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
>
> #BOTTOM ATOMALL ???
> # End Function number 9
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done,
glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method,
glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec,
glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug,
glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start,
glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init,
glob_reached_optimal_h, centuries_in_millinium, glob_dump,
glob_log10normmin, glob_smallish_float, glob_display_interval,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_optimal_expect_sec, glob_last_good_h, glob_hmax,
glob_not_yet_start_msg, glob_log10abserr, glob_current_iter,
glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours,
glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done,
MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h,
glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2,
glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr,
array_const_4D0, array_const_2, array_const_1, array_const_2D0,
array_const_3D0, array_const_0D0, array_fact_1, array_type_pole,
array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t,
array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error,
array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2,
array_x1_higher_work, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last
;
array_tmp1[1] := array_const_4D0[1]*array_x2[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_x2_higher[2, 1];
array_tmp6[1] := array_const_2D0[1]*array_x1[1];
if not array_x1_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp7[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp9[1] := array_x2_higher[2, 1];
array_tmp11[1] := array_const_2D0[1]*array_x2[1];
array_tmp13[1] := array_x1_higher[3, 1];
array_tmp15[1] := array_x1_higher[2, 1];
if not array_x2_set_initial[2, 3] then
if 1 <= glob_max_terms then
temporary := array_tmp17[1]*expt(glob_h, 2)*factorial_3(0, 2);
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_4D0[1]*array_x2[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_x2_higher[2, 2];
array_tmp6[2] := array_const_2D0[1]*array_x1[2];
if not array_x1_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp7[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp9[2] := array_x2_higher[2, 2];
array_tmp11[2] := array_const_2D0[1]*array_x2[2];
array_tmp13[2] := array_x1_higher[3, 2];
array_tmp15[2] := array_x1_higher[2, 2];
if not array_x2_set_initial[2, 4] then
if 2 <= glob_max_terms then
temporary := array_tmp17[2]*expt(glob_h, 2)*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_const_4D0[1]*array_x2[3];
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := array_x2_higher[2, 3];
array_tmp6[3] := array_const_2D0[1]*array_x1[3];
if not array_x1_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp7[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp9[3] := array_x2_higher[2, 3];
array_tmp11[3] := array_const_2D0[1]*array_x2[3];
array_tmp13[3] := array_x1_higher[3, 3];
array_tmp15[3] := array_x1_higher[2, 3];
if not array_x2_set_initial[2, 5] then
if 3 <= glob_max_terms then
temporary := array_tmp17[3]*expt(glob_h, 2)*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_const_4D0[1]*array_x2[4];
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := array_x2_higher[2, 4];
array_tmp6[4] := array_const_2D0[1]*array_x1[4];
if not array_x1_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp7[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp9[4] := array_x2_higher[2, 4];
array_tmp11[4] := array_const_2D0[1]*array_x2[4];
array_tmp13[4] := array_x1_higher[3, 4];
array_tmp15[4] := array_x1_higher[2, 4];
if not array_x2_set_initial[2, 6] then
if 4 <= glob_max_terms then
temporary := array_tmp17[4]*expt(glob_h, 2)*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_const_4D0[1]*array_x2[5];
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := array_x2_higher[2, 5];
array_tmp6[5] := array_const_2D0[1]*array_x1[5];
if not array_x1_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp7[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
array_tmp9[5] := array_x2_higher[2, 5];
array_tmp11[5] := array_const_2D0[1]*array_x2[5];
array_tmp13[5] := array_x1_higher[3, 5];
array_tmp15[5] := array_x1_higher[2, 5];
if not array_x2_set_initial[2, 7] then
if 5 <= glob_max_terms then
temporary := array_tmp17[5]*expt(glob_h, 2)*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_const_4D0[1]*array_x2[kkk];
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := array_x2_higher[2, kkk];
array_tmp6[kkk] := array_const_2D0[1]*array_x1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_x1_set_initial[1, kkk + order_d] then
temporary := array_tmp7[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x1[kkk + order_d] := temporary;
array_x1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
array_tmp9[kkk] := array_x2_higher[2, kkk];
array_tmp11[kkk] := array_const_2D0[1]*array_x2[kkk];
array_tmp13[kkk] := array_x1_higher[3, kkk];
array_tmp15[kkk] := array_x1_higher[2, kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
if not array_x2_set_initial[2, kkk + order_d] then
temporary := array_tmp17[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x2[kkk + order_d] := temporary;
array_x2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> fprintf(fd,"
");
> if (secs >= 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_minute;
> sec_int := floor(seconds);
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_minute, years_in_century;
secs := secs_in;
fprintf(fd, "");
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*min_in_hour*
hours_in_day*days_in_year*years_in_century*
centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_minute;
sec_int := floor(seconds);
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs >= 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_minute;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_minute, years_in_century;
secs := convfloat(secs_in);
if 0. <= secs then
sec_in_millinium := convfloat(sec_in_minute*min_in_hour*
hours_in_day*days_in_year*years_in_century*
centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_minute;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
>
>
>
>
>
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats;
>
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
>
>
>
>
>
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
>
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
>
> local good_digits;
>
>
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 11
> if (rel_error <> 0.0) then # if number 12
> good_digits := -trunc(log10(rel_error/100.0));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 12
> ;
> else
> fprintf(file,"Unknown");
> fi;# end if 11
> ;
> fprintf(file," | ");
>
> # End Function number 9
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if rel_error <> 0. then
good_digits := -trunc(log10(rel_error/100.0));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 10
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 10
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 11
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 12
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 11
> fprintf(file,"NA");
> elif (pole = 1) then # if number 12
> fprintf(file,"Real");
> elif (pole = 2) then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 12
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 13
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 13
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 14
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 14
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 15
> not_reached_end := proc(x,x_end)
> global neg_h;
> local ret;
>
>
>
> if ((glob_neg_h and (x > x_end)) or (( not glob_neg_h) and (x < x_end))) then # if number 13
> ret := true;
> else
> ret := false;
> fi;# end if 13
> ;
>
>
> ret;
>
> # End Function number 15
> end;
not_reached_end := proc(x, x_end)
local ret;
global neg_h;
if glob_neg_h and x_end < x or not glob_neg_h and x < x_end then
ret := true
else ret := false
end if;
ret
end proc
> # Begin Function number 16
> 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 16
> 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 17
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
>
>
>
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
>
> # End Function number 17
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # Begin Function number 18
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
>
>
>
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr;
>
> # End Function number 18
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 19
> factorial_2 := proc(nnn)
> local ret;
>
>
>
> ret := nnn!;
>
> # End Function number 19
> end;
factorial_2 := proc(nnn) local ret; ret := nnn! end proc
> # Begin Function number 20
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
>
>
>
> if (nnn <= glob_max_terms) then # if number 13
> if (array_fact_1[nnn] = 0) then # if number 14
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 20
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 21
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
>
>
>
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13
> if (array_fact_2[mmm,nnn] = 0) then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 13
> ;
> ret;
>
> # End Function number 21
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # Begin Function number 22
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 22
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 23
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 23
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_x1 := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return(2.0 * c1 + 6.0 * c3 * exp(-t));
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x1p := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return( - 6.0 * c3 * exp(-t));
> end;
exact_soln_x1p := proc(t)
local c1, c2, c3;
c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return -6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return 2.0*c2*exp(2.0*t) - c3*exp(-t)
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> t_start,t_end
> ,it, log10norm, max_terms, opt_iter, tmp,subiter;
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_dump_analytic,
> glob_h,
> glob_optimal_done,
> glob_clock_sec,
> glob_max_minutes,
> hours_in_day,
> glob_subiter_method,
> glob_normmax,
> glob_iter,
> glob_max_sec,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_disp_incr,
> days_in_year,
> sec_in_minute,
> djd_debug,
> glob_max_opt_iter,
> glob_look_poles,
> glob_hmin,
> glob_html_log,
> glob_start,
> glob_warned2,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin_init,
> glob_reached_optimal_h,
> centuries_in_millinium,
> glob_dump,
> glob_log10normmin,
> glob_smallish_float,
> glob_display_interval,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_optimal_expect_sec,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_log10abserr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_initial_pass,
> min_in_hour,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_max_trunc_err,
> glob_next_display,
> glob_neg_h,
> glob_display_flag,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_almost_1,
> djd_debug2,
> glob_good_digits,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_relerr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_4D0,
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> #END CONST
> array_fact_1,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x2_init,
> array_t,
> array_pole,
> array_1st_rel_error,
> array_x1_init,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_fact_2,
> array_x1_higher,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_poles,
> array_x2_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_x1_set_initial,
> array_x2_set_initial,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_max_terms := 30;
> ALWAYS := 1;
> INFO := 2;
> glob_iolevel := 5;
> glob_log10relerr := 0.0;
> glob_dump_analytic := false;
> glob_h := 0.1;
> glob_optimal_done := false;
> glob_clock_sec := 0.0;
> glob_max_minutes := 0.0;
> hours_in_day := 24;
> glob_subiter_method := 3;
> glob_normmax := 0.0;
> glob_iter := 0;
> glob_max_sec := 10000.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_abserr := 0.1e-10;
> glob_disp_incr := 0.1;
> days_in_year := 365;
> sec_in_minute := 60;
> djd_debug := true;
> glob_max_opt_iter := 10;
> glob_look_poles := false;
> glob_hmin := 0.00000000001;
> glob_html_log := true;
> glob_start := 0;
> glob_warned2 := false;
> glob_log10_relerr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_hmin_init := 0.001;
> glob_reached_optimal_h := false;
> centuries_in_millinium := 10;
> glob_dump := false;
> glob_log10normmin := 0.1;
> glob_smallish_float := 0.1e-100;
> glob_display_interval := 0.0;
> glob_not_yet_finished := true;
> glob_clock_start_sec := 0.0;
> years_in_century := 100;
> glob_optimal_expect_sec := 0.1;
> glob_last_good_h := 0.1;
> glob_hmax := 1.0;
> glob_not_yet_start_msg := true;
> glob_log10abserr := 0.0;
> glob_current_iter := 0;
> glob_curr_iter_when_opt := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_hours := 0.0;
> glob_log10_abserr := 0.1e-10;
> glob_initial_pass := true;
> min_in_hour := 60;
> glob_percent_done := 0.0;
> MAX_UNCHANGED := 10;
> glob_max_trunc_err := 0.1e-10;
> glob_next_display := 0.0;
> glob_neg_h := false;
> glob_display_flag := true;
> glob_orig_start_sec := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_small_float := 0.1e-50;
> glob_optimal_start := 0.0;
> glob_almost_1 := 0.9990;
> djd_debug2 := true;
> glob_good_digits := 0;
> glob_warned := false;
> glob_no_eqs := 0;
> glob_max_iter := 1000;
> glob_relerr := 0.1e-10;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest6postode.ode#################");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#");
> omniout_str(ALWAYS,"# was complicated.ode");
> omniout_str(ALWAYS,"#");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x1_init[1 + 1] := exact_soln_x1p(t_start);");
> omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1 + 1] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.005 ;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10000;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return(2.0 * c1 + 6.0 * c3 * exp(-t));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x1p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return( - 6.0 * c3 * exp(-t));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_tmp10:= Array(0..(max_terms + 1),[]);
> array_tmp11:= Array(0..(max_terms + 1),[]);
> array_tmp12:= Array(0..(max_terms + 1),[]);
> array_tmp13:= Array(0..(max_terms + 1),[]);
> array_tmp14:= Array(0..(max_terms + 1),[]);
> array_tmp15:= Array(0..(max_terms + 1),[]);
> array_tmp16:= Array(0..(max_terms + 1),[]);
> array_tmp17:= Array(0..(max_terms + 1),[]);
> array_x2_init:= Array(0..(max_terms + 1),[]);
> array_t:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_x1_init:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_x1:= Array(0..(max_terms + 1),[]);
> array_x2:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_tmp6:= Array(0..(max_terms + 1),[]);
> array_tmp7:= Array(0..(max_terms + 1),[]);
> array_tmp8:= Array(0..(max_terms + 1),[]);
> array_tmp9:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_x1_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_x2_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_x2_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x2_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[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_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_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_x1_init[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_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_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_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_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_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_x2_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_t := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_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_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_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0[1] := 2.0;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0[1] := 3.0;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #
> # was complicated.ode
> #
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[0 + 1] := exact_soln_x1(t_start);
> array_x1_init[1 + 1] := exact_soln_x1p(t_start);
> array_x2_init[0 + 1] := exact_soln_x2(t_start);
> array_x2_init[1 + 1] := exact_soln_x2p(t_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.005 ;
> glob_display_interval := 0.1;
> glob_look_poles := true;
> glob_max_iter := 10000;
> glob_max_minutes := 10;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1
> ;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_x1_set_initial[1,1] := true;
> array_x1_set_initial[1,2] := true;
> array_x1_set_initial[1,3] := false;
> array_x1_set_initial[1,4] := false;
> array_x1_set_initial[1,5] := false;
> array_x1_set_initial[1,6] := false;
> array_x1_set_initial[1,7] := false;
> array_x1_set_initial[1,8] := false;
> array_x1_set_initial[1,9] := false;
> array_x1_set_initial[1,10] := false;
> array_x1_set_initial[1,11] := false;
> array_x1_set_initial[1,12] := false;
> array_x1_set_initial[1,13] := false;
> array_x1_set_initial[1,14] := false;
> array_x1_set_initial[1,15] := false;
> array_x1_set_initial[1,16] := false;
> array_x1_set_initial[1,17] := false;
> array_x1_set_initial[1,18] := false;
> array_x1_set_initial[1,19] := false;
> array_x1_set_initial[1,20] := false;
> array_x1_set_initial[1,21] := false;
> array_x1_set_initial[1,22] := false;
> array_x1_set_initial[1,23] := false;
> array_x1_set_initial[1,24] := false;
> array_x1_set_initial[1,25] := false;
> array_x1_set_initial[1,26] := false;
> array_x1_set_initial[1,27] := false;
> array_x1_set_initial[1,28] := false;
> array_x1_set_initial[1,29] := false;
> array_x1_set_initial[1,30] := false;
> array_x2_set_initial[2,1] := true;
> array_x2_set_initial[2,2] := true;
> array_x2_set_initial[2,3] := false;
> array_x2_set_initial[2,4] := false;
> array_x2_set_initial[2,5] := false;
> array_x2_set_initial[2,6] := false;
> array_x2_set_initial[2,7] := false;
> array_x2_set_initial[2,8] := false;
> array_x2_set_initial[2,9] := false;
> array_x2_set_initial[2,10] := false;
> array_x2_set_initial[2,11] := false;
> array_x2_set_initial[2,12] := false;
> array_x2_set_initial[2,13] := false;
> array_x2_set_initial[2,14] := false;
> array_x2_set_initial[2,15] := false;
> array_x2_set_initial[2,16] := false;
> array_x2_set_initial[2,17] := false;
> array_x2_set_initial[2,18] := false;
> array_x2_set_initial[2,19] := false;
> array_x2_set_initial[2,20] := false;
> array_x2_set_initial[2,21] := false;
> array_x2_set_initial[2,22] := false;
> array_x2_set_initial[2,23] := false;
> array_x2_set_initial[2,24] := false;
> array_x2_set_initial[2,25] := false;
> array_x2_set_initial[2,26] := false;
> array_x2_set_initial[2,27] := false;
> array_x2_set_initial[2,28] := false;
> array_x2_set_initial[2,29] := false;
> array_x2_set_initial[2,30] := false;
> if (glob_html_log) then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_t[1] := t_start;
> array_t[2] := glob_h;
> glob_next_display := t_start;
> order_diff := 2;
> #Start Series array_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x1[term_no] := array_x1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x1_higher[r_order,term_no] := array_x1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 2;
> #Start Series array_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x2[term_no] := array_x2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x2_higher[r_order,term_no] := array_x2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> if (omniabs(array_x1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_x1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> if (omniabs(array_x2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_x2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and not_reached_end(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
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3
> ;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> if (glob_subiter_method = 1 ) then # if number 3
> atomall();
> elif (glob_subiter_method = 2 ) then # if number 4
> subiter := 1;
> while (subiter <= 3) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while (subiter <= 3 + glob_max_terms) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> fi;# end if 4
> ;
> if (glob_look_poles) then # if number 4
> #left paren 0004C
> check_for_pole();
> fi;# end if 4
> ;#was right paren 0004C
> if (reached_interval()) then # if number 4
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 4
> ;
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> #Jump Series array_x1
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[3,iii] := array_x1_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_x2
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 4
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 4
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 4
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if (glob_html_log) then # if number 4
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-09-21T01:00:34-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest6")
> ;
> logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
> ;
> logitem_float(html_log_file,t_start)
> ;
> logitem_float(html_log_file,t_end)
> ;
> logitem_float(html_log_file,array_t[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 5
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 5
> ;
> log_revs(html_log_file," 130 | ")
> ;
> logitem_str(html_log_file,"mtest6 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest6 maple results")
> ;
> logitem_str(html_log_file,"c c++ Maple and Maxima")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logditto(html_log_file)
> ;
> if (glob_percent_done < 100.0) then # if number 5
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 5
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 4
> ;
> if (glob_html_log) then # if number 4
> fclose(html_log_file);
> fi;# end if 4
> ;
> ;;
> #END OUTFILEMAIN
>
> # End Function number 9
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter,
tmp, subiter;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done,
glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method,
glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec,
glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug,
glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start,
glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init,
glob_reached_optimal_h, centuries_in_millinium, glob_dump,
glob_log10normmin, glob_smallish_float, glob_display_interval,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_optimal_expect_sec, glob_last_good_h, glob_hmax,
glob_not_yet_start_msg, glob_log10abserr, glob_current_iter,
glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours,
glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done,
MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h,
glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2,
glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr,
array_const_4D0, array_const_2, array_const_1, array_const_2D0,
array_const_3D0, array_const_0D0, array_fact_1, array_type_pole,
array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t,
array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error,
array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2,
array_x1_higher_work, array_complex_pole, array_poles,
array_x2_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last
;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_max_terms := 30;
ALWAYS := 1;
INFO := 2;
glob_iolevel := 5;
glob_log10relerr := 0.;
glob_dump_analytic := false;
glob_h := 0.1;
glob_optimal_done := false;
glob_clock_sec := 0.;
glob_max_minutes := 0.;
hours_in_day := 24;
glob_subiter_method := 3;
glob_normmax := 0.;
glob_iter := 0;
glob_max_sec := 10000.0;
glob_optimal_clock_start_sec := 0.;
glob_abserr := 0.1*10^(-10);
glob_disp_incr := 0.1;
days_in_year := 365;
sec_in_minute := 60;
djd_debug := true;
glob_max_opt_iter := 10;
glob_look_poles := false;
glob_hmin := 0.1*10^(-10);
glob_html_log := true;
glob_start := 0;
glob_warned2 := false;
glob_log10_relerr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_hmin_init := 0.001;
glob_reached_optimal_h := false;
centuries_in_millinium := 10;
glob_dump := false;
glob_log10normmin := 0.1;
glob_smallish_float := 0.1*10^(-100);
glob_display_interval := 0.;
glob_not_yet_finished := true;
glob_clock_start_sec := 0.;
years_in_century := 100;
glob_optimal_expect_sec := 0.1;
glob_last_good_h := 0.1;
glob_hmax := 1.0;
glob_not_yet_start_msg := true;
glob_log10abserr := 0.;
glob_current_iter := 0;
glob_curr_iter_when_opt := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_hours := 0.;
glob_log10_abserr := 0.1*10^(-10);
glob_initial_pass := true;
min_in_hour := 60;
glob_percent_done := 0.;
MAX_UNCHANGED := 10;
glob_max_trunc_err := 0.1*10^(-10);
glob_next_display := 0.;
glob_neg_h := false;
glob_display_flag := true;
glob_orig_start_sec := 0.;
glob_unchanged_h_cnt := 0;
glob_small_float := 0.1*10^(-50);
glob_optimal_start := 0.;
glob_almost_1 := 0.9990;
djd_debug2 := true;
glob_good_digits := 0;
glob_warned := false;
glob_no_eqs := 0;
glob_max_iter := 1000;
glob_relerr := 0.1*10^(-10);
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest6postode.ode#################");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
diff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#");
omniout_str(ALWAYS, "# was complicated.ode");
omniout_str(ALWAYS, "#");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x1_init[1 + 1] := exact_soln_x1p(t_start);")
;
omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[1 + 1] := exact_soln_x2p(t_start);")
;
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.005 ;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10000;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "return(2.0 * c1 + 6.0 * c3 * exp(-t));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x1p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "return( - 6.0 * c3 * exp(-t));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS,
"return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_fact_1 := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_tmp10 := Array(0 .. max_terms + 1, []);
array_tmp11 := Array(0 .. max_terms + 1, []);
array_tmp12 := Array(0 .. max_terms + 1, []);
array_tmp13 := Array(0 .. max_terms + 1, []);
array_tmp14 := Array(0 .. max_terms + 1, []);
array_tmp15 := Array(0 .. max_terms + 1, []);
array_tmp16 := Array(0 .. max_terms + 1, []);
array_tmp17 := Array(0 .. max_terms + 1, []);
array_x2_init := Array(0 .. max_terms + 1, []);
array_t := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_x1_init := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_x1 := Array(0 .. max_terms + 1, []);
array_x2 := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_tmp6 := Array(0 .. max_terms + 1, []);
array_tmp7 := Array(0 .. max_terms + 1, []);
array_tmp8 := Array(0 .. max_terms + 1, []);
array_tmp9 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_x1_higher := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 3, 0 .. 4, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_x2_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 3, 0 .. 4, []);
array_x2_higher := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x2_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_fact_1[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_tmp10[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp15[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp16[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp17[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_t[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[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_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_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_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp17 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp17[term] := 0.; term := term + 1
end do;
array_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[term] := 0.; term := term + 1
end do;
array_tmp15 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp15[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1
end do;
array_tmp9 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_x2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1
end do;
array_x1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
end do;
array_const_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_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_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x1_init[2] := exact_soln_x1p(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_h := 0.005;
glob_display_interval := 0.1;
glob_look_poles := true;
glob_max_iter := 10000;
glob_max_minutes := 10;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_x1_set_initial[1, 1] := true;
array_x1_set_initial[1, 2] := true;
array_x1_set_initial[1, 3] := false;
array_x1_set_initial[1, 4] := false;
array_x1_set_initial[1, 5] := false;
array_x1_set_initial[1, 6] := false;
array_x1_set_initial[1, 7] := false;
array_x1_set_initial[1, 8] := false;
array_x1_set_initial[1, 9] := false;
array_x1_set_initial[1, 10] := false;
array_x1_set_initial[1, 11] := false;
array_x1_set_initial[1, 12] := false;
array_x1_set_initial[1, 13] := false;
array_x1_set_initial[1, 14] := false;
array_x1_set_initial[1, 15] := false;
array_x1_set_initial[1, 16] := false;
array_x1_set_initial[1, 17] := false;
array_x1_set_initial[1, 18] := false;
array_x1_set_initial[1, 19] := false;
array_x1_set_initial[1, 20] := false;
array_x1_set_initial[1, 21] := false;
array_x1_set_initial[1, 22] := false;
array_x1_set_initial[1, 23] := false;
array_x1_set_initial[1, 24] := false;
array_x1_set_initial[1, 25] := false;
array_x1_set_initial[1, 26] := false;
array_x1_set_initial[1, 27] := false;
array_x1_set_initial[1, 28] := false;
array_x1_set_initial[1, 29] := false;
array_x1_set_initial[1, 30] := false;
array_x2_set_initial[2, 1] := true;
array_x2_set_initial[2, 2] := true;
array_x2_set_initial[2, 3] := false;
array_x2_set_initial[2, 4] := false;
array_x2_set_initial[2, 5] := false;
array_x2_set_initial[2, 6] := false;
array_x2_set_initial[2, 7] := false;
array_x2_set_initial[2, 8] := false;
array_x2_set_initial[2, 9] := false;
array_x2_set_initial[2, 10] := false;
array_x2_set_initial[2, 11] := false;
array_x2_set_initial[2, 12] := false;
array_x2_set_initial[2, 13] := false;
array_x2_set_initial[2, 14] := false;
array_x2_set_initial[2, 15] := false;
array_x2_set_initial[2, 16] := false;
array_x2_set_initial[2, 17] := false;
array_x2_set_initial[2, 18] := false;
array_x2_set_initial[2, 19] := false;
array_x2_set_initial[2, 20] := false;
array_x2_set_initial[2, 21] := false;
array_x2_set_initial[2, 22] := false;
array_x2_set_initial[2, 23] := false;
array_x2_set_initial[2, 24] := false;
array_x2_set_initial[2, 25] := false;
array_x2_set_initial[2, 26] := false;
array_x2_set_initial[2, 27] := false;
array_x2_set_initial[2, 28] := false;
array_x2_set_initial[2, 29] := false;
array_x2_set_initial[2, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
glob_next_display := t_start;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x1[term_no] := array_x1_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x1_higher[r_order, term_no] := array_x1_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x2_higher[r_order, term_no] := array_x2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
if glob_small_float < omniabs(array_x1_higher[1, 1]) then
tmp := omniabs(array_x1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
if glob_small_float < omniabs(array_x2_higher[1, 1]) then
tmp := omniabs(array_x2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
not_reached_end(array_t[1], t_end) and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 3 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
if glob_look_poles then check_for_pole() end if;
if reached_interval() then
glob_next_display := glob_next_display + glob_display_interval
end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[3, iii] := array_x1_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
term_no := glob_max_terms;
while 1 <= term_no do
array_x1[term_no] := array_x1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x1_higher[ord, term_no] :=
array_x1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1)
;
term_no := glob_max_terms;
while 1 <= term_no do
array_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
ff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-09-21T01:00:34-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest6")
;
logitem_str(html_log_file,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
;
logitem_float(html_log_file, t_start);
logitem_float(html_log_file, t_end);
logitem_float(html_log_file, array_t[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 130 | ");
logitem_str(html_log_file,
"mtest6 diffeq.mxt");
logitem_str(html_log_file,
"mtest6 maple results");
logitem_str(html_log_file, "c c++ Maple and Maxima");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \
2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_good_digits(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest6postode.ode#################
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
#
# was complicated.ode
#
t_start := 0.5;
t_end := 5.0;
array_x1_init[0 + 1] := exact_soln_x1(t_start);
array_x1_init[1 + 1] := exact_soln_x1p(t_start);
array_x2_init[0 + 1] := exact_soln_x2(t_start);
array_x2_init[1 + 1] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.005 ;
glob_display_interval := 0.1;
glob_look_poles := true;
glob_max_iter := 10000;
glob_max_minutes := 10;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return(2.0 * c1 + 6.0 * c3 * exp(-t));
end;
exact_soln_x1p := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return( - 6.0 * c3 * exp(-t));
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1] = 0.5
x1[1] (analytic) = 2.001091755187482740162486839163
x1[1] (numeric) = 2.001091755187482740162486839163
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
x2[1] (analytic) = 1.0007256155636055990741531973548
x2[1] (numeric) = 1.0007256155636055990741531973548
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
t[1] = 0.5
x1[1] (analytic) = 2.001091755187482740162486839163
x1[1] (numeric) = 2.001091755187482740162486839163
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
x2[1] (analytic) = 1.0007256155636055990741531973548
x2[1] (numeric) = 1.0007256155636055990741531973548
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3.8MB, alloc=2.8MB, time=0.18
memory used=7.6MB, alloc=3.9MB, time=0.43
memory used=11.4MB, alloc=3.9MB, time=0.68
memory used=15.2MB, alloc=3.9MB, time=0.92
memory used=19.0MB, alloc=3.9MB, time=1.17
t[1] = 0.6
x1[1] (analytic) = 2.000987860944969247578731226051
x1[1] (numeric) = 2.000982579668734466146238155247
absolute error = 5.2812762347814324930708040e-06
relative error = 0.00026393344696690676499951456627037 %
Correct digits = 5
h = 0.005
x2[1] (analytic) = 1.0008286668753755174276946911611
x2[1] (numeric) = 1.0008161509169525818808594948668
absolute error = 1.25159584229355468351962943e-05
relative error = 0.0012505595450229095203804419740368 %
Correct digits = 4
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=22.8MB, alloc=3.9MB, time=1.42
memory used=26.7MB, alloc=3.9MB, time=1.68
memory used=30.5MB, alloc=3.9MB, time=1.93
memory used=34.3MB, alloc=3.9MB, time=2.18
memory used=38.1MB, alloc=3.9MB, time=2.43
t[1] = 0.7
x1[1] (analytic) = 2.0008938535468245371264686401681
x1[1] (numeric) = 2.000873404149986192129989471331
absolute error = 2.04493968383449964791688371e-05
relative error = 0.0010220130769104011137157287405776 %
Correct digits = 4
h = 0.005
x2[1] (analytic) = 1.000960015584506357771856261807
x2[1] (numeric) = 1.0009066862702995646875657923788
absolute error = 5.33293142067930842904694282e-05
relative error = 0.0053278166336795838279499877335098 %
Correct digits = 4
h = 0.005
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=3.9MB, time=2.68
NO POLE
NO POLE
memory used=45.7MB, alloc=3.9MB, time=2.93
memory used=49.5MB, alloc=3.9MB, time=3.18
memory used=53.4MB, alloc=4.0MB, time=3.44
memory used=57.2MB, alloc=4.0MB, time=3.68
memory used=61.0MB, alloc=4.0MB, time=3.93
t[1] = 0.8
x1[1] (analytic) = 2.000808792135410998864574184293
x1[1] (numeric) = 2.000764228631237918113740787415
absolute error = 4.45635041730807508333968780e-05
relative error = 0.0022272745076014628076063407733946 %
Correct digits = 4
h = 0.005
x2[1] (analytic) = 1.0011254051741141894381598879868
x2[1] (numeric) = 1.0009972216236465474942720898908
absolute error = 0.000128183550467641943887798096
relative error = 0.01280394542033906912022378773212 %
Correct digits = 3
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=64.8MB, alloc=4.0MB, time=4.18
memory used=68.6MB, alloc=4.0MB, time=4.43
memory used=72.4MB, alloc=4.0MB, time=4.68
memory used=76.2MB, alloc=4.0MB, time=4.94
memory used=80.1MB, alloc=4.0MB, time=5.19
t[1] = 0.9
x1[1] (analytic) = 2.0007318253875330784013902176314
x1[1] (numeric) = 2.000655053112489644097492103499
absolute error = 7.67722750434343038981141324e-05
relative error = 0.0038372096684453873344705727302837 %
Correct digits = 4
h = 0.005
x2[1] (analytic) = 1.0013319003908047689503112410625
x2[1] (numeric) = 1.0010877569769935303009783874028
absolute error = 0.0002441434138112386493328536597
relative error = 0.024381867162721286488706584612248 %
Correct digits = 3
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=83.9MB, alloc=4.0MB, time=5.44
memory used=87.7MB, alloc=4.0MB, time=5.69
memory used=91.5MB, alloc=4.0MB, time=5.94
memory used=95.3MB, alloc=4.0MB, time=6.19
memory used=99.1MB, alloc=4.0MB, time=6.45
t[1] = 1
x1[1] (analytic) = 2.0006621829941085961788719427863
x1[1] (numeric) = 2.000545877593741370081243419583
absolute error = 0.0001163054003672260976285232033
relative error = 0.0058133452691732407916387672706403 %
Correct digits = 4
h = 0.005
x2[1] (analytic) = 1.0015881750521375627419247426231
x2[1] (numeric) = 1.0011782923303405131076846849148
absolute error = 0.0004098827217970496342400577083
relative error = 0.040923278849185018987870044617463 %
Correct digits = 3
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=102.9MB, alloc=4.0MB, time=6.70
memory used=106.8MB, alloc=4.0MB, time=6.95
memory used=110.6MB, alloc=4.0MB, time=7.21
memory used=114.4MB, alloc=4.0MB, time=7.47
memory used=118.2MB, alloc=4.0MB, time=7.72
t[1] = 1.1
x1[1] (analytic) = 2.0005991679506565431959199244316
x1[1] (numeric) = 2.000436702074993096064994735667
absolute error = 0.0001624658756634471309251887646
relative error = 0.0081208609033798340766463529804479 %
Correct digits = 4
h = 0.005
x2[1] (analytic) = 1.0019048640249962480512810095053
x2[1] (numeric) = 1.0012688276836874959143909824268
absolute error = 0.0006360363413087521368900270785
relative error = 0.063482708203808444798380797217593 %
Correct digits = 3
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=122.0MB, alloc=4.0MB, time=7.97
memory used=125.8MB, alloc=4.0MB, time=8.22
memory used=129.7MB, alloc=4.0MB, time=8.47
memory used=133.5MB, alloc=4.0MB, time=8.72
memory used=137.3MB, alloc=4.0MB, time=8.98
t[1] = 1.2
x1[1] (analytic) = 2.0005421495814419637739609596927
x1[1] (numeric) = 2.000327526556244822048746051751
absolute error = 0.0002146230251971417252149079417
relative error = 0.010728243103602973267566694838174 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.002294993539701980959441081236
x2[1] (numeric) = 1.0013593630370344787210972799388
absolute error = 0.0009356305026675022383438012972
relative error = 0.093348815338609282343202966865883 %
Correct digits = 3
h = 0.005
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.0MB, time=9.23
NO POLE
NO POLE
memory used=144.9MB, alloc=4.0MB, time=9.48
memory used=148.7MB, alloc=4.0MB, time=9.73
memory used=152.5MB, alloc=4.0MB, time=9.96
memory used=156.4MB, alloc=4.0MB, time=10.19
memory used=160.2MB, alloc=4.0MB, time=10.43
t[1] = 1.3
x1[1] (analytic) = 2.0004905572274612226856201997016
x1[1] (numeric) = 2.000218351037496548032497367835
absolute error = 0.0002722061899646746531228318666
relative error = 0.013606971999004745526694615434472 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0027745071449105418604868650168
x2[1] (numeric) = 1.0014498983903814615278035774508
absolute error = 0.001324608754529080332683287566
relative error = 0.13209437865552575847506281741196 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=164.0MB, alloc=4.0MB, time=10.67
memory used=167.8MB, alloc=4.0MB, time=10.90
memory used=171.6MB, alloc=4.0MB, time=11.15
memory used=175.4MB, alloc=4.0MB, time=11.40
memory used=179.2MB, alloc=4.0MB, time=11.64
t[1] = 1.4
x1[1] (analytic) = 2.0004438745350948916584917502317
x1[1] (numeric) = 2.000109175518748274016248683919
absolute error = 0.0003346990163466176422430663127
relative error = 0.01673123753219030052612551904698 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0033629084434018919173815615742
x2[1] (numeric) = 1.0015404337437284443345098749628
absolute error = 0.0018224746996734475828716866114
relative error = 0.18163664256842024633704111397444 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=183.1MB, alloc=4.0MB, time=11.89
memory used=186.9MB, alloc=4.0MB, time=12.13
memory used=190.7MB, alloc=4.0MB, time=12.39
memory used=194.5MB, alloc=4.0MB, time=12.64
memory used=198.3MB, alloc=4.0MB, time=12.89
t[1] = 1.5
x1[1] (analytic) = 2.0004016342882671736920799048474
x1[1] (numeric) = 2.000000000000000000000000000003
absolute error = 0.0004016342882671736920799048444
relative error = 0.020077682470504136984688765962524 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0040840464326820624968656900721
x2[1] (numeric) = 1.0016309690970754271412161724748
absolute error = 0.0024530773356066353556495175973
relative error = 0.24430996033867367915243917425418 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=202.1MB, alloc=4.0MB, time=13.14
memory used=205.9MB, alloc=4.0MB, time=13.39
memory used=209.8MB, alloc=4.0MB, time=13.65
memory used=213.6MB, alloc=4.0MB, time=13.90
memory used=217.4MB, alloc=4.0MB, time=14.15
t[1] = 1.6
x1[1] (analytic) = 2.0003634137323903797352733226818
x1[1] (numeric) = 1.999890824481251725983751316087
absolute error = 0.0004725892511386537515220065948
relative error = 0.023625169701382919736142239192746 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0049670749948202663512576065259
x2[1] (numeric) = 1.0017215044504224099479224699868
absolute error = 0.0032455705443978564033351365391
relative error = 0.32295292305119394130996941978113 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=221.2MB, alloc=4.0MB, time=14.40
memory used=225.0MB, alloc=4.0MB, time=14.65
memory used=228.8MB, alloc=4.0MB, time=14.90
memory used=232.6MB, alloc=4.0MB, time=15.45
memory used=236.5MB, alloc=4.0MB, time=16.04
t[1] = 1.7
x1[1] (analytic) = 2.000328830343294922370403021508
x1[1] (numeric) = 1.999781648962503451967502632171
absolute error = 0.000547181380791470402900389337
relative error = 0.027354571532999579263746454508052 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.006047625066695223064699720858
x2[1] (numeric) = 1.0018120398037693927546287674988
absolute error = 0.0042355852629258303100709533592
relative error = 0.42101240114204684395524683252874 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.0MB, time=16.65
NO POLE
NO POLE
memory used=244.1MB, alloc=4.0MB, time=17.27
memory used=247.9MB, alloc=4.0MB, time=17.89
memory used=251.7MB, alloc=4.0MB, time=18.50
memory used=255.5MB, alloc=4.0MB, time=19.11
memory used=259.4MB, alloc=4.0MB, time=19.72
t[1] = 1.8
x1[1] (analytic) = 2.0002975379987988557689342484968
x1[1] (numeric) = 1.999672473443755177951253948255
absolute error = 0.0006250645550436778176803002418
relative error = 0.031248578932363469128233079563575 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0073692365552020735120079945959
x2[1] (numeric) = 1.0019025751571163755613350650108
absolute error = 0.0054666613980856979506729295851
relative error = 0.5426670975956624282453648109687 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=263.2MB, alloc=4.0MB, time=20.33
memory used=267.0MB, alloc=4.0MB, time=20.94
memory used=270.8MB, alloc=4.0MB, time=21.56
memory used=274.6MB, alloc=4.0MB, time=22.16
memory used=278.4MB, alloc=4.0MB, time=22.77
t[1] = 1.9
x1[1] (analytic) = 2.0002692235146007430947538217244
x1[1] (numeric) = 1.999563297925006903935005264339
absolute error = 0.0007059255895938391597485573854
relative error = 0.035291528824979010846167288836246 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0089851074844269551233038693665
x2[1] (numeric) = 1.0019931105104633583680413625228
absolute error = 0.0069919969739635967552625068437
relative error = 0.69297325818770955365598220149544 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=282.2MB, alloc=4.0MB, time=23.38
memory used=286.1MB, alloc=4.0MB, time=24.00
memory used=289.9MB, alloc=4.0MB, time=24.60
memory used=293.7MB, alloc=4.0MB, time=25.20
memory used=297.5MB, alloc=4.0MB, time=25.80
t[1] = 2
x1[1] (analytic) = 2.000243603509825902845409199091
x1[1] (numeric) = 1.999454122406258629918756580423
absolute error = 0.000789481103567272926652618668
relative error = 0.039469247754722027122054277820973 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0109602305915998316231902520891
x2[1] (numeric) = 1.0020836458638103411747476600348
absolute error = 0.0088765847277894904484425920543
relative error = 0.87803500663869209054597749059994 %
Correct digits = 2
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=301.3MB, alloc=4.0MB, time=26.40
memory used=305.1MB, alloc=4.0MB, time=27.05
memory used=308.9MB, alloc=4.0MB, time=27.66
memory used=312.8MB, alloc=4.0MB, time=28.27
memory used=316.6MB, alloc=4.0MB, time=28.87
t[1] = 2.1
x1[1] (analytic) = 2.0002204215708553674383935652769
x1[1] (numeric) = 1.999344946887510355902507896507
absolute error = 0.0008754746833450115358856687699
relative error = 0.043768910361262348186930318301609 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0133740031366609229020699411436
x2[1] (numeric) = 1.0021741812171573239814539575468
absolute error = 0.0111998219195035989206159835968
relative error = 1.1052012272702066468448288880726 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=320.4MB, alloc=4.0MB, time=29.49
memory used=324.2MB, alloc=4.0MB, time=30.11
memory used=328.0MB, alloc=4.0MB, time=30.72
memory used=331.8MB, alloc=4.0MB, time=31.34
memory used=335.6MB, alloc=4.0MB, time=31.92
t[1] = 2.2
x1[1] (analytic) = 2.0001994456850522009900014599665
x1[1] (numeric) = 1.999235771368762081886259212591
absolute error = 0.0009636743162901191037422473755
relative error = 0.048178911276523647452037070237065 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.016323414680502323653880405673
x2[1] (numeric) = 1.0022647165705043067881602550588
absolute error = 0.0140586981099980168657201506142
relative error = 1.3832897980036793334604848709813 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.0MB, time=32.52
NO POLE
NO POLE
memory used=343.3MB, alloc=4.0MB, time=33.12
memory used=347.1MB, alloc=4.0MB, time=33.73
memory used=350.9MB, alloc=4.0MB, time=34.34
memory used=354.7MB, alloc=4.0MB, time=34.93
memory used=358.5MB, alloc=4.0MB, time=35.53
t[1] = 2.3
x1[1] (analytic) = 2.0001804659187010467207138932488
x1[1] (numeric) = 1.999126595850013807870010528675
absolute error = 0.0010538700686872388507033645738
relative error = 0.052688749172599621432191138355332 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0199269407815036028672097929056
x2[1] (numeric) = 1.0023552519238512895948665525708
absolute error = 0.0175716888576523132723432403348
relative error = 1.7228379950615160993171030558086 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=362.4MB, alloc=4.0MB, time=36.13
memory used=366.2MB, alloc=4.0MB, time=36.72
memory used=370.0MB, alloc=4.0MB, time=37.31
memory used=373.8MB, alloc=4.0MB, time=37.89
memory used=377.6MB, alloc=4.0MB, time=38.46
t[1] = 2.4
x1[1] (analytic) = 2.0001632923159209425060753099961
x1[1] (numeric) = 1.999017420331265533853761844759
absolute error = 0.0011458719846554086523134652371
relative error = 0.057288921812410751440394329043843 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0243292988897337999024221749256
x2[1] (numeric) = 1.0024457872771982724015728500828
absolute error = 0.0218835116125355275008493248428
relative error = 2.136374663524217582901032842887 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=381.4MB, alloc=4.0MB, time=39.04
memory used=385.2MB, alloc=4.0MB, time=39.62
memory used=389.1MB, alloc=4.0MB, time=40.19
memory used=392.9MB, alloc=4.0MB, time=40.79
memory used=396.7MB, alloc=4.0MB, time=41.38
t[1] = 2.5
x1[1] (analytic) = 2.000147752997523017831305151614
x1[1] (numeric) = 1.998908244812517259837513160843
absolute error = 0.001239508185005757993791990771
relative error = 0.061970831062263678688701106703575 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0297072573201024903227739746104
x2[1] (numeric) = 1.0025363226305452552082791475948
absolute error = 0.0271709346895572351144948270156
relative error = 2.6387047868606674663348114391756 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=400.5MB, alloc=4.0MB, time=41.95
memory used=404.3MB, alloc=4.0MB, time=42.53
memory used=408.1MB, alloc=4.0MB, time=43.13
memory used=411.9MB, alloc=4.0MB, time=43.75
memory used=415.8MB, alloc=4.0MB, time=44.35
t[1] = 2.6
x1[1] (analytic) = 2.0001336924407858009847707790263
x1[1] (numeric) = 1.998799069293768985821264476927
absolute error = 0.0013346231470168151635063020993
relative error = 0.066726696923352129503652399618679 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0362767304484945360381252899358
x2[1] (numeric) = 1.0026268579838922380149854451068
absolute error = 0.033649872464602298023139844829
relative error = 3.2471898167624423179099928646102 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=419.6MB, alloc=4.0MB, time=44.95
memory used=423.4MB, alloc=4.0MB, time=45.57
memory used=427.2MB, alloc=4.0MB, time=46.16
memory used=431.0MB, alloc=4.0MB, time=46.72
memory used=434.8MB, alloc=4.0MB, time=47.30
t[1] = 2.7
x1[1] (analytic) = 2.0001209699229315495772277930615
x1[1] (numeric) = 1.998689893775020711805015793011
absolute error = 0.0014310761479108377722120000505
relative error = 0.071549479728017643229046230056891 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0443014448946593423345569015332
x2[1] (numeric) = 1.0027173933372392208216917426188
absolute error = 0.0415840515574201215128651589144
relative error = 3.9819969378300327139155802587732 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
memory used=438.6MB, alloc=4.0MB, time=47.86
NO POLE
NO POLE
memory used=442.5MB, alloc=4.0MB, time=48.43
memory used=446.3MB, alloc=4.0MB, time=48.98
memory used=450.1MB, alloc=4.0MB, time=49.54
memory used=453.9MB, alloc=4.0MB, time=50.10
memory used=457.7MB, alloc=4.0MB, time=50.66
t[1] = 2.8
x1[1] (analytic) = 2.0001094581127253923369921184987
x1[1] (numeric) = 1.998580718256272437788767109095
absolute error = 0.0015287398564529545482250094037
relative error = 0.07643280972709621393060546797345 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0541035245040180910200828957228
x2[1] (numeric) = 1.0028079286905862036283980401308
absolute error = 0.051295595813431887391684855592
relative error = 4.8662768524152065823460385923252 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=461.5MB, alloc=4.0MB, time=51.22
memory used=465.3MB, alloc=4.0MB, time=51.80
memory used=469.2MB, alloc=4.0MB, time=52.37
memory used=473.0MB, alloc=4.0MB, time=52.95
memory used=476.8MB, alloc=4.0MB, time=53.51
t[1] = 2.9
x1[1] (analytic) = 2.0000990417961015330122539037555
x1[1] (numeric) = 1.998471542737524163772518425179
absolute error = 0.0016274990585773692397354785765
relative error = 0.081370923367668074962056176034187 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0660764189479466529927580297123
x2[1] (numeric) = 1.0028984640439331864351043376428
absolute error = 0.0631779549040134665576536920695
relative error = 5.9262125848689519281865263419286 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=480.6MB, alloc=4.0MB, time=54.06
memory used=484.4MB, alloc=4.0MB, time=54.62
memory used=488.2MB, alloc=4.0MB, time=55.18
memory used=492.1MB, alloc=4.0MB, time=55.75
memory used=495.9MB, alloc=4.0MB, time=56.32
t[1] = 3
x1[1] (analytic) = 2.0000896167230621550973628163482
x1[1] (numeric) = 1.998362367218775889756269741263
absolute error = 0.0017272495042862653410930750852
relative error = 0.086358605626691026535317531639289 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.0807006948190573837045712388334
x2[1] (numeric) = 1.0029889993972801692418106351548
absolute error = 0.0777116954217772144627606036786
relative error = 7.1908619837418119056855429617648 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=499.7MB, alloc=4.0MB, time=56.88
memory used=503.5MB, alloc=4.0MB, time=57.44
memory used=507.3MB, alloc=4.0MB, time=58.00
memory used=511.1MB, alloc=4.0MB, time=58.56
memory used=514.9MB, alloc=4.0MB, time=59.14
t[1] = 3.1
x1[1] (analytic) = 2.0000810885643084040509230031659
x1[1] (numeric) = 1.998253191700027615740021057347
absolute error = 0.0018278968642807883109019458189
relative error = 0.091391137825961006216578247803942 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.098563322979369318255832918741
x2[1] (numeric) = 1.0030795347506271520485169326668
absolute error = 0.0954837882287421662073159860742
relative error = 8.6916963484439323866934564733202 %
Correct digits = 1
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=518.8MB, alloc=4.0MB, time=59.70
memory used=522.6MB, alloc=4.0MB, time=60.28
memory used=526.4MB, alloc=4.0MB, time=60.84
memory used=530.2MB, alloc=4.0MB, time=61.40
memory used=534.0MB, alloc=4.0MB, time=61.95
t[1] = 3.2
x1[1] (analytic) = 2.0000733719671610591872989426719
x1[1] (numeric) = 1.998144016181279341723772373431
absolute error = 0.0019293557858817174635265692409
relative error = 0.096464250408179290615720820478411 %
Correct digits = 3
h = 0.005
x2[1] (analytic) = 1.120381236235609921186409479002
x2[1] (numeric) = 1.0031700701039741348552232301788
absolute error = 0.1172111661316357863311862488232
relative error = 10.461721630170797705469540673281 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
memory used=537.8MB, alloc=4.0MB, time=62.54
NO POLE
NO POLE
memory used=541.6MB, alloc=4.0MB, time=63.11
memory used=545.5MB, alloc=4.0MB, time=63.67
memory used=549.3MB, alloc=4.0MB, time=64.22
memory used=553.1MB, alloc=4.0MB, time=64.77
memory used=556.9MB, alloc=4.0MB, time=65.32
t[1] = 3.3
x1[1] (analytic) = 2.0000663897013222320098020866685
x1[1] (numeric) = 1.998034840662531067707523689515
absolute error = 0.0020315490387911643022783971535
relative error = 0.10157408020313483183354197336803 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 1.1470301027986149509830540232634
x2[1] (numeric) = 1.0032606054573211176619295276908
absolute error = 0.1437694973412938333211244955726
relative error = 12.534064885525987458295749631505 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=560.7MB, alloc=4.0MB, time=65.88
memory used=564.5MB, alloc=4.0MB, time=66.46
memory used=568.3MB, alloc=4.0MB, time=67.03
memory used=572.2MB, alloc=4.0MB, time=67.60
memory used=576.0MB, alloc=4.0MB, time=68.16
t[1] = 3.4
x1[1] (analytic) = 2.0000600718859285869430683202366
x1[1] (numeric) = 1.997925665143782793691275005599
absolute error = 0.0021344067421457932517933146376
relative error = 0.10671713175760687811796106862931 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 1.1795794703110716373394135141758
x2[1] (numeric) = 1.0033511408106681004686358252028
absolute error = 0.176228329500403536870777688973
relative error = 14.939928502988413036655673760769 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=579.8MB, alloc=4.0MB, time=68.72
memory used=583.6MB, alloc=4.0MB, time=69.31
memory used=587.4MB, alloc=4.0MB, time=69.87
memory used=591.2MB, alloc=4.0MB, time=70.46
memory used=595.0MB, alloc=4.0MB, time=71.06
t[1] = 3.5
x1[1] (analytic) = 2.0000543552901601733013316153263
x1[1] (numeric) = 1.997816489625034519675026321683
absolute error = 0.0022378656651256536263052936433
relative error = 0.11189024234298835869466151052165 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 1.2193356909007184154029659835453
x2[1] (numeric) = 1.0034416761640150832753421227148
absolute error = 0.2158940147367033321276238608305
relative error = 17.705871840528450688779234498993 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=598.9MB, alloc=4.0MB, time=71.65
memory used=602.7MB, alloc=4.0MB, time=72.25
memory used=606.5MB, alloc=4.0MB, time=72.81
memory used=610.3MB, alloc=4.0MB, time=73.38
memory used=614.1MB, alloc=4.0MB, time=73.96
t[1] = 3.6
x1[1] (analytic) = 2.0000491827004051266094428135124
x1[1] (numeric) = 1.997707314106286245658777637767
absolute error = 0.0023418685941188809506651757454
relative error = 0.11709055029121642537939789673816 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 1.2678943499956177537057107719784
x2[1] (numeric) = 1.0035322115173620660820484202268
absolute error = 0.2643621384782556876236623517516
relative error = 20.850486357886949120754590759501 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=617.9MB, alloc=4.0MB, time=74.53
memory used=621.8MB, alloc=4.0MB, time=75.10
memory used=625.6MB, alloc=4.0MB, time=75.66
memory used=629.4MB, alloc=4.0MB, time=76.21
memory used=633.2MB, alloc=4.0MB, time=76.76
t[1] = 3.7
x1[1] (analytic) = 2.0000445023476466109041649632894
x1[1] (numeric) = 1.997598138587537971642528953851
absolute error = 0.0024463637601086392616360094384
relative error = 0.12231546634272909234916049763024 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 1.3272043030571264098306275940663
x2[1] (numeric) = 1.0036227468707090488887547177388
absolute error = 0.3235815561864173609418728763275
relative error = 24.38068920068062411259078777179 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
memory used=637.0MB, alloc=4.0MB, time=77.31
NO POLE
NO POLE
memory used=640.8MB, alloc=4.0MB, time=77.87
memory used=644.6MB, alloc=4.0MB, time=78.42
memory used=648.5MB, alloc=4.0MB, time=78.97
memory used=652.3MB, alloc=4.0MB, time=79.53
memory used=656.1MB, alloc=4.0MB, time=80.08
t[1] = 3.8
x1[1] (analytic) = 2.0000402673893410980724014499806
x1[1] (numeric) = 1.997488963068789697626280269935
absolute error = 0.0025513043205514004461211800456
relative error = 0.1275626477201694576060874431041 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 1.3996458902523804415291985419666
x2[1] (numeric) = 1.0037132822240560316954610152508
absolute error = 0.3959326080283244098337375267158
relative error = 28.288055627908205420443702432971 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=659.9MB, alloc=4.0MB, time=80.64
memory used=663.7MB, alloc=4.0MB, time=81.25
memory used=667.5MB, alloc=4.0MB, time=81.84
memory used=671.3MB, alloc=4.0MB, time=82.42
memory used=675.2MB, alloc=4.0MB, time=82.98
t[1] = 3.9
x1[1] (analytic) = 2.0000364354406024478992496495787
x1[1] (numeric) = 1.997379787550041423610031586019
absolute error = 0.0026566478905610242892180635597
relative error = 0.13282997466872508096502290107137 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 1.4881264680983335567662847164884
x2[1] (numeric) = 1.0038038175774030145021673127628
absolute error = 0.4843226505209305422641174037256
relative error = 32.545799090573470025824939871073 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=679.0MB, alloc=4.0MB, time=83.53
memory used=682.8MB, alloc=4.0MB, time=84.10
memory used=686.6MB, alloc=4.0MB, time=84.66
memory used=690.4MB, alloc=4.0MB, time=85.21
memory used=694.2MB, alloc=4.0MB, time=85.79
t[1] = 4
x1[1] (analytic) = 2.0000329681499997215245286924383
x1[1] (numeric) = 1.997270612031293149593782902103
absolute error = 0.0027623561187065719307457903353
relative error = 0.13811552922858614706199093428871 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 1.596197092100012275202806535297
x2[1] (numeric) = 1.0038943529307499973088736102748
absolute error = 0.5923027391692622778939329250222
relative error = 37.107118043299292320514900252767 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=698.0MB, alloc=4.0MB, time=86.34
memory used=701.9MB, alloc=4.0MB, time=86.91
memory used=705.7MB, alloc=4.0MB, time=87.47
memory used=709.5MB, alloc=4.0MB, time=88.02
memory used=713.3MB, alloc=4.0MB, time=88.59
t[1] = 4.1
x1[1] (analytic) = 2.0000298308157231702455755706566
x1[1] (numeric) = 1.997161436512544875577534218187
absolute error = 0.0028683943031782946680413524696
relative error = 0.1434175760272737667208851732164 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 1.7281950332690914726879769619009
x2[1] (numeric) = 1.0039848882840969801155799077868
absolute error = 0.7242101449849944925723970541141
relative error = 41.90557958120402440358726434631 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=717.1MB, alloc=4.0MB, time=89.15
memory used=720.9MB, alloc=4.0MB, time=89.70
memory used=724.7MB, alloc=4.0MB, time=90.25
memory used=728.6MB, alloc=4.0MB, time=90.83
memory used=732.4MB, alloc=4.0MB, time=91.39
t[1] = 4.2
x1[1] (analytic) = 2.0000269920382768598711815718484
x1[1] (numeric) = 1.997052260993796601561285534271
absolute error = 0.0029747310444802583098960375774
relative error = 0.14873454489974840282379155229707 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 1.8894178482130173604315585987732
x2[1] (numeric) = 1.0040754236374439629222862052988
absolute error = 0.8853424245755733975092723934744
relative error = 46.857947563738576182677864661969 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
memory used=736.2MB, alloc=4.0MB, time=91.97
NO POLE
NO POLE
memory used=740.0MB, alloc=4.0MB, time=92.52
memory used=743.8MB, alloc=4.0MB, time=93.07
memory used=747.6MB, alloc=4.0MB, time=93.65
memory used=751.5MB, alloc=4.0MB, time=94.21
memory used=755.3MB, alloc=4.0MB, time=94.79
t[1] = 4.3
x1[1] (analytic) = 2.0000244234062219616771630150341
x1[1] (numeric) = 1.996943085475048327545036850355
absolute error = 0.0030813379311736341321261646791
relative error = 0.15406501516245675392310017884966 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 2.0863359888402997245931410071143
x2[1] (numeric) = 1.0041659589907909457289925028108
absolute error = 1.0821700298495087788641485043035
relative error = 51.869403376923886199088643976764 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=759.1MB, alloc=4.0MB, time=95.34
memory used=762.9MB, alloc=4.0MB, time=95.89
memory used=766.7MB, alloc=4.0MB, time=96.45
memory used=770.5MB, alloc=4.0MB, time=97.02
memory used=774.3MB, alloc=4.0MB, time=97.58
t[1] = 4.4
x1[1] (analytic) = 2.0000220992118255231941220908952
x1[1] (numeric) = 1.996833909956300053528788166439
absolute error = 0.0031881892555254696653339244562
relative error = 0.15940770138399373095454761444332 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 2.3268524844575479522378282673268
x2[1] (numeric) = 1.0042564943441379285356988003228
absolute error = 1.322595990113410023702129467004
relative error = 56.840560325496646477238051995811 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=778.2MB, alloc=4.0MB, time=98.12
memory used=782.0MB, alloc=4.0MB, time=98.70
memory used=785.8MB, alloc=4.0MB, time=99.30
memory used=789.6MB, alloc=4.0MB, time=99.89
memory used=793.4MB, alloc=4.0MB, time=100.48
t[1] = 4.5
x1[1] (analytic) = 2.0000199961937688361516930576417
x1[1] (numeric) = 1.996724734437551779512539482523
absolute error = 0.0032952617562170566391535751187
relative error = 0.16476144051000779661457789148857 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 2.6206201182140382742339481808269
x2[1] (numeric) = 1.0043470296974849113424050978348
absolute error = 1.6162730885165533628915430829921
relative error = 61.675214857850099026818244640629 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=797.2MB, alloc=4.0MB, time=101.04
memory used=801.0MB, alloc=4.0MB, time=101.62
memory used=804.9MB, alloc=4.0MB, time=102.18
memory used=808.7MB, alloc=4.0MB, time=102.73
memory used=812.5MB, alloc=4.0MB, time=103.29
t[1] = 4.6
x1[1] (analytic) = 2.0000180933043403404469558395698
x1[1] (numeric) = 1.996615558918803505496290798607
absolute error = 0.0034025343855368349506650409628
relative error = 0.17012518021351096837388683204131 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 2.9794288272995065674453606895232
x2[1] (numeric) = 1.0044375650508318941491113953468
absolute error = 1.9749912622486746732962492941764
relative error = 66.287579825787159785623929877997 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=816.3MB, alloc=4.0MB, time=103.85
memory used=820.1MB, alloc=4.0MB, time=104.40
memory used=823.9MB, alloc=4.0MB, time=104.95
memory used=827.7MB, alloc=4.0MB, time=105.50
memory used=831.6MB, alloc=4.0MB, time=106.07
t[1] = 4.7
x1[1] (analytic) = 2.0000163714987830524707656973337
x1[1] (numeric) = 1.996506383400055231480042114691
absolute error = 0.0035099880987278209907235826427
relative error = 0.17549796835400338166248471057802 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 3.4176788746265273882567947609929
x2[1] (numeric) = 1.0045281004041788769558176928588
absolute error = 2.4131507742223485113009770681341
relative error = 70.60788513918088995493815735887 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
memory used=835.4MB, alloc=4.0MB, time=106.65
NO POLE
NO POLE
memory used=839.2MB, alloc=4.0MB, time=107.21
memory used=843.0MB, alloc=4.0MB, time=107.78
memory used=846.8MB, alloc=4.0MB, time=108.33
memory used=850.6MB, alloc=4.0MB, time=108.89
memory used=854.5MB, alloc=4.0MB, time=109.45
t[1] = 4.8
x1[1] (analytic) = 2.0000148135446882360519144516482
x1[1] (numeric) = 1.996397207881306957463793430775
absolute error = 0.0036176056633812785881210208732
relative error = 0.18087894343990802540665211652891 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 3.952958782039569229119504631582
x2[1] (numeric) = 1.0046186357575258597625239903708
absolute error = 2.9483401462820433693569806412112
relative error = 74.585653654623166297717865271655 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=858.3MB, alloc=4.0MB, time=110.00
memory used=862.1MB, alloc=4.0MB, time=110.55
memory used=865.9MB, alloc=4.0MB, time=111.11
memory used=869.7MB, alloc=4.0MB, time=111.69
memory used=873.5MB, alloc=4.0MB, time=112.26
t[1] = 4.9
x1[1] (analytic) = 2.0000134038495276638129328248836
x1[1] (numeric) = 1.996288032362558683447544746859
absolute error = 0.0037253714869689803653880780246
relative error = 0.18626732599884421386466464257326 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 4.6067512195406235265012085377755
x2[1] (numeric) = 1.0047091711108728425692302878828
absolute error = 3.6020420484297506839319782498927
relative error = 78.190505125408952927741856407738 %
Correct digits = 0
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=877.3MB, alloc=4.0MB, time=112.81
memory used=881.2MB, alloc=4.0MB, time=113.36
memory used=885.0MB, alloc=4.0MB, time=113.92
memory used=888.8MB, alloc=4.0MB, time=114.48
memory used=892.6MB, alloc=4.0MB, time=115.03
t[1] = 5
x1[1] (analytic) = 2.0000121283045983538407739448872
x1[1] (numeric) = 1.996178856843810409431296062943
absolute error = 0.0038332714607879444094778819442
relative error = 0.19166241076934828773912839087652 %
Correct digits = 2
h = 0.005
x2[1] (analytic) = 5.4052951803454430290317091198713
x2[1] (numeric) = 1.0047997064642198253759365853948
absolute error = 4.4004954738812232036557725344765
relative error = 81.4108263667479336270907071395 %
Correct digits = 0
h = 0.005
Finished!
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
Iterations = 900
Total Elapsed Time = 1 Minutes 55 Seconds
Elapsed Time(since restart) = 1 Minutes 55 Seconds
Time to Timeout = 8 Minutes 4 Seconds
Percent Done = 100.1 %
> quit
memory used=894.2MB, alloc=4.0MB, time=115.26