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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_normmax,
> glob_warned,
> glob_max_iter,
> glob_look_poles,
> glob_optimal_done,
> sec_in_minute,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_h,
> glob_almost_1,
> days_in_year,
> hours_in_day,
> glob_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_finished,
> glob_current_iter,
> glob_dump_analytic,
> glob_display_interval,
> glob_hmin,
> glob_max_opt_iter,
> glob_good_digits,
> glob_iter,
> glob_orig_start_sec,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_optimal_expect_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> glob_curr_iter_when_opt,
> glob_start,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_clock_start_sec,
> djd_debug,
> glob_log10relerr,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_clock_sec,
> glob_html_log,
> glob_neg_h,
> glob_hmin_init,
> glob_initial_pass,
> glob_log10normmin,
> glob_subiter_method,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_abserr,
> glob_next_display,
> centuries_in_millinium,
> min_in_hour,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_fact_1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_1st_rel_error,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_y1,
> array_x,
> array_y2,
> array_norms,
> array_type_pole,
> array_poles,
> array_fact_2,
> array_y2_set_initial,
> array_y2_higher,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_complex_pole,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> array_y2_higher_work2,
> array_y2_higher_work,
> glob_last;
>
>
>
> local ret;
>
> if ((((array_x[1] >= glob_next_display) and not glob_neg_h) or ((array_x[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 glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL,
glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles,
glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h,
glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr,
glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter,
glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter,
glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec,
glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start,
glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug,
glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr,
glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init,
glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float,
glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h,
years_in_century, djd_debug2, glob_abserr, glob_next_display,
centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0,
array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1,
array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2,
array_y2_set_initial, array_y2_higher, array_y1_higher_work2,
array_y1_higher_work, array_complex_pole, array_y1_set_initial,
array_real_pole, array_y1_higher, array_y2_higher_work2,
array_y2_higher_work, glob_last;
if glob_next_display <= array_x[1] and not glob_neg_h or
array_x[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
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_normmax,
> glob_warned,
> glob_max_iter,
> glob_look_poles,
> glob_optimal_done,
> sec_in_minute,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_h,
> glob_almost_1,
> days_in_year,
> hours_in_day,
> glob_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_finished,
> glob_current_iter,
> glob_dump_analytic,
> glob_display_interval,
> glob_hmin,
> glob_max_opt_iter,
> glob_good_digits,
> glob_iter,
> glob_orig_start_sec,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_optimal_expect_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> glob_curr_iter_when_opt,
> glob_start,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_clock_start_sec,
> djd_debug,
> glob_log10relerr,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_clock_sec,
> glob_html_log,
> glob_neg_h,
> glob_hmin_init,
> glob_initial_pass,
> glob_log10normmin,
> glob_subiter_method,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_abserr,
> glob_next_display,
> centuries_in_millinium,
> min_in_hour,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_fact_1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_1st_rel_error,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_y1,
> array_x,
> array_y2,
> array_norms,
> array_type_pole,
> array_poles,
> array_fact_2,
> array_y2_set_initial,
> array_y2_higher,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_complex_pole,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> array_y2_higher_work2,
> array_y2_higher_work,
> 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_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y1(ind_var);
> omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y1[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_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[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 glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL,
glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles,
glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h,
glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr,
glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter,
glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter,
glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec,
glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start,
glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug,
glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr,
glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init,
glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float,
glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h,
years_in_century, djd_debug2, glob_abserr, glob_next_display,
centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0,
array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1,
array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2,
array_y2_set_initial, array_y2_higher, array_y1_higher_work2,
array_y1_higher_work, array_complex_pole, array_y1_set_initial,
array_real_pole, array_y1_higher, array_y2_higher_work2,
array_y2_higher_work, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y1(ind_var);
omniout_float(ALWAYS, "y1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y1[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_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y2[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
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_normmax,
> glob_warned,
> glob_max_iter,
> glob_look_poles,
> glob_optimal_done,
> sec_in_minute,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_h,
> glob_almost_1,
> days_in_year,
> hours_in_day,
> glob_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_finished,
> glob_current_iter,
> glob_dump_analytic,
> glob_display_interval,
> glob_hmin,
> glob_max_opt_iter,
> glob_good_digits,
> glob_iter,
> glob_orig_start_sec,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_optimal_expect_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> glob_curr_iter_when_opt,
> glob_start,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_clock_start_sec,
> djd_debug,
> glob_log10relerr,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_clock_sec,
> glob_html_log,
> glob_neg_h,
> glob_hmin_init,
> glob_initial_pass,
> glob_log10normmin,
> glob_subiter_method,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_abserr,
> glob_next_display,
> centuries_in_millinium,
> min_in_hour,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_fact_1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_1st_rel_error,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_y1,
> array_x,
> array_y2,
> array_norms,
> array_type_pole,
> array_poles,
> array_fact_2,
> array_y2_set_initial,
> array_y2_higher,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_complex_pole,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> array_y2_higher_work2,
> array_y2_higher_work,
> glob_last;
>
> local hnew, sz2, tmp;
>
>
>
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y1_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_y2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y2_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_x[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 glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL,
glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles,
glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h,
glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr,
glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter,
glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter,
glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec,
glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start,
glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug,
glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr,
glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init,
glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float,
glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h,
years_in_century, djd_debug2, glob_abserr, glob_next_display,
centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0,
array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1,
array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2,
array_y2_set_initial, array_y2_higher, array_y1_higher_work2,
array_y1_higher_work, array_complex_pole, array_y1_set_initial,
array_real_pole, array_y1_higher, array_y2_higher_work2,
array_y2_higher_work, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_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_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # Begin Function number 6
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_normmax,
> glob_warned,
> glob_max_iter,
> glob_look_poles,
> glob_optimal_done,
> sec_in_minute,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_h,
> glob_almost_1,
> days_in_year,
> hours_in_day,
> glob_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_finished,
> glob_current_iter,
> glob_dump_analytic,
> glob_display_interval,
> glob_hmin,
> glob_max_opt_iter,
> glob_good_digits,
> glob_iter,
> glob_orig_start_sec,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_optimal_expect_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> glob_curr_iter_when_opt,
> glob_start,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_clock_start_sec,
> djd_debug,
> glob_log10relerr,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_clock_sec,
> glob_html_log,
> glob_neg_h,
> glob_hmin_init,
> glob_initial_pass,
> glob_log10normmin,
> glob_subiter_method,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_abserr,
> glob_next_display,
> centuries_in_millinium,
> min_in_hour,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_fact_1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_1st_rel_error,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_y1,
> array_x,
> array_y2,
> array_norms,
> array_type_pole,
> array_poles,
> array_fact_2,
> array_y2_set_initial,
> array_y2_higher,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_complex_pole,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> array_y2_higher_work2,
> array_y2_higher_work,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
>
>
>
>
>
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[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(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[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(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL,
glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles,
glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h,
glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr,
glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter,
glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter,
glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec,
glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start,
glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug,
glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr,
glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init,
glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float,
glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h,
years_in_century, djd_debug2, glob_abserr, glob_next_display,
centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0,
array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1,
array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2,
array_y2_set_initial, array_y2_higher, array_y1_higher_work2,
array_y1_higher_work, array_complex_pole, array_y1_set_initial,
array_real_pole, array_y1_higher, array_y2_higher_work2,
array_y2_higher_work, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[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(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[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
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_normmax,
> glob_warned,
> glob_max_iter,
> glob_look_poles,
> glob_optimal_done,
> sec_in_minute,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_h,
> glob_almost_1,
> days_in_year,
> hours_in_day,
> glob_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_finished,
> glob_current_iter,
> glob_dump_analytic,
> glob_display_interval,
> glob_hmin,
> glob_max_opt_iter,
> glob_good_digits,
> glob_iter,
> glob_orig_start_sec,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_optimal_expect_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> glob_curr_iter_when_opt,
> glob_start,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_clock_start_sec,
> djd_debug,
> glob_log10relerr,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_clock_sec,
> glob_html_log,
> glob_neg_h,
> glob_hmin_init,
> glob_initial_pass,
> glob_log10normmin,
> glob_subiter_method,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_abserr,
> glob_next_display,
> centuries_in_millinium,
> min_in_hour,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_fact_1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_1st_rel_error,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_y1,
> array_x,
> array_y2,
> array_norms,
> array_type_pole,
> array_poles,
> array_fact_2,
> array_y2_set_initial,
> array_y2_higher,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_complex_pole,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> array_y2_higher_work2,
> array_y2_higher_work,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
>
>
>
>
>
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float) or (omniabs(array_y1_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_y1_higher[1,m]/array_y1_higher[1,m-1];
> rm1 := array_y1_higher[1,m-1]/array_y1_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 - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) < glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float) or (omniabs(array_y2_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_y2_higher[1,m]/array_y2_higher[1,m-1];
> rm1 := array_y2_higher[1,m-1]/array_y2_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_y1_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_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_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_y1_higher[1,m])/(array_y1_higher[1,m-1]);
> rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]);
> rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]);
> rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]);
> rm4 := (array_y1_higher[1,m-4])/(array_y1_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 - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y2_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_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_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_y2_higher[1,m])/(array_y2_higher[1,m-1]);
> rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]);
> rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]);
> rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]);
> rm4 := (array_y2_higher[1,m-4])/(array_y2_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 glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL,
glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles,
glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h,
glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr,
glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter,
glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter,
glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec,
glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start,
glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug,
glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr,
glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init,
glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float,
glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h,
years_in_century, djd_debug2, glob_abserr, glob_next_display,
centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0,
array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1,
array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2,
array_y2_set_initial, array_y2_higher, array_y1_higher_work2,
array_y1_higher_work, array_complex_pole, array_y1_set_initial,
array_real_pole, array_y1_higher, array_y2_higher_work2,
array_y2_higher_work, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y1_higher[1, m]) < glob_small_float
or omniabs(array_y1_higher[1, m - 1]) < glob_small_float or
omniabs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_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 - 2;
while 10 <= m and (omniabs(array_y2_higher[1, m]) < glob_small_float
or omniabs(array_y2_higher[1, m - 1]) < glob_small_float or
omniabs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_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_y1_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_y1_higher[1, m]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_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 - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y2_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_y2_higher[1, m]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_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
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_normmax,
> glob_warned,
> glob_max_iter,
> glob_look_poles,
> glob_optimal_done,
> sec_in_minute,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_h,
> glob_almost_1,
> days_in_year,
> hours_in_day,
> glob_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_finished,
> glob_current_iter,
> glob_dump_analytic,
> glob_display_interval,
> glob_hmin,
> glob_max_opt_iter,
> glob_good_digits,
> glob_iter,
> glob_orig_start_sec,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_optimal_expect_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> glob_curr_iter_when_opt,
> glob_start,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_clock_start_sec,
> djd_debug,
> glob_log10relerr,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_clock_sec,
> glob_html_log,
> glob_neg_h,
> glob_hmin_init,
> glob_initial_pass,
> glob_log10normmin,
> glob_subiter_method,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_abserr,
> glob_next_display,
> centuries_in_millinium,
> min_in_hour,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_fact_1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_1st_rel_error,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_y1,
> array_x,
> array_y2,
> array_norms,
> array_type_pole,
> array_poles,
> array_fact_2,
> array_y2_set_initial,
> array_y2_higher,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_complex_pole,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> array_y2_higher_work2,
> array_y2_higher_work,
> glob_last;
>
> local iii;
>
>
>
> if ( not glob_initial_pass) then # if number 3
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2
> ;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y1[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_y2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y2[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 glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL,
glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles,
glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h,
glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr,
glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter,
glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter,
glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec,
glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start,
glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug,
glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr,
glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init,
glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float,
glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h,
years_in_century, djd_debug2, glob_abserr, glob_next_display,
centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0,
array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1,
array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2,
array_y2_set_initial, array_y2_higher, array_y1_higher_work2,
array_y1_higher_work, array_complex_pole, array_y1_set_initial,
array_real_pole, array_y1_higher, array_y2_higher_work2,
array_y2_higher_work, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y1[iii]) then
array_norms[iii] := omniabs(array_y1[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y2[iii]) then
array_norms[iii] := omniabs(array_y2[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 9
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_normmax,
> glob_warned,
> glob_max_iter,
> glob_look_poles,
> glob_optimal_done,
> sec_in_minute,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_h,
> glob_almost_1,
> days_in_year,
> hours_in_day,
> glob_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_finished,
> glob_current_iter,
> glob_dump_analytic,
> glob_display_interval,
> glob_hmin,
> glob_max_opt_iter,
> glob_good_digits,
> glob_iter,
> glob_orig_start_sec,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_optimal_expect_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> glob_curr_iter_when_opt,
> glob_start,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_clock_start_sec,
> djd_debug,
> glob_log10relerr,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_clock_sec,
> glob_html_log,
> glob_neg_h,
> glob_hmin_init,
> glob_initial_pass,
> glob_log10normmin,
> glob_subiter_method,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_abserr,
> glob_next_display,
> centuries_in_millinium,
> min_in_hour,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_fact_1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_1st_rel_error,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_y1,
> array_x,
> array_y2,
> array_norms,
> array_type_pole,
> array_poles,
> array_fact_2,
> array_y2_set_initial,
> array_y2_higher,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_complex_pole,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> array_y2_higher_work2,
> array_y2_higher_work,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
>
>
>
>
>
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp1[1] := (array_m1[1] * (array_y2[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #emit pre sub FULL - CONST $eq_no = 2 i = 1
> array_tmp5[1] := array_y1[1] - array_const_1D0[1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[2,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #emit pre sub FULL CONST $eq_no = 2 i = 2
> array_tmp5[2] := array_y1[2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[2,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #emit pre sub FULL CONST $eq_no = 2 i = 3
> array_tmp5[3] := array_y1[3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[2,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #emit pre sub FULL CONST $eq_no = 2 i = 4
> array_tmp5[4] := array_y1[4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[2,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #emit pre sub FULL CONST $eq_no = 2 i = 5
> array_tmp5[5] := array_y1[5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[2,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,5] := 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 FULL FULL $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_m1,array_y2,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y1[kkk + order_d] := temporary;
> array_y1_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_y1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> #emit FULL - NOT FULL sub $eq_no = 2
> array_tmp5[kkk] := array_y1[kkk];
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2
> temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y2[kkk + order_d] := temporary;
> array_y2_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_y2_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 glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL,
glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles,
glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h,
glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr,
glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter,
glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter,
glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec,
glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start,
glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug,
glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr,
glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init,
glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float,
glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h,
years_in_century, djd_debug2, glob_abserr, glob_next_display,
centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0,
array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1,
array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2,
array_y2_set_initial, array_y2_higher, array_y1_higher_work2,
array_y1_higher_work, array_complex_pole, array_y1_set_initial,
array_real_pole, array_y1_higher, array_y2_higher_work2,
array_y2_higher_work, glob_last;
array_tmp1[1] := array_m1[1]*array_y2[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
if not array_y1_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp5[1] := array_y1[1] - array_const_1D0[1];
if not array_y2_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_m1, array_y2, 1);
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2];
if not array_y1_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp5[2] := array_y1[2];
if not array_y2_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_m1, array_y2, 1);
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := array_tmp2[3];
if not array_y1_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp5[3] := array_y1[3];
if not array_y2_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_m1, array_y2, 1);
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := array_tmp2[4];
if not array_y1_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp5[4] := array_y1[4];
if not array_y2_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_m1, array_y2, 1);
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := array_tmp2[5];
if not array_y1_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
array_tmp5[5] := array_y1[5];
if not array_y2_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_m1, array_y2, 1);
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y1_set_initial[1, kkk + order_d] then
temporary := array_tmp3[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y1[kkk + order_d] := temporary;
array_y1_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_y1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
array_tmp5[kkk] := array_y1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y2_set_initial[2, kkk + order_d] then
temporary := array_tmp5[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y2[kkk + order_d] := temporary;
array_y2_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_y2_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_y1 := proc(x)
> return(1.0 + cos(x));
> end;
exact_soln_y1 := proc(x) return 1.0 + cos(x) end proc
> exact_soln_y2 := proc(x)
> return(1.0 + sin(x));
> end;
exact_soln_y2 := proc(x) return 1.0 + sin(x) 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,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp,subiter;
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_normmax,
> glob_warned,
> glob_max_iter,
> glob_look_poles,
> glob_optimal_done,
> sec_in_minute,
> glob_max_minutes,
> MAX_UNCHANGED,
> glob_h,
> glob_almost_1,
> days_in_year,
> hours_in_day,
> glob_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmax,
> glob_not_yet_finished,
> glob_current_iter,
> glob_dump_analytic,
> glob_display_interval,
> glob_hmin,
> glob_max_opt_iter,
> glob_good_digits,
> glob_iter,
> glob_orig_start_sec,
> glob_warned2,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_optimal_expect_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> glob_curr_iter_when_opt,
> glob_start,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_clock_start_sec,
> djd_debug,
> glob_log10relerr,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_clock_sec,
> glob_html_log,
> glob_neg_h,
> glob_hmin_init,
> glob_initial_pass,
> glob_log10normmin,
> glob_subiter_method,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_abserr,
> glob_next_display,
> centuries_in_millinium,
> min_in_hour,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_fact_1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_1st_rel_error,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_y1,
> array_x,
> array_y2,
> array_norms,
> array_type_pole,
> array_poles,
> array_fact_2,
> array_y2_set_initial,
> array_y2_higher,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_complex_pole,
> array_y1_set_initial,
> array_real_pole,
> array_y1_higher,
> array_y2_higher_work2,
> array_y2_higher_work,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> INFO := 2;
> DEBUGL := 3;
> glob_log10abserr := 0.0;
> glob_normmax := 0.0;
> glob_warned := false;
> glob_max_iter := 1000;
> glob_look_poles := false;
> glob_optimal_done := false;
> sec_in_minute := 60;
> glob_max_minutes := 0.0;
> MAX_UNCHANGED := 10;
> glob_h := 0.1;
> glob_almost_1 := 0.9990;
> days_in_year := 365;
> hours_in_day := 24;
> glob_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_hmax := 1.0;
> glob_not_yet_finished := true;
> glob_current_iter := 0;
> glob_dump_analytic := false;
> glob_display_interval := 0.0;
> glob_hmin := 0.00000000001;
> glob_max_opt_iter := 10;
> glob_good_digits := 0;
> glob_iter := 0;
> glob_orig_start_sec := 0.0;
> glob_warned2 := false;
> glob_optimal_start := 0.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_hours := 0.0;
> glob_disp_incr := 0.1;
> glob_display_flag := true;
> glob_dump := false;
> glob_optimal_expect_sec := 0.1;
> glob_no_eqs := 0;
> glob_not_yet_start_msg := true;
> glob_curr_iter_when_opt := 0;
> glob_start := 0;
> glob_smallish_float := 0.1e-100;
> glob_max_trunc_err := 0.1e-10;
> glob_clock_start_sec := 0.0;
> djd_debug := true;
> glob_log10relerr := 0.0;
> glob_max_sec := 10000.0;
> glob_unchanged_h_cnt := 0;
> glob_log10_relerr := 0.1e-10;
> glob_clock_sec := 0.0;
> glob_html_log := true;
> glob_neg_h := false;
> glob_hmin_init := 0.001;
> glob_initial_pass := true;
> glob_log10normmin := 0.1;
> glob_subiter_method := 3;
> glob_small_float := 0.1e-50;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_reached_optimal_h := false;
> years_in_century := 100;
> djd_debug2 := true;
> glob_abserr := 0.1e-10;
> glob_next_display := 0.0;
> centuries_in_millinium := 10;
> min_in_hour := 60;
> glob_percent_done := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_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/mtest2postode.ode#################");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
> omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = y1 - 1.0;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 10.0;");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"# testing comment");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.005 ;");
> 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_y1 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> 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_y2_init:= Array(0..(max_terms + 1),[]);
> array_y1_init:= Array(0..(max_terms + 1),[]);
> array_fact_1:= 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_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y1:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_y2:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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 <=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_y2_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 <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_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 <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_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 <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_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_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_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_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1D0[1] := 1.0;
> 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
> x_start := 0.1;
> x_end := 10.0;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> # testing comment
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #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_y1_set_initial[1,1] := true;
> array_y1_set_initial[1,2] := false;
> array_y1_set_initial[1,3] := false;
> array_y1_set_initial[1,4] := false;
> array_y1_set_initial[1,5] := false;
> array_y1_set_initial[1,6] := false;
> array_y1_set_initial[1,7] := false;
> array_y1_set_initial[1,8] := false;
> array_y1_set_initial[1,9] := false;
> array_y1_set_initial[1,10] := false;
> array_y1_set_initial[1,11] := false;
> array_y1_set_initial[1,12] := false;
> array_y1_set_initial[1,13] := false;
> array_y1_set_initial[1,14] := false;
> array_y1_set_initial[1,15] := false;
> array_y1_set_initial[1,16] := false;
> array_y1_set_initial[1,17] := false;
> array_y1_set_initial[1,18] := false;
> array_y1_set_initial[1,19] := false;
> array_y1_set_initial[1,20] := false;
> array_y1_set_initial[1,21] := false;
> array_y1_set_initial[1,22] := false;
> array_y1_set_initial[1,23] := false;
> array_y1_set_initial[1,24] := false;
> array_y1_set_initial[1,25] := false;
> array_y1_set_initial[1,26] := false;
> array_y1_set_initial[1,27] := false;
> array_y1_set_initial[1,28] := false;
> array_y1_set_initial[1,29] := false;
> array_y1_set_initial[1,30] := false;
> array_y2_set_initial[2,1] := true;
> array_y2_set_initial[2,2] := false;
> array_y2_set_initial[2,3] := false;
> array_y2_set_initial[2,4] := false;
> array_y2_set_initial[2,5] := false;
> array_y2_set_initial[2,6] := false;
> array_y2_set_initial[2,7] := false;
> array_y2_set_initial[2,8] := false;
> array_y2_set_initial[2,9] := false;
> array_y2_set_initial[2,10] := false;
> array_y2_set_initial[2,11] := false;
> array_y2_set_initial[2,12] := false;
> array_y2_set_initial[2,13] := false;
> array_y2_set_initial[2,14] := false;
> array_y2_set_initial[2,15] := false;
> array_y2_set_initial[2,16] := false;
> array_y2_set_initial[2,17] := false;
> array_y2_set_initial[2,18] := false;
> array_y2_set_initial[2,19] := false;
> array_y2_set_initial[2,20] := false;
> array_y2_set_initial[2,21] := false;
> array_y2_set_initial[2,22] := false;
> array_y2_set_initial[2,23] := false;
> array_y2_set_initial[2,24] := false;
> array_y2_set_initial[2,25] := false;
> array_y2_set_initial[2,26] := false;
> array_y2_set_initial[2,27] := false;
> array_y2_set_initial[2,28] := false;
> array_y2_set_initial[2,29] := false;
> array_y2_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_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_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_y1_higher[r_order,term_no] := array_y1_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 := 1;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_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_y2_higher[r_order,term_no] := array_y2_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_y1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y1_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_y2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y2_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_x[1] , x_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 <= 2) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while (subiter <= 2 + 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_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y1
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[2,iii] := array_y1_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_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_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_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_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_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_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_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_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_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_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_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y1_higher[ord,term_no] := array_y1_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_y2
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_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_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y2_higher[ord,term_no] := array_y2_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 ( y1 , x , 1 ) = m1 * y2 + 1.0;");
> omniout_str(INFO,"diff ( y2 , x , 1 ) = y1 - 1.0;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 4
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-09-21T00:02:57-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest2")
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[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,"mtest2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest2 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 ( y2 , x , 1 ) = y1 - 1.0;")
> ;
> 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, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp, subiter;
global glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL,
glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles,
glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h,
glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr,
glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter,
glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter,
glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec,
glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start,
glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug,
glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr,
glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init,
glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float,
glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h,
years_in_century, djd_debug2, glob_abserr, glob_next_display,
centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0,
array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1,
array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2,
array_y2_set_initial, array_y2_higher, array_y1_higher_work2,
array_y1_higher_work, array_complex_pole, array_y1_set_initial,
array_real_pole, array_y1_higher, array_y2_higher_work2,
array_y2_higher_work, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
ALWAYS := 1;
DEBUGMASSIVE := 4;
INFO := 2;
DEBUGL := 3;
glob_log10abserr := 0.;
glob_normmax := 0.;
glob_warned := false;
glob_max_iter := 1000;
glob_look_poles := false;
glob_optimal_done := false;
sec_in_minute := 60;
glob_max_minutes := 0.;
MAX_UNCHANGED := 10;
glob_h := 0.1;
glob_almost_1 := 0.9990;
days_in_year := 365;
hours_in_day := 24;
glob_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_hmax := 1.0;
glob_not_yet_finished := true;
glob_current_iter := 0;
glob_dump_analytic := false;
glob_display_interval := 0.;
glob_hmin := 0.1*10^(-10);
glob_max_opt_iter := 10;
glob_good_digits := 0;
glob_iter := 0;
glob_orig_start_sec := 0.;
glob_warned2 := false;
glob_optimal_start := 0.;
glob_optimal_clock_start_sec := 0.;
glob_max_hours := 0.;
glob_disp_incr := 0.1;
glob_display_flag := true;
glob_dump := false;
glob_optimal_expect_sec := 0.1;
glob_no_eqs := 0;
glob_not_yet_start_msg := true;
glob_curr_iter_when_opt := 0;
glob_start := 0;
glob_smallish_float := 0.1*10^(-100);
glob_max_trunc_err := 0.1*10^(-10);
glob_clock_start_sec := 0.;
djd_debug := true;
glob_log10relerr := 0.;
glob_max_sec := 10000.0;
glob_unchanged_h_cnt := 0;
glob_log10_relerr := 0.1*10^(-10);
glob_clock_sec := 0.;
glob_html_log := true;
glob_neg_h := false;
glob_hmin_init := 0.001;
glob_initial_pass := true;
glob_log10normmin := 0.1;
glob_subiter_method := 3;
glob_small_float := 0.1*10^(-50);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_reached_optimal_h := false;
years_in_century := 100;
djd_debug2 := true;
glob_abserr := 0.1*10^(-10);
glob_next_display := 0.;
centuries_in_millinium := 10;
min_in_hour := 60;
glob_percent_done := 0.;
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/mtest2postode.ode#################");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 10.0;");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "# testing comment");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.005 ;");
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_y1 := proc(x)");
omniout_str(ALWAYS, "return(1.0 + cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(1.0 + sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
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_y2_init := Array(0 .. max_terms + 1, []);
array_y1_init := Array(0 .. max_terms + 1, []);
array_fact_1 := 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_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y1 := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_y2 := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y2_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 3, 0 .. 4, []);
array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 3, 0 .. 4, []);
array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1_init[term] := 0.; term := term + 1
end do;
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_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_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
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 <= 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_y2_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_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 <= 3 do
term := 1;
while term <= max_terms do
array_y1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_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_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 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;
x_start := 0.1;
x_end := 10.0;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
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_y1_set_initial[1, 1] := true;
array_y1_set_initial[1, 2] := false;
array_y1_set_initial[1, 3] := false;
array_y1_set_initial[1, 4] := false;
array_y1_set_initial[1, 5] := false;
array_y1_set_initial[1, 6] := false;
array_y1_set_initial[1, 7] := false;
array_y1_set_initial[1, 8] := false;
array_y1_set_initial[1, 9] := false;
array_y1_set_initial[1, 10] := false;
array_y1_set_initial[1, 11] := false;
array_y1_set_initial[1, 12] := false;
array_y1_set_initial[1, 13] := false;
array_y1_set_initial[1, 14] := false;
array_y1_set_initial[1, 15] := false;
array_y1_set_initial[1, 16] := false;
array_y1_set_initial[1, 17] := false;
array_y1_set_initial[1, 18] := false;
array_y1_set_initial[1, 19] := false;
array_y1_set_initial[1, 20] := false;
array_y1_set_initial[1, 21] := false;
array_y1_set_initial[1, 22] := false;
array_y1_set_initial[1, 23] := false;
array_y1_set_initial[1, 24] := false;
array_y1_set_initial[1, 25] := false;
array_y1_set_initial[1, 26] := false;
array_y1_set_initial[1, 27] := false;
array_y1_set_initial[1, 28] := false;
array_y1_set_initial[1, 29] := false;
array_y1_set_initial[1, 30] := false;
array_y2_set_initial[2, 1] := true;
array_y2_set_initial[2, 2] := false;
array_y2_set_initial[2, 3] := false;
array_y2_set_initial[2, 4] := false;
array_y2_set_initial[2, 5] := false;
array_y2_set_initial[2, 6] := false;
array_y2_set_initial[2, 7] := false;
array_y2_set_initial[2, 8] := false;
array_y2_set_initial[2, 9] := false;
array_y2_set_initial[2, 10] := false;
array_y2_set_initial[2, 11] := false;
array_y2_set_initial[2, 12] := false;
array_y2_set_initial[2, 13] := false;
array_y2_set_initial[2, 14] := false;
array_y2_set_initial[2, 15] := false;
array_y2_set_initial[2, 16] := false;
array_y2_set_initial[2, 17] := false;
array_y2_set_initial[2, 18] := false;
array_y2_set_initial[2, 19] := false;
array_y2_set_initial[2, 20] := false;
array_y2_set_initial[2, 21] := false;
array_y2_set_initial[2, 22] := false;
array_y2_set_initial[2, 23] := false;
array_y2_set_initial[2, 24] := false;
array_y2_set_initial[2, 25] := false;
array_y2_set_initial[2, 26] := false;
array_y2_set_initial[2, 27] := false;
array_y2_set_initial[2, 28] := false;
array_y2_set_initial[2, 29] := false;
array_y2_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_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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 := 1;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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_y1_higher[1, 1]) then
tmp := omniabs(array_y1_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_y2_higher[1, 1]) then
tmp := omniabs(array_y2_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_x[1], x_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 <= 2 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 2 + 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_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_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 ( y1 , x , 1 ) = m1 * y2 + 1.0;");
omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-09-21T00:02:57-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest2")
;
logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;")
;
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[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,
"mtest2 diffeq.mxt");
logitem_str(html_log_file,
"mtest2 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 ( y2 , x , 1 ) = y1 - 1.0;");
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/mtest2postode.ode#################
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
diff ( y2 , x , 1 ) = y1 - 1.0;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 10.0;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
# testing comment
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#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_y1 := proc(x)
return(1.0 + cos(x));
end;
exact_soln_y2 := proc(x)
return(1.0 + sin(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y1[1] (analytic) = 1.9950041652780257660955619878039
y1[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
y2[1] (analytic) = 1.0998334166468281523068141984106
y2[1] (numeric) = 1.0998334166468281523068141984106
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
x[1] = 0.1
y1[1] (analytic) = 1.9950041652780257660955619878039
y1[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.005
y2[1] (analytic) = 1.0998334166468281523068141984106
y2[1] (numeric) = 1.0998334166468281523068141984106
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=3.1MB, time=0.43
memory used=7.6MB, alloc=4.3MB, time=1.04
memory used=11.4MB, alloc=4.3MB, time=1.62
memory used=15.2MB, alloc=4.4MB, time=2.21
memory used=19.0MB, alloc=4.4MB, time=2.81
memory used=22.8MB, alloc=4.4MB, time=3.45
memory used=26.7MB, alloc=4.4MB, time=4.06
memory used=30.5MB, alloc=4.4MB, time=4.65
memory used=34.3MB, alloc=4.4MB, time=5.24
memory used=38.1MB, alloc=4.4MB, time=5.84
x[1] = 0.2
y1[1] (analytic) = 1.9800665778412416311241965167482
y1[1] (numeric) = 1.9800665778412268551841859998226
absolute error = 1.47759400105169256e-14
relative error = 7.4623450422693995529372187961907e-13 %
Correct digits = 14
h = 0.005
y2[1] (analytic) = 1.1986693307950612154594126271184
y2[1] (numeric) = 1.1986693307950577409432354359246
absolute error = 3.4745161771911938e-15
relative error = 2.8986444283900999098554668281786e-13 %
Correct digits = 14
h = 0.005
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.4MB, time=6.47
NO POLE
NO POLE
memory used=45.7MB, alloc=4.4MB, time=7.07
memory used=49.5MB, alloc=4.4MB, time=7.67
memory used=53.4MB, alloc=4.4MB, time=8.30
memory used=57.2MB, alloc=4.4MB, time=8.93
memory used=61.0MB, alloc=4.4MB, time=9.53
memory used=64.8MB, alloc=4.4MB, time=10.19
memory used=68.6MB, alloc=4.4MB, time=10.81
memory used=72.4MB, alloc=4.4MB, time=11.46
memory used=76.2MB, alloc=4.4MB, time=12.19
memory used=80.1MB, alloc=4.4MB, time=12.80
x[1] = 0.3
y1[1] (analytic) = 1.955336489125606019642310227568
y1[1] (numeric) = 1.9553364891255773091442398299759
absolute error = 2.87104980703975921e-14
relative error = 1.4683149539768702250457943562275e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.295520206661339575105320745685
y2[1] (numeric) = 1.2955202066613297105240326465762
absolute error = 9.8645812880991088e-15
relative error = 7.6143785618913140419113888735939e-13 %
Correct digits = 14
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=83.9MB, alloc=4.4MB, time=13.41
memory used=87.7MB, alloc=4.4MB, time=14.00
memory used=91.5MB, alloc=4.4MB, time=14.58
memory used=95.3MB, alloc=4.4MB, time=15.18
memory used=99.1MB, alloc=4.4MB, time=15.79
memory used=102.9MB, alloc=4.4MB, time=16.39
memory used=106.8MB, alloc=4.4MB, time=16.97
memory used=110.6MB, alloc=4.4MB, time=17.56
memory used=114.4MB, alloc=4.4MB, time=18.13
memory used=118.2MB, alloc=4.4MB, time=18.69
x[1] = 0.4
y1[1] (analytic) = 1.9210609940028850827985267320518
y1[1] (numeric) = 1.9210609940028437094230565258272
absolute error = 4.13733754702062246e-14
relative error = 2.1536731836919535801808498131944e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.3894183423086504916663117567957
y2[1] (numeric) = 1.3894183423086314693164321835832
absolute error = 1.90223498795732125e-14
relative error = 1.3690872864083377603172378220777e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.4MB, time=19.28
NO POLE
NO POLE
memory used=125.8MB, alloc=4.4MB, time=19.85
memory used=129.7MB, alloc=4.4MB, time=20.44
memory used=133.5MB, alloc=4.4MB, time=21.03
memory used=137.3MB, alloc=4.4MB, time=21.61
memory used=141.1MB, alloc=4.4MB, time=22.19
memory used=144.9MB, alloc=4.4MB, time=22.78
memory used=148.7MB, alloc=4.4MB, time=23.38
memory used=152.5MB, alloc=4.4MB, time=24.00
memory used=156.4MB, alloc=4.4MB, time=24.61
memory used=160.2MB, alloc=4.4MB, time=25.21
x[1] = 0.5
y1[1] (analytic) = 1.8775825618903727161162815826038
y1[1] (numeric) = 1.8775825618903203592966237993703
absolute error = 5.23568196577832335e-14
relative error = 2.7885228975001641186420965099657e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.4794255386042030002732879352156
y2[1] (numeric) = 1.4794255386041722565895613300533
absolute error = 3.07436837266051623e-14
relative error = 2.0780825343606665034626212675162e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=164.0MB, alloc=4.4MB, time=25.81
memory used=167.8MB, alloc=4.4MB, time=26.43
memory used=171.6MB, alloc=4.4MB, time=27.04
memory used=175.4MB, alloc=4.4MB, time=27.64
memory used=179.2MB, alloc=4.4MB, time=28.25
memory used=183.1MB, alloc=4.4MB, time=28.85
memory used=186.9MB, alloc=4.4MB, time=29.46
memory used=190.7MB, alloc=4.4MB, time=30.07
memory used=194.5MB, alloc=4.4MB, time=30.68
memory used=198.3MB, alloc=4.4MB, time=31.30
x[1] = 0.6
y1[1] (analytic) = 1.8253356149096782972409524989554
y1[1] (numeric) = 1.8253356149096170147326356640928
absolute error = 6.12825083168348626e-14
relative error = 3.3573282532958882000221878937471e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.5646424733950353572009454456587
y2[1] (numeric) = 1.5646424733949905858840014951248
absolute error = 4.47713169439505339e-14
relative error = 2.8614407256121335847492862249450e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=202.1MB, alloc=4.4MB, time=31.89
memory used=205.9MB, alloc=4.4MB, time=32.51
memory used=209.8MB, alloc=4.4MB, time=33.11
memory used=213.6MB, alloc=4.4MB, time=33.72
memory used=217.4MB, alloc=4.4MB, time=34.31
memory used=221.2MB, alloc=4.4MB, time=34.92
memory used=225.0MB, alloc=4.4MB, time=35.52
memory used=228.8MB, alloc=4.4MB, time=36.13
memory used=232.7MB, alloc=4.4MB, time=36.74
memory used=236.5MB, alloc=4.4MB, time=37.36
x[1] = 0.7
y1[1] (analytic) = 1.7648421872844884262558599901919
y1[1] (numeric) = 1.7648421872844206182428652186915
absolute error = 6.78080129947715004e-14
relative error = 3.8421573035437081577920099401987e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.6442176872376910536726143513987
y2[1] (numeric) = 1.6442176872376302548457781470133
absolute error = 6.07988268362043854e-14
relative error = 3.6977358477603579082182945999739e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.4MB, time=37.96
NO POLE
NO POLE
memory used=244.1MB, alloc=4.4MB, time=38.59
memory used=247.9MB, alloc=4.4MB, time=39.20
memory used=251.7MB, alloc=4.4MB, time=39.82
memory used=255.5MB, alloc=4.4MB, time=40.42
memory used=259.4MB, alloc=4.4MB, time=41.02
memory used=263.2MB, alloc=4.4MB, time=41.62
memory used=267.0MB, alloc=4.4MB, time=42.23
memory used=270.8MB, alloc=4.4MB, time=42.83
memory used=274.6MB, alloc=4.4MB, time=43.42
memory used=278.4MB, alloc=4.4MB, time=44.03
x[1] = 0.8
y1[1] (analytic) = 1.6967067093471654209207499816423
y1[1] (numeric) = 1.6967067093470937881698658273435
absolute error = 7.16327508841542988e-14
relative error = 4.2218699607615818167897249941518e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.7173560908995227616271746105814
y2[1] (numeric) = 1.7173560908994442862703553796332
absolute error = 7.84753568192309482e-14
relative error = 4.5695448506620925754269164389001e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=282.2MB, alloc=4.4MB, time=44.64
memory used=286.1MB, alloc=4.4MB, time=45.26
memory used=289.9MB, alloc=4.4MB, time=45.86
memory used=293.7MB, alloc=4.4MB, time=46.47
memory used=297.5MB, alloc=4.4MB, time=47.07
memory used=301.3MB, alloc=4.4MB, time=47.68
memory used=305.1MB, alloc=4.4MB, time=48.30
memory used=308.9MB, alloc=4.4MB, time=48.92
memory used=312.8MB, alloc=4.4MB, time=49.53
memory used=316.6MB, alloc=4.4MB, time=50.11
x[1] = 0.9
y1[1] (analytic) = 1.6216099682706644564847161514071
y1[1] (numeric) = 1.6216099682705919531447090503113
absolute error = 7.25033400071010958e-14
relative error = 4.4710714305993643604270695719680e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.7833269096274833884613823157136
y2[1] (numeric) = 1.783326909627385977433757870366
absolute error = 9.74110276244453476e-14
relative error = 5.4623202901588805193483146217636e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=320.4MB, alloc=4.4MB, time=50.69
memory used=324.2MB, alloc=4.4MB, time=51.26
memory used=328.0MB, alloc=4.4MB, time=51.82
memory used=331.8MB, alloc=4.4MB, time=52.38
memory used=335.7MB, alloc=4.4MB, time=52.95
memory used=339.5MB, alloc=4.4MB, time=53.51
memory used=343.3MB, alloc=4.4MB, time=54.07
memory used=347.1MB, alloc=4.4MB, time=54.66
memory used=350.9MB, alloc=4.4MB, time=55.22
memory used=354.7MB, alloc=4.4MB, time=55.81
x[1] = 1
y1[1] (analytic) = 1.540302305868139717400936607443
y1[1] (numeric) = 1.5403023058680694991201401994235
absolute error = 7.02182807964080195e-14
relative error = 4.5587337322612031902196251374917e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.8414709848078965066525023216303
y2[1] (numeric) = 1.8414709848077793236888230770753
absolute error = 1.171829636792445550e-13
relative error = 6.3635519997872331772078300197915e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.4MB, time=56.39
NO POLE
NO POLE
memory used=362.4MB, alloc=4.4MB, time=56.95
memory used=366.2MB, alloc=4.4MB, time=57.50
memory used=370.0MB, alloc=4.4MB, time=58.06
memory used=373.8MB, alloc=4.4MB, time=58.64
memory used=377.6MB, alloc=4.4MB, time=59.21
memory used=381.4MB, alloc=4.4MB, time=59.78
memory used=385.2MB, alloc=4.4MB, time=60.35
memory used=389.1MB, alloc=4.4MB, time=60.92
memory used=392.9MB, alloc=4.4MB, time=61.48
memory used=396.7MB, alloc=4.4MB, time=62.05
x[1] = 1.1
y1[1] (analytic) = 1.4535961214255773877713700517847
y1[1] (numeric) = 1.4535961214255127558755542879812
absolute error = 6.46318958157638035e-14
relative error = 4.4463448177322953501048323498404e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.8912073600614353399518025778717
y2[1] (numeric) = 1.8912073600612979980986431970244
absolute error = 1.373418531593808473e-13
relative error = 7.2621255637943020575044827947272e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=400.5MB, alloc=4.4MB, time=62.62
memory used=404.3MB, alloc=4.4MB, time=63.18
memory used=408.1MB, alloc=4.4MB, time=63.74
memory used=411.9MB, alloc=4.4MB, time=64.30
memory used=415.8MB, alloc=4.4MB, time=64.87
memory used=419.6MB, alloc=4.4MB, time=65.47
memory used=423.4MB, alloc=4.4MB, time=66.03
memory used=427.2MB, alloc=4.4MB, time=66.60
memory used=431.0MB, alloc=4.4MB, time=67.17
memory used=434.8MB, alloc=4.4MB, time=67.74
x[1] = 1.2
y1[1] (analytic) = 1.3623577544766735776383733556231
y1[1] (numeric) = 1.3623577544766179201693666643354
absolute error = 5.56574690066912877e-14
relative error = 4.0853783687729771213608574626706e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.9320390859672263496701344354948
y2[1] (numeric) = 1.9320390859670689307172957765928
absolute error = 1.574189528386589020e-13
relative error = 8.1478140883392686238253378507823e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
memory used=438.6MB, alloc=4.4MB, time=68.33
NO POLE
NO POLE
memory used=442.5MB, alloc=4.4MB, time=68.89
memory used=446.3MB, alloc=4.4MB, time=69.47
memory used=450.1MB, alloc=4.4MB, time=70.04
memory used=453.9MB, alloc=4.4MB, time=70.62
memory used=457.7MB, alloc=4.4MB, time=71.18
memory used=461.5MB, alloc=4.4MB, time=71.73
memory used=465.4MB, alloc=4.4MB, time=72.32
memory used=469.2MB, alloc=4.4MB, time=72.89
memory used=473.0MB, alloc=4.4MB, time=73.48
x[1] = 1.3
y1[1] (analytic) = 1.2674988286245874069979841092929
y1[1] (numeric) = 1.2674988286245441374617110464206
absolute error = 4.32695362730628723e-14
relative error = 3.4137732750424976582796417123258e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.9635581854171929647013486300396
y2[1] (numeric) = 1.9635581854170160312587366056011
absolute error = 1.769334426120244385e-13
relative error = 9.0108581414118763317834124459018e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
memory used=476.8MB, alloc=4.4MB, time=74.08
NO POLE
NO POLE
memory used=480.6MB, alloc=4.4MB, time=74.68
memory used=484.4MB, alloc=4.4MB, time=75.29
memory used=488.2MB, alloc=4.4MB, time=75.85
memory used=492.1MB, alloc=4.4MB, time=76.42
memory used=495.9MB, alloc=4.4MB, time=76.98
memory used=499.7MB, alloc=4.4MB, time=77.54
memory used=503.5MB, alloc=4.4MB, time=78.12
memory used=507.3MB, alloc=4.5MB, time=78.68
memory used=511.1MB, alloc=4.5MB, time=79.25
memory used=514.9MB, alloc=4.5MB, time=79.82
x[1] = 1.4
y1[1] (analytic) = 1.1699671429002409386167480352036
y1[1] (numeric) = 1.1699671429002134333264612078888
absolute error = 2.75052902868273148e-14
relative error = 2.3509455332774756391281919247605e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.9854497299884601806594745788061
y2[1] (numeric) = 1.9854497299882647806299542043322
absolute error = 1.954000295203744739e-13
relative error = 9.8416004479504085360000435635517e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=518.8MB, alloc=4.5MB, time=80.37
memory used=522.6MB, alloc=4.5MB, time=80.92
memory used=526.4MB, alloc=4.5MB, time=81.47
memory used=530.2MB, alloc=4.5MB, time=82.02
memory used=534.0MB, alloc=4.5MB, time=82.58
memory used=537.8MB, alloc=4.5MB, time=83.13
memory used=541.6MB, alloc=4.5MB, time=83.68
memory used=545.5MB, alloc=4.5MB, time=84.24
memory used=549.3MB, alloc=4.5MB, time=84.80
memory used=553.1MB, alloc=4.5MB, time=85.37
x[1] = 1.5
y1[1] (analytic) = 1.0707372016677029100881898514343
y1[1] (numeric) = 1.070737201667694445014205443701
absolute error = 8.4650739844077333e-15
relative error = 7.9058371850937331959100308830216e-13 %
Correct digits = 14
h = 0.005
y2[1] (analytic) = 1.9974949866040544309417233711415
y2[1] (numeric) = 1.9974949866038420942443981527412
absolute error = 2.123366973252184003e-13
relative error = 1.0630149199333535300584211335981e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=556.9MB, alloc=4.5MB, time=85.94
NO POLE
NO POLE
memory used=560.7MB, alloc=4.5MB, time=86.50
memory used=564.5MB, alloc=4.5MB, time=87.07
memory used=568.4MB, alloc=4.5MB, time=87.63
memory used=572.2MB, alloc=4.5MB, time=88.21
memory used=576.0MB, alloc=4.5MB, time=88.77
memory used=579.8MB, alloc=4.5MB, time=89.33
memory used=583.6MB, alloc=4.5MB, time=89.91
memory used=587.4MB, alloc=4.5MB, time=90.47
memory used=591.2MB, alloc=4.5MB, time=91.02
memory used=595.1MB, alloc=4.5MB, time=91.57
x[1] = 1.6
y1[1] (analytic) = 0.9708004776987112737942295370535
y1[1] (numeric) = 0.97080047769872496184505054506185
absolute error = 1.368805082100800835e-14
relative error = 1.4099756989670648033229314323353e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.9995736030415051643421138255462
y2[1] (numeric) = 1.9995736030412778918468945379703
absolute error = 2.272724952192875759e-13
relative error = 1.1366047985109857394160480749911e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=598.9MB, alloc=4.5MB, time=92.15
memory used=602.7MB, alloc=4.5MB, time=92.72
memory used=606.5MB, alloc=4.5MB, time=93.28
memory used=610.3MB, alloc=4.5MB, time=93.83
memory used=614.1MB, alloc=4.5MB, time=94.40
memory used=617.9MB, alloc=4.5MB, time=94.98
memory used=621.8MB, alloc=4.5MB, time=95.54
memory used=625.6MB, alloc=4.5MB, time=96.11
memory used=629.4MB, alloc=4.5MB, time=96.67
memory used=633.2MB, alloc=4.5MB, time=97.22
x[1] = 1.7
y1[1] (analytic) = 0.87115550570447531591235714266513
y1[1] (numeric) = 0.87115550570451404557346544275717
absolute error = 3.872966110830009204e-14
relative error = 4.4457804438692798266002000786847e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.9916648104524686153461333986479
y2[1] (numeric) = 1.9916648104522288600879834007932
absolute error = 2.397552581499978547e-13
relative error = 1.2037932130534052558405411434430e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=637.0MB, alloc=4.5MB, time=97.82
NO POLE
NO POLE
memory used=640.8MB, alloc=4.5MB, time=98.37
memory used=644.6MB, alloc=4.5MB, time=98.95
memory used=648.5MB, alloc=4.5MB, time=99.49
memory used=652.3MB, alloc=4.5MB, time=100.04
memory used=656.1MB, alloc=4.5MB, time=100.60
memory used=659.9MB, alloc=4.5MB, time=101.15
memory used=663.7MB, alloc=4.5MB, time=101.71
memory used=667.5MB, alloc=4.5MB, time=102.26
memory used=671.4MB, alloc=4.5MB, time=102.82
memory used=675.2MB, alloc=4.5MB, time=103.39
x[1] = 1.8
y1[1] (analytic) = 0.77279790530691294468332569346942
y1[1] (numeric) = 0.77279790530697932092907233453104
absolute error = 6.637624574664106162e-14
relative error = 8.5890819955419078350396120446288e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.9738476308781951865323731788434
y2[1] (numeric) = 1.973847630877945827380878606098
absolute error = 2.493591514945727454e-13
relative error = 1.2633150988641865001017339280344e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=679.0MB, alloc=4.5MB, time=103.95
memory used=682.8MB, alloc=4.5MB, time=104.51
memory used=686.6MB, alloc=4.5MB, time=105.09
memory used=690.4MB, alloc=4.5MB, time=105.66
memory used=694.2MB, alloc=4.5MB, time=106.22
memory used=698.1MB, alloc=4.5MB, time=106.79
memory used=701.9MB, alloc=4.5MB, time=107.34
memory used=705.7MB, alloc=4.5MB, time=107.92
memory used=709.5MB, alloc=4.5MB, time=108.48
memory used=713.3MB, alloc=4.5MB, time=109.04
x[1] = 1.9
y1[1] (analytic) = 0.67671043313649657772116630491969
y1[1] (numeric) = 0.67671043313659286609217025074981
absolute error = 9.628837100394583012e-14
relative error = 1.4228888205204290780030793455715e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.946300087687414488489709611635
y2[1] (numeric) = 1.9463000876871587965552493833071
absolute error = 2.556919344602283279e-13
relative error = 1.3137333552917854524867147896095e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=717.1MB, alloc=4.5MB, time=109.62
memory used=720.9MB, alloc=4.5MB, time=110.18
memory used=724.8MB, alloc=4.5MB, time=110.74
memory used=728.6MB, alloc=4.5MB, time=111.29
memory used=732.4MB, alloc=4.5MB, time=111.84
memory used=736.2MB, alloc=4.5MB, time=112.40
memory used=740.0MB, alloc=4.5MB, time=112.95
memory used=743.8MB, alloc=4.5MB, time=113.51
memory used=747.6MB, alloc=4.5MB, time=114.07
memory used=751.5MB, alloc=4.5MB, time=114.65
x[1] = 2
y1[1] (analytic) = 0.58385316345285761300243177049924
y1[1] (numeric) = 0.58385316345298568770594378642314
absolute error = 1.2807470351201592390e-13
relative error = 2.1936115367534037913763214974487e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.9092974268256816953960198659117
y2[1] (numeric) = 1.9092974268254232935564448903142
absolute error = 2.584018395749755975e-13
relative error = 1.3533870414552630670566959479251e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=755.3MB, alloc=4.5MB, time=115.21
NO POLE
NO POLE
memory used=759.1MB, alloc=4.5MB, time=115.78
memory used=762.9MB, alloc=4.5MB, time=116.34
memory used=766.7MB, alloc=4.5MB, time=116.90
memory used=770.5MB, alloc=4.5MB, time=117.46
memory used=774.3MB, alloc=4.5MB, time=118.03
memory used=778.2MB, alloc=4.5MB, time=118.61
memory used=782.0MB, alloc=4.5MB, time=119.17
memory used=785.8MB, alloc=4.5MB, time=119.73
memory used=789.6MB, alloc=4.5MB, time=120.29
memory used=793.4MB, alloc=4.5MB, time=120.85
x[1] = 2.1
y1[1] (analytic) = 0.49515389540014254837906147628083
y1[1] (numeric) = 0.49515389540030384522324442176089
absolute error = 1.6129684418294548006e-13
relative error = 3.2575093457075334318837952555909e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.863209366648873770680759313269
y2[1] (numeric) = 1.8632093666486165867108067142891
absolute error = 2.571839699525989799e-13
relative error = 1.3803278072563807034501821446099e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=797.2MB, alloc=4.5MB, time=121.43
memory used=801.1MB, alloc=4.5MB, time=121.99
memory used=804.9MB, alloc=4.5MB, time=122.54
memory used=808.7MB, alloc=4.5MB, time=123.09
memory used=812.5MB, alloc=4.5MB, time=123.65
memory used=816.3MB, alloc=4.5MB, time=124.20
memory used=820.1MB, alloc=4.5MB, time=124.79
memory used=823.9MB, alloc=4.5MB, time=125.34
memory used=827.8MB, alloc=4.5MB, time=125.90
memory used=831.6MB, alloc=4.5MB, time=126.46
x[1] = 2.2
y1[1] (analytic) = 0.41149888274465429147585738734507
y1[1] (numeric) = 0.41149888274484976639140455013269
absolute error = 1.9547491554716278762e-13
relative error = 4.7503146118736860009446826860069e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.8084964038195901843040369104161
y2[1] (numeric) = 1.8084964038193383981824256501836
absolute error = 2.517861216112602325e-13
relative error = 1.3922401011109647221869500395275e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=835.4MB, alloc=4.5MB, time=127.03
NO POLE
NO POLE
memory used=839.2MB, alloc=4.5MB, time=127.60
memory used=843.0MB, alloc=4.5MB, time=128.16
memory used=846.8MB, alloc=4.5MB, time=128.74
memory used=850.6MB, alloc=4.5MB, time=129.30
memory used=854.5MB, alloc=4.5MB, time=129.87
memory used=858.3MB, alloc=4.5MB, time=130.43
memory used=862.1MB, alloc=4.5MB, time=130.98
memory used=865.9MB, alloc=4.5MB, time=131.56
memory used=869.7MB, alloc=4.5MB, time=132.12
x[1] = 2.3
y1[1] (analytic) = 0.33372397872017580668211942883398
y1[1] (numeric) = 0.33372397872040590051674576369185
absolute error = 2.3009383462633485787e-13
relative error = 6.8947348497024308707486112665796e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.7457052121767201773854062116435
y2[1] (numeric) = 1.7457052121764781634404709391154
absolute error = 2.420139449352725281e-13
relative error = 1.3863391324443907220219132368945e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=873.5MB, alloc=4.5MB, time=132.70
NO POLE
NO POLE
memory used=877.3MB, alloc=4.5MB, time=133.28
memory used=881.2MB, alloc=4.5MB, time=133.83
memory used=885.0MB, alloc=4.5MB, time=134.42
memory used=888.8MB, alloc=4.5MB, time=135.00
memory used=892.6MB, alloc=4.5MB, time=135.59
memory used=896.4MB, alloc=4.5MB, time=136.18
memory used=900.2MB, alloc=4.5MB, time=136.77
memory used=904.1MB, alloc=4.5MB, time=137.38
memory used=907.9MB, alloc=4.5MB, time=138.00
memory used=911.7MB, alloc=4.5MB, time=138.63
x[1] = 2.4
y1[1] (analytic) = 0.26260628445875450039117777266522
y1[1] (numeric) = 0.26260628445901911058507378997338
absolute error = 2.6461019389601730816e-13
relative error = 1.0076308510338698540634304092200e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.6754631805511509265657715253413
y2[1] (numeric) = 1.6754631805509231911984563247144
absolute error = 2.277353673152006269e-13
relative error = 1.3592382689083390287738305454536e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=915.5MB, alloc=4.5MB, time=139.26
memory used=919.3MB, alloc=4.5MB, time=139.89
memory used=923.1MB, alloc=4.5MB, time=140.50
memory used=926.9MB, alloc=4.5MB, time=141.11
memory used=930.8MB, alloc=4.5MB, time=141.69
memory used=934.6MB, alloc=4.5MB, time=142.28
memory used=938.4MB, alloc=4.5MB, time=142.89
memory used=942.2MB, alloc=4.5MB, time=143.52
memory used=946.0MB, alloc=4.5MB, time=144.14
memory used=949.8MB, alloc=4.5MB, time=144.77
x[1] = 2.5
y1[1] (analytic) = 0.19885638445306628516649720953265
y1[1] (numeric) = 0.19885638445336474483075316561033
absolute error = 2.9845966425595607768e-13
relative error = 1.5008804724919353734660172507799e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.5984721441039564940518547021862
y2[1] (numeric) = 1.598472144103747609843864936697
absolute error = 2.088842079897654892e-13
relative error = 1.3067741515561920437736644390877e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=953.6MB, alloc=4.5MB, time=145.39
NO POLE
NO POLE
memory used=957.5MB, alloc=4.5MB, time=146.00
memory used=961.3MB, alloc=4.5MB, time=146.61
memory used=965.1MB, alloc=4.5MB, time=147.22
memory used=968.9MB, alloc=4.5MB, time=147.83
memory used=972.7MB, alloc=4.5MB, time=148.44
memory used=976.5MB, alloc=4.5MB, time=149.07
memory used=980.3MB, alloc=4.5MB, time=149.72
memory used=984.2MB, alloc=4.5MB, time=150.38
memory used=988.0MB, alloc=4.5MB, time=151.03
x[1] = 2.6
y1[1] (analytic) = 0.1431112466310527662022978483548
y1[1] (numeric) = 0.14311124663138383102862007743344
absolute error = 3.3106482632222907864e-13
relative error = 2.3133389870869415229266033353798e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.5155013718214642352577269352094
y2[1] (numeric) = 1.5155013718212787723316887273464
absolute error = 1.854629260382078630e-13
relative error = 1.2237727361163786734686516660081e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=991.8MB, alloc=4.5MB, time=151.69
NO POLE
NO POLE
memory used=995.6MB, alloc=4.5MB, time=152.34
memory used=999.4MB, alloc=4.5MB, time=153.00
memory used=1003.2MB, alloc=4.5MB, time=153.66
memory used=1007.0MB, alloc=4.5MB, time=154.31
memory used=1010.9MB, alloc=4.5MB, time=154.96
memory used=1014.7MB, alloc=4.5MB, time=155.62
memory used=1018.5MB, alloc=4.5MB, time=156.28
memory used=1022.3MB, alloc=4.5MB, time=156.94
memory used=1026.1MB, alloc=4.5MB, time=157.60
memory used=1029.9MB, alloc=4.5MB, time=158.25
x[1] = 2.7
y1[1] (analytic) = 0.09592785798293885201747271805667
y1[1] (numeric) = 0.09592785798330069534735750672717
absolute error = 3.61843329884788670500e-13
relative error = 3.7720359600768312184171274621642e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.4273798802338299345560530858579
y2[1] (numeric) = 1.4273798802336723901028369834047
absolute error = 1.575444532161024532e-13
relative error = 1.1037317773478346932670226918687e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1033.8MB, alloc=4.5MB, time=158.91
memory used=1037.6MB, alloc=4.5MB, time=159.51
memory used=1041.4MB, alloc=4.5MB, time=160.12
memory used=1045.2MB, alloc=4.5MB, time=160.73
memory used=1049.0MB, alloc=4.5MB, time=161.34
memory used=1052.8MB, alloc=4.5MB, time=161.95
memory used=1056.6MB, alloc=4.5MB, time=162.56
memory used=1060.5MB, alloc=4.5MB, time=163.17
memory used=1064.3MB, alloc=4.5MB, time=163.79
memory used=1068.1MB, alloc=4.5MB, time=164.39
x[1] = 2.8
y1[1] (analytic) = 0.05777765933134184741321188263385
y1[1] (numeric) = 0.057777659331732063689334856351803
absolute error = 3.90216276122973717953e-13
relative error = 6.7537570860247447562645365120756e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.3349881501559049195438537527124
y2[1] (numeric) = 1.3349881501557796464690908076208
absolute error = 1.252730747629450916e-13
relative error = 9.3838342121849720105279134309571e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
memory used=1071.9MB, alloc=4.5MB, time=165.00
NO POLE
NO POLE
memory used=1075.7MB, alloc=4.5MB, time=165.62
memory used=1079.5MB, alloc=4.5MB, time=166.22
memory used=1083.3MB, alloc=4.5MB, time=166.84
memory used=1087.2MB, alloc=4.5MB, time=167.45
memory used=1091.0MB, alloc=4.5MB, time=168.06
memory used=1094.8MB, alloc=4.5MB, time=168.64
memory used=1098.6MB, alloc=4.5MB, time=169.25
memory used=1102.4MB, alloc=4.5MB, time=169.85
memory used=1106.2MB, alloc=4.5MB, time=170.45
memory used=1110.0MB, alloc=4.5MB, time=171.06
x[1] = 2.9
y1[1] (analytic) = 0.02904183485040947821889333065447
y1[1] (numeric) = 0.029041834850825094932105704075745
absolute error = 4.15616713212373421275e-13
relative error = 1.4310966071984029355404212528531e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 1.2392493292139823281842569187396
y2[1] (numeric) = 1.2392493292138934638509579117236
absolute error = 8.88643332990070160e-14
relative error = 7.1708195602067361986990055573548e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1113.9MB, alloc=4.5MB, time=171.67
memory used=1117.7MB, alloc=4.5MB, time=172.28
memory used=1121.5MB, alloc=4.5MB, time=172.89
memory used=1125.3MB, alloc=4.5MB, time=173.51
memory used=1129.1MB, alloc=4.5MB, time=174.11
memory used=1132.9MB, alloc=4.5MB, time=174.73
memory used=1136.8MB, alloc=4.5MB, time=175.33
memory used=1140.6MB, alloc=4.5MB, time=175.93
memory used=1144.4MB, alloc=4.5MB, time=176.54
memory used=1148.2MB, alloc=4.5MB, time=177.14
x[1] = 3
y1[1] (analytic) = 0.01000750339955454272842720526874
y1[1] (numeric) = 0.01000750339999204086177312842861
absolute error = 4.37498133345923159870e-13
relative error = 4.3717010714720038984378243778446e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 1.1411200080598672221007448028081
y2[1] (numeric) = 1.1411200080598186181574173792561
absolute error = 4.86039433274235520e-14
relative error = 4.2593191762591210239098128245489e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
memory used=1152.0MB, alloc=4.5MB, time=177.75
NO POLE
NO POLE
memory used=1155.8MB, alloc=4.5MB, time=178.36
memory used=1159.6MB, alloc=4.5MB, time=178.94
memory used=1163.5MB, alloc=4.5MB, time=179.55
memory used=1167.3MB, alloc=4.5MB, time=180.17
memory used=1171.1MB, alloc=4.5MB, time=180.78
memory used=1174.9MB, alloc=4.5MB, time=181.39
memory used=1178.7MB, alloc=4.5MB, time=181.99
memory used=1182.5MB, alloc=4.5MB, time=182.59
memory used=1186.3MB, alloc=4.5MB, time=183.20
x[1] = 3.1
y1[1] (analytic) = 0.00086484972672053550762394545853
y1[1] (numeric) = 0.00086484972717587836559508701913851
absolute error = 4.5534285797114156060851e-13
relative error = 5.2649939510043858381949150619671e-08 %
Correct digits = 9
h = 0.005
y2[1] (analytic) = 1.0415806624332905791946982715967
y2[1] (numeric) = 1.0415806624332857334781832469608
absolute error = 4.8457165150246359e-15
relative error = 4.6522719649040971593570606745628e-13 %
Correct digits = 14
h = 0.005
TOP MAIN SOLVE Loop
memory used=1190.2MB, alloc=4.5MB, time=183.80
NO POLE
NO POLE
memory used=1194.0MB, alloc=4.5MB, time=184.40
memory used=1197.8MB, alloc=4.5MB, time=184.99
memory used=1201.6MB, alloc=4.5MB, time=185.60
memory used=1205.4MB, alloc=4.5MB, time=186.21
memory used=1209.2MB, alloc=4.5MB, time=186.81
memory used=1213.0MB, alloc=4.5MB, time=187.40
memory used=1216.9MB, alloc=4.5MB, time=188.01
memory used=1220.7MB, alloc=4.5MB, time=188.61
memory used=1224.5MB, alloc=4.5MB, time=189.21
memory used=1228.3MB, alloc=4.5MB, time=189.81
x[1] = 3.2
y1[1] (analytic) = 0.00170522420524691533833927771642
y1[1] (numeric) = 0.0017052242057155855365775134984371
absolute error = 4.686701982382357820171e-13
relative error = 2.7484374007602868090052409035117e-08 %
Correct digits = 9
h = 0.005
y2[1] (analytic) = 0.9416258565724200908627825853809
y2[1] (numeric) = 0.94162585657246208235209472887287
absolute error = 4.199148931214349197e-14
relative error = 4.4594664663304030992364962002050e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1232.1MB, alloc=4.5MB, time=190.42
memory used=1235.9MB, alloc=4.5MB, time=191.03
memory used=1239.8MB, alloc=4.5MB, time=191.64
memory used=1243.6MB, alloc=4.5MB, time=192.24
memory used=1247.4MB, alloc=4.5MB, time=192.85
memory used=1251.2MB, alloc=4.5MB, time=193.45
memory used=1255.0MB, alloc=4.5MB, time=194.06
memory used=1258.8MB, alloc=4.5MB, time=194.66
memory used=1262.6MB, alloc=4.5MB, time=195.26
memory used=1266.5MB, alloc=4.5MB, time=195.86
x[1] = 3.3
y1[1] (analytic) = 0.01252023009113511606340894889715
y1[1] (numeric) = 0.012520230091612160342676664116588
absolute error = 4.77044279267715219438e-13
relative error = 3.8101877984293910503683099604535e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 0.84225430585675161798834572239752
y2[1] (numeric) = 0.84225430585684304576015731365784
absolute error = 9.142777181159126032e-14
relative error = 1.0855126673242683741736270564109e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=1270.3MB, alloc=4.5MB, time=196.46
NO POLE
NO POLE
memory used=1274.1MB, alloc=4.5MB, time=197.07
memory used=1277.9MB, alloc=4.5MB, time=197.67
memory used=1281.7MB, alloc=4.5MB, time=198.27
memory used=1285.5MB, alloc=4.5MB, time=198.86
memory used=1289.3MB, alloc=4.5MB, time=199.45
memory used=1293.2MB, alloc=4.5MB, time=200.04
memory used=1297.0MB, alloc=4.5MB, time=200.64
memory used=1300.8MB, alloc=4.5MB, time=201.24
memory used=1304.6MB, alloc=4.5MB, time=201.83
memory used=1308.4MB, alloc=4.5MB, time=202.43
x[1] = 3.4
y1[1] (analytic) = 0.03320180742053898571779846023431
y1[1] (numeric) = 0.033201807421019067137669812821059
absolute error = 4.80081419871352586749e-13
relative error = 1.4459496550611554767630908430866e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 0.74445889797316868075009757063626
y2[1] (numeric) = 0.74445889797331160784835286570578
absolute error = 1.4292709825529506952e-13
relative error = 1.9198789704095437929418535191483e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1312.2MB, alloc=4.5MB, time=203.05
memory used=1316.0MB, alloc=4.5MB, time=203.64
memory used=1319.9MB, alloc=4.5MB, time=204.22
memory used=1323.7MB, alloc=4.5MB, time=204.81
memory used=1327.5MB, alloc=4.5MB, time=205.40
memory used=1331.3MB, alloc=4.5MB, time=205.99
memory used=1335.1MB, alloc=4.5MB, time=206.58
memory used=1338.9MB, alloc=4.5MB, time=207.18
memory used=1342.8MB, alloc=4.5MB, time=207.77
memory used=1346.6MB, alloc=4.5MB, time=208.36
x[1] = 3.5
y1[1] (analytic) = 0.06354331270920366230134237332824
y1[1] (numeric) = 0.063543312709681119265112297435446
absolute error = 4.77456963769924107206e-13
relative error = 7.5138821602665495472480421213141e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 0.64921677231038015187963119995636
y2[1] (numeric) = 0.64921677231057605496148951006228
absolute error = 1.9590308185831010592e-13
relative error = 3.0175295866301491172819755257866e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=1350.4MB, alloc=4.5MB, time=208.95
NO POLE
NO POLE
memory used=1354.2MB, alloc=4.5MB, time=209.55
memory used=1358.0MB, alloc=4.5MB, time=210.16
memory used=1361.8MB, alloc=4.5MB, time=210.75
memory used=1365.6MB, alloc=4.5MB, time=211.34
memory used=1369.5MB, alloc=4.5MB, time=211.93
memory used=1373.3MB, alloc=4.5MB, time=212.54
memory used=1377.1MB, alloc=4.5MB, time=213.13
memory used=1380.9MB, alloc=4.5MB, time=213.72
memory used=1384.7MB, alloc=4.5MB, time=214.31
memory used=1388.5MB, alloc=4.5MB, time=214.89
x[1] = 3.6
y1[1] (analytic) = 0.10324158366585299412970827473406
y1[1] (numeric) = 0.10324158366632190559380968432465
absolute error = 4.6891146410140959059e-13
relative error = 4.5418856186773255152339182762321e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 0.55747955670514761573327265250731
y2[1] (numeric) = 0.55747955670539734129166140796885
absolute error = 2.4972555838875546154e-13
relative error = 4.4795464763712574565163516475715e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1392.3MB, alloc=4.5MB, time=215.49
memory used=1396.2MB, alloc=4.5MB, time=216.10
memory used=1400.0MB, alloc=4.5MB, time=216.69
memory used=1403.8MB, alloc=4.5MB, time=217.30
memory used=1407.6MB, alloc=4.5MB, time=217.88
memory used=1411.4MB, alloc=4.5MB, time=218.47
memory used=1415.2MB, alloc=4.5MB, time=219.07
memory used=1419.0MB, alloc=4.5MB, time=219.66
memory used=1422.9MB, alloc=4.5MB, time=220.26
memory used=1426.7MB, alloc=4.5MB, time=220.85
x[1] = 3.7
y1[1] (analytic) = 0.1518999682895918411643298936456
y1[1] (numeric) = 0.1518999682900460972943739819315
absolute error = 4.5425613004408828590e-13
relative error = 2.9904952262930382403020630525947e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 0.47016385909150678678922237429879
y2[1] (numeric) = 0.47016385909181051467939994041942
absolute error = 3.0372789017756612063e-13
relative error = 6.4600433296692917408669089879626e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1430.5MB, alloc=4.5MB, time=221.44
memory used=1434.3MB, alloc=4.5MB, time=222.04
memory used=1438.1MB, alloc=4.5MB, time=222.63
memory used=1441.9MB, alloc=4.5MB, time=223.22
memory used=1445.7MB, alloc=4.5MB, time=223.82
memory used=1449.6MB, alloc=4.5MB, time=224.41
memory used=1453.4MB, alloc=4.5MB, time=225.01
memory used=1457.2MB, alloc=4.5MB, time=225.61
memory used=1461.0MB, alloc=4.5MB, time=226.20
memory used=1464.8MB, alloc=4.5MB, time=226.80
x[1] = 3.8
y1[1] (analytic) = 0.20903228808558330000343182564927
y1[1] (numeric) = 0.20903228808601667745604611851446
absolute error = 4.3337745261429286519e-13
relative error = 2.0732560341915062042083327042650e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 0.38814210905728092426641391388112
y2[1] (numeric) = 0.38814210905763813918089489813139
absolute error = 3.5721491448098425027e-13
relative error = 9.2031991929086847588656658022567e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=1468.6MB, alloc=4.5MB, time=227.40
NO POLE
NO POLE
memory used=1472.5MB, alloc=4.5MB, time=228.02
memory used=1476.3MB, alloc=4.5MB, time=228.62
memory used=1480.1MB, alloc=4.5MB, time=229.23
memory used=1483.9MB, alloc=4.5MB, time=229.82
memory used=1487.7MB, alloc=4.5MB, time=230.43
memory used=1491.5MB, alloc=4.5MB, time=231.03
memory used=1495.3MB, alloc=4.5MB, time=231.63
memory used=1499.2MB, alloc=4.5MB, time=232.23
memory used=1503.0MB, alloc=4.5MB, time=232.86
memory used=1506.8MB, alloc=4.5MB, time=233.45
x[1] = 3.9
y1[1] (analytic) = 0.27406769579985987062766951538565
y1[1] (numeric) = 0.27406769580026611156371709340264
absolute error = 4.0624093604757801699e-13
relative error = 1.4822649377263298969412909387938e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 0.31223384081602618190911187462131
y2[1] (numeric) = 0.31223384081643565335302558706921
absolute error = 4.0947144391371244790e-13
relative error = 1.3114255739978563626945875186375e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1510.6MB, alloc=4.5MB, time=234.05
memory used=1514.4MB, alloc=4.5MB, time=234.66
memory used=1518.2MB, alloc=4.5MB, time=235.28
memory used=1522.0MB, alloc=4.5MB, time=235.89
memory used=1525.9MB, alloc=4.5MB, time=236.49
memory used=1529.7MB, alloc=4.5MB, time=237.09
memory used=1533.5MB, alloc=4.5MB, time=237.70
memory used=1537.3MB, alloc=4.5MB, time=238.31
memory used=1541.1MB, alloc=4.5MB, time=238.92
memory used=1544.9MB, alloc=4.5MB, time=239.52
x[1] = 4
y1[1] (analytic) = 0.34635637913638808536083181690225
y1[1] (numeric) = 0.34635637913676097923236166052503
absolute error = 3.7289387152984362278e-13
relative error = 1.0766190374770190492015963042693e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 0.24319750469207174862736090548817
y2[1] (numeric) = 0.24319750469253151984584709881395
absolute error = 4.5977121848619332578e-13
relative error = 1.8905260523472052365573950667333e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1548.7MB, alloc=4.5MB, time=240.12
memory used=1552.6MB, alloc=4.5MB, time=240.72
memory used=1556.4MB, alloc=4.5MB, time=241.33
memory used=1560.2MB, alloc=4.5MB, time=241.95
memory used=1564.0MB, alloc=4.5MB, time=242.56
memory used=1567.8MB, alloc=4.5MB, time=243.17
memory used=1571.6MB, alloc=4.5MB, time=243.78
memory used=1575.5MB, alloc=4.5MB, time=244.38
memory used=1579.3MB, alloc=4.5MB, time=245.01
memory used=1583.1MB, alloc=4.5MB, time=245.65
x[1] = 4.1
y1[1] (analytic) = 0.42517605346673108846497132034021
y1[1] (numeric) = 0.42517605346706455556626515529844
absolute error = 3.3346710129383495823e-13
relative error = 7.8430358101041992169307780605731e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.18172288893558949573496297564155
y2[1] (numeric) = 0.18172288893609688193671702636873
absolute error = 5.0738620175405072718e-13
relative error = 2.7920874729979143643698544257117e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
memory used=1586.9MB, alloc=4.5MB, time=246.31
NO POLE
NO POLE
memory used=1590.7MB, alloc=4.5MB, time=246.96
memory used=1594.5MB, alloc=4.5MB, time=247.52
memory used=1598.3MB, alloc=4.5MB, time=248.11
memory used=1602.2MB, alloc=4.5MB, time=248.68
memory used=1606.0MB, alloc=4.5MB, time=249.26
memory used=1609.8MB, alloc=4.5MB, time=249.87
memory used=1613.6MB, alloc=4.5MB, time=250.45
memory used=1617.4MB, alloc=4.5MB, time=251.05
memory used=1621.2MB, alloc=4.5MB, time=251.62
memory used=1625.0MB, alloc=4.5MB, time=252.24
x[1] = 4.2
y1[1] (analytic) = 0.50973917865930042234445511862287
y1[1] (numeric) = 0.50973917865958859807756235771369
absolute error = 2.8817573310723909082e-13
relative error = 5.6533957987139545911605828349551e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.12842422758641193998142290209118
y2[1] (numeric) = 0.12842422758696353608923953639559
absolute error = 5.5159610781663430441e-13
relative error = 4.2951094056258626763973562536424e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1628.9MB, alloc=4.5MB, time=252.79
memory used=1632.7MB, alloc=4.5MB, time=253.34
memory used=1636.5MB, alloc=4.5MB, time=253.91
memory used=1640.3MB, alloc=4.5MB, time=254.47
memory used=1644.1MB, alloc=4.5MB, time=255.05
memory used=1647.9MB, alloc=4.5MB, time=255.62
memory used=1651.7MB, alloc=4.5MB, time=256.17
memory used=1655.6MB, alloc=4.5MB, time=256.73
memory used=1659.4MB, alloc=4.5MB, time=257.28
memory used=1663.2MB, alloc=4.5MB, time=257.84
x[1] = 4.3
y1[1] (analytic) = 0.59920082792002470309323760366397
y1[1] (numeric) = 0.59920082792026202187104969079202
absolute error = 2.3731877781208712805e-13
relative error = 3.9605882828279745039748367975776e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.08383406325054501596829063971536
y2[1] (numeric) = 0.083834063251136714009756462666521
absolute error = 5.91698041465822951161e-13
relative error = 7.0579668755585009355985643769715e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1667.0MB, alloc=4.5MB, time=258.39
memory used=1670.8MB, alloc=4.5MB, time=258.95
memory used=1674.6MB, alloc=4.5MB, time=259.49
memory used=1678.5MB, alloc=4.5MB, time=260.04
memory used=1682.3MB, alloc=4.5MB, time=260.59
memory used=1686.1MB, alloc=4.5MB, time=261.17
memory used=1689.9MB, alloc=4.5MB, time=261.74
memory used=1693.7MB, alloc=4.5MB, time=262.29
memory used=1697.5MB, alloc=4.5MB, time=262.84
memory used=1701.3MB, alloc=4.5MB, time=263.38
x[1] = 4.4
y1[1] (analytic) = 0.69266713002158031688086025778229
y1[1] (numeric) = 0.69266713002176159457654394070658
absolute error = 1.8127769568368292429e-13
relative error = 2.6170968395459323496333670209768e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.04839792611048404596460766661961
y2[1] (numeric) = 0.048397926111111062095359025650559
absolute error = 6.27016130751359030949e-13
relative error = 1.2955433861359891345738228045377e-09 %
Correct digits = 10
h = 0.005
TOP MAIN SOLVE Loop
memory used=1705.2MB, alloc=4.5MB, time=263.94
NO POLE
NO POLE
memory used=1709.0MB, alloc=4.5MB, time=264.49
memory used=1712.8MB, alloc=4.5MB, time=265.05
memory used=1716.6MB, alloc=4.5MB, time=265.60
memory used=1720.4MB, alloc=4.5MB, time=266.15
memory used=1724.2MB, alloc=4.5MB, time=266.70
memory used=1728.0MB, alloc=4.5MB, time=267.26
memory used=1731.9MB, alloc=4.5MB, time=267.84
memory used=1735.7MB, alloc=4.5MB, time=268.39
memory used=1739.5MB, alloc=4.5MB, time=268.96
memory used=1743.3MB, alloc=4.5MB, time=269.51
x[1] = 4.5
y1[1] (analytic) = 0.78920420056922029401951817520617
y1[1] (numeric) = 0.78920420056934080787032454917954
absolute error = 1.2051385080637397337e-13
relative error = 1.5270300223877714479722755084912e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.02246988233490294461086498550137
y2[1] (numeric) = 0.022469882335559855640509340902349
absolute error = 6.56911029644355400979e-13
relative error = 2.9235178887606437154152031435494e-09 %
Correct digits = 10
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1747.1MB, alloc=4.5MB, time=270.06
memory used=1750.9MB, alloc=4.5MB, time=270.62
memory used=1754.7MB, alloc=4.5MB, time=271.18
memory used=1758.6MB, alloc=4.5MB, time=271.75
memory used=1762.4MB, alloc=4.5MB, time=272.31
memory used=1766.2MB, alloc=4.5MB, time=272.86
memory used=1770.0MB, alloc=4.5MB, time=273.43
memory used=1773.8MB, alloc=4.5MB, time=274.00
memory used=1777.6MB, alloc=4.5MB, time=274.56
memory used=1781.4MB, alloc=4.5MB, time=275.11
x[1] = 4.6
y1[1] (analytic) = 0.88784747306494548257009217877081
y1[1] (numeric) = 0.88784747306500104745634591642952
absolute error = 5.556488625373765871e-14
relative error = 6.2583819788236444451504678671598e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 0.00630899636653554386189534009117
y2[1] (numeric) = 0.0063089963672163330302740042708927
absolute error = 6.807891683786641797227e-13
relative error = 1.0790768116300336499900499934160e-08 %
Correct digits = 9
h = 0.005
TOP MAIN SOLVE Loop
memory used=1785.3MB, alloc=4.5MB, time=275.68
NO POLE
NO POLE
memory used=1789.1MB, alloc=4.5MB, time=276.23
memory used=1792.9MB, alloc=4.5MB, time=276.80
memory used=1796.7MB, alloc=4.5MB, time=277.35
memory used=1800.5MB, alloc=4.5MB, time=277.90
memory used=1804.3MB, alloc=4.5MB, time=278.45
memory used=1808.2MB, alloc=4.5MB, time=279.00
memory used=1812.0MB, alloc=4.5MB, time=279.58
memory used=1815.8MB, alloc=4.5MB, time=280.14
memory used=1819.6MB, alloc=4.5MB, time=280.71
memory used=1823.4MB, alloc=4.5MB, time=281.26
x[1] = 4.7
y1[1] (analytic) = 0.98761133653710926284949170367289
y1[1] (numeric) = 0.98761133653709630289594131721513
absolute error = 1.295995355038645776e-14
relative error = 1.3122524085059943582855708670141e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 7.674243589911582046345842503e-05
y2[1] (numeric) = 7.6742436597227450908984381888466e-05
absolute error = 6.98111630445525956858466e-13
relative error = 9.0968135460705277566467727978186e-07 %
Correct digits = 8
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1827.2MB, alloc=4.5MB, time=281.81
memory used=1831.0MB, alloc=4.5MB, time=282.37
memory used=1834.9MB, alloc=4.5MB, time=282.93
memory used=1838.7MB, alloc=4.5MB, time=283.50
memory used=1842.5MB, alloc=4.5MB, time=284.06
memory used=1846.3MB, alloc=4.5MB, time=284.61
memory used=1850.1MB, alloc=4.5MB, time=285.16
memory used=1853.9MB, alloc=4.5MB, time=285.71
memory used=1857.7MB, alloc=4.5MB, time=286.26
memory used=1861.6MB, alloc=4.5MB, time=286.81
x[1] = 4.8
y1[1] (analytic) = 1.0874989834394465693202152576495
y1[1] (numeric) = 1.087498983439362183806725316674
absolute error = 8.43855134899409755e-14
relative error = 7.7595947007742353717947706861462e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 0.00383539116415932821840353349637
y2[1] (numeric) = 0.0038353911648677307565111630440808
absolute error = 7.084025381076295477108e-13
relative error = 1.8470150964716603942258912192038e-08 %
Correct digits = 9
h = 0.005
TOP MAIN SOLVE Loop
memory used=1865.4MB, alloc=4.5MB, time=287.36
NO POLE
NO POLE
memory used=1869.2MB, alloc=4.5MB, time=287.92
memory used=1873.0MB, alloc=4.5MB, time=288.47
memory used=1876.8MB, alloc=4.5MB, time=289.01
memory used=1880.6MB, alloc=4.5MB, time=289.56
memory used=1884.4MB, alloc=4.5MB, time=290.11
memory used=1888.3MB, alloc=4.5MB, time=290.69
memory used=1892.1MB, alloc=4.5MB, time=291.24
memory used=1895.9MB, alloc=4.5MB, time=291.80
memory used=1899.7MB, alloc=4.5MB, time=292.35
memory used=1903.5MB, alloc=4.5MB, time=292.90
x[1] = 4.9
y1[1] (analytic) = 1.1865123694225754044943291441219
y1[1] (numeric) = 1.1865123694224174271157907429258
absolute error = 1.579773785384011961e-13
relative error = 1.3314431657824351148068624514006e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.01754738737566748772362275008167
y2[1] (numeric) = 0.017547387376378744556286661960681
absolute error = 7.11256832663911879011e-13
relative error = 4.0533488971138432665231279838623e-09 %
Correct digits = 10
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1907.3MB, alloc=4.5MB, time=293.47
memory used=1911.2MB, alloc=4.5MB, time=294.02
memory used=1915.0MB, alloc=4.5MB, time=294.59
memory used=1918.8MB, alloc=4.5MB, time=295.14
memory used=1922.6MB, alloc=4.5MB, time=295.71
memory used=1926.4MB, alloc=4.5MB, time=296.26
memory used=1930.2MB, alloc=4.5MB, time=296.81
memory used=1934.0MB, alloc=4.5MB, time=297.20
memory used=1937.9MB, alloc=4.5MB, time=297.43
memory used=1941.7MB, alloc=4.5MB, time=297.67
x[1] = 5
y1[1] (analytic) = 1.2836621854632262644666391715136
y1[1] (numeric) = 1.2836621854629933150474766951284
absolute error = 2.329494191624763852e-13
relative error = 1.8147252587207244477405428153556e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.04107572533686153110684559384401
y2[1] (numeric) = 0.041075725337567878448343543949034
absolute error = 7.06347341497950105024e-13
relative error = 1.7196223212255024701053815502286e-09 %
Correct digits = 10
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1945.5MB, alloc=4.5MB, time=297.90
memory used=1949.3MB, alloc=4.5MB, time=298.13
memory used=1953.1MB, alloc=4.5MB, time=298.36
memory used=1956.9MB, alloc=4.5MB, time=298.59
memory used=1960.7MB, alloc=4.5MB, time=298.83
memory used=1964.6MB, alloc=4.5MB, time=299.06
memory used=1968.4MB, alloc=4.5MB, time=299.29
memory used=1972.2MB, alloc=4.5MB, time=299.52
memory used=1976.0MB, alloc=4.5MB, time=299.75
memory used=1979.8MB, alloc=4.5MB, time=299.98
x[1] = 5.1
y1[1] (analytic) = 1.377977742712980563320575552929
y1[1] (numeric) = 1.3779777427126720911666909584752
absolute error = 3.084721538845944538e-13
relative error = 2.2385858952791969736637031894606e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.07418531767226770305385375245514
y2[1] (numeric) = 0.074185317672961134084978886384954
absolute error = 6.93431031125133929814e-13
relative error = 9.3472812799500285743027580968634e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
memory used=1983.6MB, alloc=4.5MB, time=300.21
NO POLE
NO POLE
memory used=1987.4MB, alloc=4.5MB, time=300.45
memory used=1991.3MB, alloc=4.5MB, time=300.68
memory used=1995.1MB, alloc=4.5MB, time=300.91
memory used=1998.9MB, alloc=4.5MB, time=301.15
memory used=2002.7MB, alloc=4.5MB, time=301.38
memory used=2006.5MB, alloc=4.5MB, time=301.61
memory used=2010.3MB, alloc=4.5MB, time=301.84
memory used=2014.1MB, alloc=4.5MB, time=302.08
memory used=2018.0MB, alloc=4.5MB, time=302.31
memory used=2021.8MB, alloc=4.5MB, time=302.54
x[1] = 5.2
y1[1] (analytic) = 1.4685166713003769586390939266086
y1[1] (numeric) = 1.4685166712999932767987196466876
absolute error = 3.836818403742799210e-13
relative error = 2.6127169535945971141749852267213e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.1165453442798467353269155595782
y2[1] (numeric) = 0.11654534428051908968086019073817
absolute error = 6.7235435394463115997e-13
relative error = 5.7690365762718509640226915864836e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2025.6MB, alloc=4.5MB, time=302.77
memory used=2029.4MB, alloc=4.5MB, time=303.01
memory used=2033.2MB, alloc=4.5MB, time=303.24
memory used=2037.0MB, alloc=4.5MB, time=303.47
memory used=2040.9MB, alloc=4.5MB, time=303.71
memory used=2044.7MB, alloc=4.5MB, time=303.94
memory used=2048.5MB, alloc=4.5MB, time=304.17
memory used=2052.3MB, alloc=4.5MB, time=304.41
memory used=2056.1MB, alloc=4.5MB, time=304.64
memory used=2059.9MB, alloc=4.5MB, time=304.87
x[1] = 5.3
y1[1] (analytic) = 1.5543743361791609294449466335608
y1[1] (numeric) = 1.5543743361787032392487385637881
absolute error = 4.576901962080697727e-13
relative error = 2.9445300630292656762759942198937e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.16773255777609883643544033214541
y2[1] (numeric) = 0.16773255777674189404155339540194
absolute error = 6.4305760611306325653e-13
relative error = 3.8338269840936998002128243640833e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
memory used=2063.7MB, alloc=4.5MB, time=305.11
NO POLE
NO POLE
memory used=2067.6MB, alloc=4.5MB, time=305.35
memory used=2071.4MB, alloc=4.5MB, time=305.58
memory used=2075.2MB, alloc=4.5MB, time=305.81
memory used=2079.0MB, alloc=4.5MB, time=306.04
memory used=2082.8MB, alloc=4.5MB, time=306.27
memory used=2086.6MB, alloc=4.5MB, time=306.50
memory used=2090.4MB, alloc=4.5MB, time=306.74
memory used=2094.3MB, alloc=4.5MB, time=306.96
memory used=2098.1MB, alloc=4.5MB, time=307.20
x[1] = 5.4
y1[1] (analytic) = 1.6346928759426343624067518389807
y1[1] (numeric) = 1.6346928759421047677654767274989
absolute error = 5.295946412751114818e-13
relative error = 3.2397195159349084932666552596512e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.22723551244401263764153021726577
y2[1] (numeric) = 0.22723551244461821586631442966396
absolute error = 6.0557822478421239819e-13
relative error = 2.6649805669499727991244694546599e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
memory used=2101.9MB, alloc=4.5MB, time=307.44
NO POLE
NO POLE
memory used=2105.7MB, alloc=4.5MB, time=307.67
memory used=2109.5MB, alloc=4.5MB, time=307.91
memory used=2113.3MB, alloc=4.5MB, time=308.16
memory used=2117.1MB, alloc=4.5MB, time=308.41
memory used=2121.0MB, alloc=4.5MB, time=308.65
memory used=2124.8MB, alloc=4.5MB, time=308.89
memory used=2128.6MB, alloc=4.5MB, time=309.12
memory used=2132.4MB, alloc=4.5MB, time=309.35
memory used=2136.2MB, alloc=4.5MB, time=309.58
memory used=2140.0MB, alloc=4.5MB, time=309.81
x[1] = 5.5
y1[1] (analytic) = 1.7086697742912600000274211813258
y1[1] (numeric) = 1.7086697742906615110815898939676
absolute error = 5.984889458312873582e-13
relative error = 3.5026601092626858854238168498395e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.29445967442960809376808082447793
y2[1] (numeric) = 0.29445967443016814673286616722957
absolute error = 5.6005296478534275164e-13
relative error = 1.9019682945388365070860017251521e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2143.9MB, alloc=4.5MB, time=310.05
memory used=2147.7MB, alloc=4.5MB, time=310.29
memory used=2151.5MB, alloc=4.5MB, time=310.52
memory used=2155.3MB, alloc=4.5MB, time=310.75
memory used=2159.1MB, alloc=4.5MB, time=310.99
memory used=2162.9MB, alloc=4.5MB, time=311.23
memory used=2166.7MB, alloc=4.5MB, time=311.46
memory used=2170.6MB, alloc=4.5MB, time=311.70
memory used=2174.4MB, alloc=4.5MB, time=311.93
memory used=2178.2MB, alloc=4.5MB, time=312.17
x[1] = 5.6
y1[1] (analytic) = 1.7755658785102497976558096621573
y1[1] (numeric) = 1.775565878509586323494283777152
absolute error = 6.634741615258850053e-13
relative error = 3.7366913250358171506257426544814e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.36873336212767868853633084628333
y2[1] (numeric) = 0.36873336212818540744382624112538
absolute error = 5.0671890749539484205e-13
relative error = 1.3742149735828267051570889514393e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
memory used=2182.0MB, alloc=4.5MB, time=312.40
NO POLE
NO POLE
memory used=2185.8MB, alloc=4.5MB, time=312.63
memory used=2189.6MB, alloc=4.5MB, time=312.87
memory used=2193.4MB, alloc=4.5MB, time=313.10
memory used=2197.3MB, alloc=4.5MB, time=313.33
memory used=2201.1MB, alloc=4.5MB, time=313.56
memory used=2204.9MB, alloc=4.5MB, time=313.79
memory used=2208.7MB, alloc=4.5MB, time=314.03
memory used=2212.5MB, alloc=4.5MB, time=314.27
memory used=2216.3MB, alloc=4.5MB, time=314.50
x[1] = 5.7
y1[1] (analytic) = 1.8347127848391596827492340309974
y1[1] (numeric) = 1.8347127848384360130417995781169
absolute error = 7.236697074344528805e-13
relative error = 3.9443214949739038994000459922952e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.44931445740236223877264939212753
y2[1] (numeric) = 0.44931445740280815204076098295426
absolute error = 4.4591326811159082673e-13
relative error = 9.9243026963691569268412502896690e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=2220.1MB, alloc=4.5MB, time=314.74
NO POLE
NO POLE
memory used=2224.0MB, alloc=4.5MB, time=314.97
memory used=2227.8MB, alloc=4.5MB, time=315.20
memory used=2231.6MB, alloc=4.5MB, time=315.43
memory used=2235.4MB, alloc=4.5MB, time=315.67
memory used=2239.2MB, alloc=4.5MB, time=315.90
memory used=2243.0MB, alloc=4.5MB, time=316.13
memory used=2246.8MB, alloc=4.5MB, time=316.36
memory used=2250.7MB, alloc=4.5MB, time=316.59
memory used=2254.5MB, alloc=4.5MB, time=316.82
memory used=2258.3MB, alloc=4.5MB, time=317.05
x[1] = 5.8
y1[1] (analytic) = 1.8855195169413190041646581017615
y1[1] (numeric) = 1.8855195169405407796853510896093
absolute error = 7.782244793070121522e-13
relative error = 4.1273742982488151863592912964510e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.53539782058624278858177347329741
y2[1] (numeric) = 0.53539782058662086056326072675867
absolute error = 3.7807198148725346126e-13
relative error = 7.0615151379076819672904044479590e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2262.1MB, alloc=4.5MB, time=317.29
memory used=2265.9MB, alloc=4.5MB, time=317.52
memory used=2269.7MB, alloc=4.5MB, time=317.75
memory used=2273.6MB, alloc=4.5MB, time=317.98
memory used=2277.4MB, alloc=4.5MB, time=318.22
memory used=2281.2MB, alloc=4.5MB, time=318.45
memory used=2285.0MB, alloc=4.5MB, time=318.68
memory used=2288.8MB, alloc=4.5MB, time=318.91
memory used=2292.6MB, alloc=4.5MB, time=319.14
memory used=2296.4MB, alloc=4.5MB, time=319.38
x[1] = 5.9
y1[1] (analytic) = 1.9274784307440357409061046800325
y1[1] (numeric) = 1.9274784307432094130581614880085
absolute error = 8.263278479431920240e-13
relative error = 4.2870925804560988708793396397221e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.62612333516976364018515353101662
y2[1] (numeric) = 0.62612333517006736724628869255859
absolute error = 3.0372706113516154197e-13
relative error = 4.8509142540233012681294745692787e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=2300.3MB, alloc=4.5MB, time=319.61
NO POLE
NO POLE
memory used=2304.1MB, alloc=4.5MB, time=319.84
memory used=2307.9MB, alloc=4.5MB, time=320.08
memory used=2311.7MB, alloc=4.5MB, time=320.31
memory used=2315.5MB, alloc=4.5MB, time=320.54
memory used=2319.3MB, alloc=4.5MB, time=320.78
memory used=2323.1MB, alloc=4.5MB, time=321.01
memory used=2327.0MB, alloc=4.5MB, time=321.25
memory used=2330.8MB, alloc=4.5MB, time=321.48
memory used=2334.6MB, alloc=4.5MB, time=321.71
memory used=2338.4MB, alloc=4.5MB, time=321.94
x[1] = 6
y1[1] (analytic) = 1.9601702866503660205456522979229
y1[1] (numeric) = 1.9601702866494988001337735863112
absolute error = 8.672204118787116117e-13
relative error = 4.4242095586534977973227413601885e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.72058450180107412718844455338811
y2[1] (numeric) = 0.72058450180129762992909604217176
absolute error = 2.2350274065148878365e-13
relative error = 3.1016867569709313312687446267454e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2342.2MB, alloc=4.5MB, time=322.18
memory used=2346.0MB, alloc=4.5MB, time=322.41
memory used=2349.8MB, alloc=4.5MB, time=322.64
memory used=2353.7MB, alloc=4.5MB, time=322.87
memory used=2357.5MB, alloc=4.5MB, time=323.11
memory used=2361.3MB, alloc=4.5MB, time=323.34
memory used=2365.1MB, alloc=4.5MB, time=323.57
memory used=2368.9MB, alloc=4.5MB, time=323.81
memory used=2372.7MB, alloc=4.5MB, time=324.04
memory used=2376.6MB, alloc=4.5MB, time=324.27
x[1] = 6.1
y1[1] (analytic) = 1.983268438442584596585021274648
y1[1] (numeric) = 1.983268438441684392214584727743
absolute error = 9.002043704365469050e-13
relative error = 4.5389940816254648557473763973924e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.81783749572790445997587163677534
y2[1] (numeric) = 0.81783749572804257039742644713165
absolute error = 1.3811042155481035631e-13
relative error = 1.6887269448545785838040164868466e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=2380.4MB, alloc=4.5MB, time=324.50
NO POLE
NO POLE
memory used=2384.2MB, alloc=4.5MB, time=324.73
memory used=2388.0MB, alloc=4.5MB, time=324.97
memory used=2391.8MB, alloc=4.5MB, time=325.20
memory used=2395.6MB, alloc=4.5MB, time=325.44
memory used=2399.4MB, alloc=4.5MB, time=325.66
memory used=2403.3MB, alloc=4.5MB, time=325.89
memory used=2407.1MB, alloc=4.5MB, time=326.13
memory used=2410.9MB, alloc=4.5MB, time=326.36
memory used=2414.7MB, alloc=4.5MB, time=326.60
x[1] = 6.2
y1[1] (analytic) = 1.9965420970232174751394026238693
y1[1] (numeric) = 1.9965420970222928217537343634301
absolute error = 9.246533856682604392e-13
relative error = 4.6312741767222942251531162078931e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 0.91691059718250342199942071090163
y2[1] (numeric) = 0.91691059718255176446560053455173
absolute error = 4.834246617982365010e-14
relative error = 5.2723205870202724475555447122703e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
memory used=2418.5MB, alloc=4.5MB, time=326.83
NO POLE
NO POLE
memory used=2422.3MB, alloc=4.5MB, time=327.07
memory used=2426.1MB, alloc=4.5MB, time=327.31
memory used=2430.0MB, alloc=4.5MB, time=327.54
memory used=2433.8MB, alloc=4.5MB, time=327.77
memory used=2437.6MB, alloc=4.5MB, time=328.00
memory used=2441.4MB, alloc=4.5MB, time=328.24
memory used=2445.2MB, alloc=4.5MB, time=328.47
memory used=2449.0MB, alloc=4.5MB, time=328.70
memory used=2452.8MB, alloc=4.5MB, time=328.93
memory used=2456.7MB, alloc=4.5MB, time=329.16
x[1] = 6.3
y1[1] (analytic) = 1.9998586363834151422866736621397
y1[1] (numeric) = 1.9998586363824751204808988293657
absolute error = 9.400218057748327740e-13
relative error = 4.7004412645625154995893473946841e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.0168139004843498903109663674941
y2[1] (numeric) = 1.0168139004843049551996091852313
absolute error = 4.49351113571822628e-14
relative error = 4.4192070285209356800437456488451e-12 %
Correct digits = 13
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2460.5MB, alloc=4.5MB, time=329.39
memory used=2464.3MB, alloc=4.5MB, time=329.62
memory used=2468.1MB, alloc=4.5MB, time=329.86
memory used=2471.9MB, alloc=4.5MB, time=330.10
memory used=2475.7MB, alloc=4.5MB, time=330.33
memory used=2479.6MB, alloc=4.5MB, time=330.56
memory used=2483.4MB, alloc=4.5MB, time=330.80
memory used=2487.2MB, alloc=4.5MB, time=331.03
memory used=2491.0MB, alloc=4.5MB, time=331.26
memory used=2494.8MB, alloc=4.5MB, time=331.49
x[1] = 6.4
y1[1] (analytic) = 1.9931849187581926585947390986722
y1[1] (numeric) = 1.9931849187572468054665173636342
absolute error = 9.458531282217350380e-13
relative error = 4.7454359067247345655910873952328e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.116549204850493289480420488799
y2[1] (numeric) = 1.1165492048503524984912540222154
absolute error = 1.407909891664665836e-13
relative error = 1.2609474670246941279518961964540e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=2498.6MB, alloc=4.5MB, time=331.73
NO POLE
NO POLE
memory used=2502.4MB, alloc=4.5MB, time=331.96
memory used=2506.3MB, alloc=4.5MB, time=332.19
memory used=2510.1MB, alloc=4.5MB, time=332.43
memory used=2513.9MB, alloc=4.5MB, time=332.68
memory used=2517.7MB, alloc=4.5MB, time=332.94
memory used=2521.5MB, alloc=4.5MB, time=333.20
memory used=2525.3MB, alloc=4.5MB, time=333.45
memory used=2529.1MB, alloc=4.5MB, time=333.68
memory used=2533.0MB, alloc=4.5MB, time=333.91
memory used=2536.8MB, alloc=4.5MB, time=334.14
x[1] = 6.5
y1[1] (analytic) = 1.9765876257280234998863132539441
y1[1] (numeric) = 1.9765876257270817122984120018375
absolute error = 9.417875879012521066e-13
relative error = 4.7647145800296593891138330708805e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.2151199880878155242969457490747
y2[1] (numeric) = 1.2151199880875772864606631211124
absolute error = 2.382378362826279623e-13
relative error = 1.9606116154630381127805392669551e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2540.6MB, alloc=4.5MB, time=334.37
memory used=2544.4MB, alloc=4.5MB, time=334.61
memory used=2548.2MB, alloc=4.5MB, time=334.84
memory used=2552.0MB, alloc=4.5MB, time=335.07
memory used=2555.8MB, alloc=4.5MB, time=335.30
memory used=2559.7MB, alloc=4.5MB, time=335.53
memory used=2563.5MB, alloc=4.5MB, time=335.76
memory used=2567.3MB, alloc=4.5MB, time=335.99
memory used=2571.1MB, alloc=4.5MB, time=336.23
memory used=2574.9MB, alloc=4.5MB, time=336.46
x[1] = 6.6
y1[1] (analytic) = 1.9502325919585294662197377216682
y1[1] (numeric) = 1.9502325919576018974554582577568
absolute error = 9.275687642794639114e-13
relative error = 4.7561955845889591633161624064587e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.3115413635133781743549851055926
y2[1] (numeric) = 1.3115413635130419318817750028553
absolute error = 3.362424732101027373e-13
relative error = 2.5637199295748551363052740288597e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=2578.7MB, alloc=4.5MB, time=336.69
NO POLE
NO POLE
memory used=2582.6MB, alloc=4.5MB, time=336.93
memory used=2586.4MB, alloc=4.5MB, time=337.16
memory used=2590.2MB, alloc=4.5MB, time=337.39
memory used=2594.0MB, alloc=4.5MB, time=337.63
memory used=2597.8MB, alloc=4.5MB, time=337.86
memory used=2601.6MB, alloc=4.5MB, time=338.09
memory used=2605.4MB, alloc=4.5MB, time=338.32
memory used=2609.3MB, alloc=4.5MB, time=338.57
memory used=2613.1MB, alloc=4.5MB, time=338.80
x[1] = 6.7
y1[1] (analytic) = 1.9143831482353194411379018434766
y1[1] (numeric) = 1.9143831482344163920264902209375
absolute error = 9.030491114116225391e-13
relative error = 4.7171806346292498184446574458389e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.4048499206165981616321928483868
y2[1] (numeric) = 1.4048499206161644248423494373857
absolute error = 4.337367898434110011e-13
relative error = 3.0874243823357371958090554940112e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=2616.9MB, alloc=4.5MB, time=339.05
NO POLE
NO POLE
memory used=2620.7MB, alloc=4.5MB, time=339.31
memory used=2624.5MB, alloc=4.5MB, time=339.54
memory used=2628.3MB, alloc=4.5MB, time=339.78
memory used=2632.1MB, alloc=4.5MB, time=340.01
memory used=2636.0MB, alloc=4.5MB, time=340.25
memory used=2639.8MB, alloc=4.5MB, time=340.48
memory used=2643.6MB, alloc=4.5MB, time=340.71
memory used=2647.4MB, alloc=4.5MB, time=340.95
memory used=2651.2MB, alloc=4.5MB, time=341.18
memory used=2655.0MB, alloc=4.5MB, time=341.41
x[1] = 6.8
y1[1] (analytic) = 1.8693974903498251724416246398463
y1[1] (numeric) = 1.8693974903489569781157075373864
absolute error = 8.681943259171024599e-13
relative error = 4.6442467714805534329166970759452e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.4941133511386083222220793776203
y2[1] (numeric) = 1.4941133511380786929163478452901
absolute error = 5.296293057315323302e-13
relative error = 3.5447732618674580249533316812957e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2658.8MB, alloc=4.5MB, time=341.64
memory used=2662.7MB, alloc=4.5MB, time=341.87
memory used=2666.5MB, alloc=4.5MB, time=342.11
memory used=2670.3MB, alloc=4.5MB, time=342.34
memory used=2674.1MB, alloc=4.5MB, time=342.57
memory used=2677.9MB, alloc=4.5MB, time=342.82
memory used=2681.7MB, alloc=4.5MB, time=343.07
memory used=2685.5MB, alloc=4.5MB, time=343.31
memory used=2689.4MB, alloc=4.5MB, time=343.54
memory used=2693.2MB, alloc=4.5MB, time=343.77
x[1] = 6.9
y1[1] (analytic) = 1.8157251001253570726567558363581
y1[1] (numeric) = 1.8157251001245339861763986142407
absolute error = 8.230864803572221174e-13
relative error = 4.5331007447129331056692595450996e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.5784397643881998701737832329889
y2[1] (numeric) = 1.5784397643875770529254763768184
absolute error = 6.228172483068561705e-13
relative error = 3.9457777379820312860420129281921e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=2697.0MB, alloc=4.5MB, time=344.00
NO POLE
NO POLE
memory used=2700.8MB, alloc=4.5MB, time=344.24
memory used=2704.6MB, alloc=4.5MB, time=344.48
memory used=2708.4MB, alloc=4.5MB, time=344.71
memory used=2712.3MB, alloc=4.5MB, time=344.95
memory used=2716.1MB, alloc=4.5MB, time=345.18
memory used=2719.9MB, alloc=4.5MB, time=345.41
memory used=2723.7MB, alloc=4.5MB, time=345.65
memory used=2727.5MB, alloc=4.5MB, time=345.88
memory used=2731.3MB, alloc=4.5MB, time=346.11
memory used=2735.1MB, alloc=4.5MB, time=346.35
x[1] = 7
y1[1] (analytic) = 1.7539022543433046381411975217192
y1[1] (numeric) = 1.7539022543425367122783723105878
absolute error = 7.679258628252111314e-13
relative error = 4.3783846045214054281623545316121e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.6569865987187890903969990915936
y2[1] (numeric) = 1.6569865987180768913803174589222
absolute error = 7.121990166816326714e-13
relative error = 4.2981579768497666819617513452123e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2739.0MB, alloc=4.5MB, time=346.58
memory used=2742.8MB, alloc=4.5MB, time=346.82
memory used=2746.6MB, alloc=4.5MB, time=347.07
memory used=2750.4MB, alloc=4.5MB, time=347.32
memory used=2754.2MB, alloc=4.5MB, time=347.58
memory used=2758.0MB, alloc=4.5MB, time=347.85
memory used=2761.8MB, alloc=4.5MB, time=348.09
memory used=2765.7MB, alloc=4.5MB, time=348.35
memory used=2769.5MB, alloc=4.5MB, time=348.60
memory used=2773.3MB, alloc=4.5MB, time=348.86
x[1] = 7.1
y1[1] (analytic) = 1.6845466664428063406217999420893
y1[1] (numeric) = 1.6845466664421033091440063563372
absolute error = 7.030314777935857521e-13
relative error = 4.1734164555865395375226261400146e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.7289690401258761520759857678532
y2[1] (numeric) = 1.7289690401250794651839485130786
absolute error = 7.966868920372547746e-13
relative error = 4.6078725156307752534861500047707e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2777.1MB, alloc=4.5MB, time=349.11
memory used=2780.9MB, alloc=4.5MB, time=349.34
memory used=2784.7MB, alloc=4.5MB, time=349.60
memory used=2788.5MB, alloc=4.5MB, time=349.86
memory used=2792.4MB, alloc=4.5MB, time=350.11
memory used=2796.2MB, alloc=4.5MB, time=350.37
memory used=2800.0MB, alloc=4.5MB, time=350.65
memory used=2803.8MB, alloc=4.5MB, time=350.94
memory used=2807.6MB, alloc=4.5MB, time=351.18
memory used=2811.4MB, alloc=4.5MB, time=351.41
x[1] = 7.2
y1[1] (analytic) = 1.6083513145322546710048504790937
y1[1] (numeric) = 1.6083513145316258308266356023584
absolute error = 6.288401782148767353e-13
relative error = 3.9098434063067734323968130062200e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.7936678638491530524644457476436
y2[1] (numeric) = 1.7936678638482778326138587662411
absolute error = 8.752198505869814025e-13
relative error = 4.8794978614869532963386869343875e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=2815.3MB, alloc=4.5MB, time=351.64
NO POLE
NO POLE
memory used=2819.1MB, alloc=4.5MB, time=351.87
memory used=2822.9MB, alloc=4.5MB, time=352.11
memory used=2826.7MB, alloc=4.5MB, time=352.34
memory used=2830.5MB, alloc=4.5MB, time=352.57
memory used=2834.3MB, alloc=4.5MB, time=352.80
memory used=2838.1MB, alloc=4.5MB, time=353.03
memory used=2842.0MB, alloc=4.5MB, time=353.27
memory used=2845.8MB, alloc=4.5MB, time=353.50
memory used=2849.6MB, alloc=4.5MB, time=353.74
memory used=2853.4MB, alloc=4.5MB, time=353.98
x[1] = 7.3
y1[1] (analytic) = 1.5260775173811051889154065767377
y1[1] (numeric) = 1.5260775173805592845010346615213
absolute error = 5.459044143719152164e-13
relative error = 3.5771735587110892212457731286241e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.8504366206285645175173662279669
y2[1] (numeric) = 1.8504366206276177411857091711811
absolute error = 9.467763316570567858e-13
relative error = 5.1165023492425890422941701088846e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2857.2MB, alloc=4.5MB, time=354.21
memory used=2861.0MB, alloc=4.5MB, time=354.44
memory used=2864.8MB, alloc=4.5MB, time=354.68
memory used=2868.7MB, alloc=4.5MB, time=354.91
memory used=2872.5MB, alloc=4.5MB, time=355.15
memory used=2876.3MB, alloc=4.5MB, time=355.38
memory used=2880.1MB, alloc=4.5MB, time=355.61
memory used=2883.9MB, alloc=4.5MB, time=355.84
memory used=2887.7MB, alloc=4.5MB, time=356.08
memory used=2891.5MB, alloc=4.5MB, time=356.31
x[1] = 7.4
y1[1] (analytic) = 1.4385473275743906491340984687003
y1[1] (numeric) = 1.4385473275739357605332478455027
absolute error = 4.548886008506231976e-13
relative error = 3.1621385833557140539279128387410e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.8987080958116267592694988965346
y2[1] (numeric) = 1.8987080958106163724578358886144
absolute error = 1.0103868116630079202e-12
relative error = 5.3214436378705454181780566813798e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2895.4MB, alloc=4.5MB, time=356.54
memory used=2899.2MB, alloc=4.5MB, time=356.77
memory used=2903.0MB, alloc=4.5MB, time=357.00
memory used=2906.8MB, alloc=4.5MB, time=357.23
memory used=2910.6MB, alloc=4.5MB, time=357.47
memory used=2914.4MB, alloc=4.5MB, time=357.70
memory used=2918.2MB, alloc=4.5MB, time=357.93
memory used=2922.1MB, alloc=4.5MB, time=358.16
memory used=2925.9MB, alloc=4.5MB, time=358.39
memory used=2929.7MB, alloc=4.5MB, time=358.62
x[1] = 7.5
y1[1] (analytic) = 1.3466353178350258109716193361719
y1[1] (numeric) = 1.3466353178346692468525370358664
absolute error = 3.565641190823003055e-13
relative error = 2.6478149975714688532486096513685e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.937999976774738857948463798149
y2[1] (numeric) = 1.937999976773673711913766772617
absolute error = 1.0651460346970255320e-12
relative error = 5.4961096360262316212874350785223e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=2933.5MB, alloc=4.5MB, time=358.86
NO POLE
NO POLE
memory used=2937.3MB, alloc=4.5MB, time=359.09
memory used=2941.1MB, alloc=4.5MB, time=359.32
memory used=2945.0MB, alloc=4.5MB, time=359.56
memory used=2948.8MB, alloc=4.5MB, time=359.80
memory used=2952.6MB, alloc=4.5MB, time=360.02
memory used=2956.4MB, alloc=4.5MB, time=360.25
memory used=2960.2MB, alloc=4.5MB, time=360.49
memory used=2964.0MB, alloc=4.5MB, time=360.72
memory used=2967.8MB, alloc=4.5MB, time=360.95
memory used=2971.7MB, alloc=4.5MB, time=361.18
x[1] = 7.6
y1[1] (analytic) = 1.2512598425822553800581527493518
y1[1] (numeric) = 1.2512598425820035770691622573167
absolute error = 2.518029889904920351e-13
relative error = 2.0123956705174848447149802511379e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.9679196720314864259034630180288
y2[1] (numeric) = 1.9679196720303762011513536695897
absolute error = 1.1102247521093484391e-12
relative error = 5.6416162096863525129891250869679e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=2975.5MB, alloc=4.5MB, time=361.42
memory used=2979.3MB, alloc=4.5MB, time=361.65
memory used=2983.1MB, alloc=4.5MB, time=361.87
memory used=2986.9MB, alloc=4.5MB, time=362.11
memory used=2990.7MB, alloc=4.5MB, time=362.34
memory used=2994.5MB, alloc=4.5MB, time=362.57
memory used=2998.4MB, alloc=4.5MB, time=362.80
memory used=3002.2MB, alloc=4.5MB, time=363.03
memory used=3006.0MB, alloc=4.5MB, time=363.27
memory used=3009.8MB, alloc=4.5MB, time=363.50
x[1] = 7.7
y1[1] (analytic) = 1.153373862037864525977384239572
y1[1] (numeric) = 1.1533738620377229557181898507918
absolute error = 1.415702591943887802e-13
relative error = 1.2274446634697632775505428374369e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.9881682338770003685523936187237
y2[1] (numeric) = 1.988168233875855487725531172718
absolute error = 1.1448808268624460057e-12
relative error = 5.7584705728342050430127202300232e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=3013.6MB, alloc=4.5MB, time=363.73
NO POLE
NO POLE
memory used=3017.4MB, alloc=4.5MB, time=363.96
memory used=3021.2MB, alloc=4.5MB, time=364.19
memory used=3025.1MB, alloc=4.5MB, time=364.43
memory used=3028.9MB, alloc=4.5MB, time=364.66
memory used=3032.7MB, alloc=4.5MB, time=364.89
memory used=3036.5MB, alloc=4.5MB, time=365.12
memory used=3040.3MB, alloc=4.5MB, time=365.36
memory used=3044.1MB, alloc=4.5MB, time=365.59
memory used=3048.0MB, alloc=4.5MB, time=365.82
x[1] = 7.8
y1[1] (analytic) = 1.0539554205626495730325679129525
y1[1] (numeric) = 1.0539554205626226578517867776119
absolute error = 2.69151807811353406e-14
relative error = 2.5537304762631029478365496890653e-12 %
Correct digits = 13
h = 0.005
memory used=3051.8MB, alloc=4.5MB, time=366.05
y2[1] (analytic) = 1.9985433453746049634387733205961
y2[1] (numeric) = 1.99854334537343649387523063419
absolute error = 1.1684695635426864061e-12
relative error = 5.8466060605939454425144302056950e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3055.6MB, alloc=4.5MB, time=366.28
memory used=3059.4MB, alloc=4.5MB, time=366.53
memory used=3063.2MB, alloc=4.5MB, time=366.76
memory used=3067.0MB, alloc=4.5MB, time=366.99
memory used=3070.8MB, alloc=4.5MB, time=367.22
memory used=3074.7MB, alloc=4.5MB, time=367.46
memory used=3078.5MB, alloc=4.5MB, time=367.69
memory used=3082.3MB, alloc=4.5MB, time=367.92
memory used=3086.1MB, alloc=4.5MB, time=368.16
memory used=3089.9MB, alloc=4.5MB, time=368.39
x[1] = 7.9
y1[1] (analytic) = 0.95399787436046340550224704004151
y1[1] (numeric) = 0.9539978743605544442575666311571
absolute error = 9.103875531959111559e-14
relative error = 9.5428677323438741310463564279958e-12 %
Correct digits = 13
h = 0.005
y2[1] (analytic) = 1.9989413418397720363049105120439
y2[1] (numeric) = 1.9989413418385915831732190382528
absolute error = 1.1804531316914737911e-12
relative error = 5.9053915539363269492624250752968e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3093.7MB, alloc=4.5MB, time=368.62
memory used=3097.5MB, alloc=4.5MB, time=368.85
memory used=3101.4MB, alloc=4.5MB, time=369.08
memory used=3105.2MB, alloc=4.5MB, time=369.32
memory used=3109.0MB, alloc=4.5MB, time=369.56
memory used=3112.8MB, alloc=4.5MB, time=369.79
memory used=3116.6MB, alloc=4.5MB, time=370.02
memory used=3120.4MB, alloc=4.5MB, time=370.25
memory used=3124.2MB, alloc=4.5MB, time=370.50
memory used=3128.1MB, alloc=4.5MB, time=370.73
x[1] = 8
y1[1] (analytic) = 0.85449996619138647413115861816881
y1[1] (numeric) = 0.85449996619159757895418119740613
absolute error = 2.1110482302257923732e-13
relative error = 2.4705070962553680554876443463391e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.9893582466233817778081235982453
y2[1] (numeric) = 1.9893582466222013688496151907816
absolute error = 1.1804089585084074637e-12
relative error = 5.9336168360422932214873387949265e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=3131.9MB, alloc=4.5MB, time=370.96
NO POLE
NO POLE
memory used=3135.7MB, alloc=4.5MB, time=371.19
memory used=3139.5MB, alloc=4.5MB, time=371.42
memory used=3143.3MB, alloc=4.5MB, time=371.65
memory used=3147.1MB, alloc=4.5MB, time=371.88
memory used=3151.0MB, alloc=4.5MB, time=372.11
memory used=3154.8MB, alloc=4.5MB, time=372.35
memory used=3158.6MB, alloc=4.5MB, time=372.58
memory used=3162.4MB, alloc=4.5MB, time=372.81
memory used=3166.2MB, alloc=4.5MB, time=373.05
memory used=3170.0MB, alloc=4.5MB, time=373.28
x[1] = 8.1
y1[1] (analytic) = 0.75645584626420853553494823189785
y1[1] (numeric) = 0.75645584626454058053503548494036
absolute error = 3.3204500008725304251e-13
relative error = 4.3894828987980239320575952298983e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.9698898108450862432243199360998
y2[1] (numeric) = 1.9698898108439182062474142297979
absolute error = 1.1680369769057063019e-12
relative error = 5.9294533657424034036558383951963e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3173.8MB, alloc=4.5MB, time=373.52
memory used=3177.7MB, alloc=4.5MB, time=373.75
memory used=3181.5MB, alloc=4.5MB, time=373.98
memory used=3185.3MB, alloc=4.5MB, time=374.22
memory used=3189.1MB, alloc=4.5MB, time=374.45
memory used=3192.9MB, alloc=4.5MB, time=374.68
memory used=3196.7MB, alloc=4.5MB, time=374.91
memory used=3200.5MB, alloc=4.5MB, time=375.15
memory used=3204.4MB, alloc=4.5MB, time=375.38
memory used=3208.2MB, alloc=4.5MB, time=375.61
x[1] = 8.2
y1[1] (analytic) = 0.66084513901616479259951187548036
y1[1] (numeric) = 0.66084513901661737532083677105669
absolute error = 4.5258272132489557633e-13
relative error = 6.8485443049286777987516674583424e-11 %
Correct digits = 12
h = 0.005
y2[1] (analytic) = 1.9407305566797729011536487499456
y2[1] (numeric) = 1.9407305566786297355273882753246
absolute error = 1.1431656262604746210e-12
relative error = 5.8903881444326679484392822299817e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=3212.0MB, alloc=4.5MB, time=375.84
NO POLE
NO POLE
memory used=3215.8MB, alloc=4.5MB, time=376.07
memory used=3219.6MB, alloc=4.5MB, time=376.31
memory used=3223.4MB, alloc=4.5MB, time=376.54
memory used=3227.2MB, alloc=4.5MB, time=376.77
memory used=3231.1MB, alloc=4.5MB, time=377.01
memory used=3234.9MB, alloc=4.5MB, time=377.24
memory used=3238.7MB, alloc=4.5MB, time=377.47
memory used=3242.5MB, alloc=4.5MB, time=377.71
memory used=3246.3MB, alloc=4.5MB, time=377.94
memory used=3250.1MB, alloc=4.5MB, time=378.17
x[1] = 8.3
y1[1] (analytic) = 0.56862315502937982629067353455349
y1[1] (numeric) = 0.56862315502995124260543084107344
absolute error = 5.7141631475730651995e-13
relative error = 1.0049121455980496884178789183114e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.902171833756293640000504405253
y2[1] (numeric) = 1.9021718337551878834845979267977
absolute error = 1.1057565159064784553e-12
relative error = 5.8131263237291107999726963929190e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3253.9MB, alloc=4.5MB, time=378.40
memory used=3257.8MB, alloc=4.5MB, time=378.63
memory used=3261.6MB, alloc=4.5MB, time=378.87
memory used=3265.4MB, alloc=4.5MB, time=379.10
memory used=3269.2MB, alloc=4.5MB, time=379.33
memory used=3273.0MB, alloc=4.5MB, time=379.57
memory used=3276.8MB, alloc=4.5MB, time=379.80
memory used=3280.7MB, alloc=4.5MB, time=380.04
memory used=3284.5MB, alloc=4.5MB, time=380.28
memory used=3288.3MB, alloc=4.5MB, time=380.51
x[1] = 8.4
y1[1] (analytic) = 0.48071134588331470085519515941454
y1[1] (numeric) = 0.48071134588400193383486665886312
absolute error = 6.8723297967149944858e-13
relative error = 1.4296167243747866598640423838443e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.8545989080882806628332392814224
y2[1] (numeric) = 1.854598908087224755157938495443
absolute error = 1.0559076753007859794e-12
relative error = 5.6934557153881586075180838088076e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3292.1MB, alloc=4.5MB, time=380.74
memory used=3295.9MB, alloc=4.5MB, time=380.97
memory used=3299.7MB, alloc=4.5MB, time=381.20
memory used=3303.5MB, alloc=4.5MB, time=381.44
memory used=3307.4MB, alloc=4.5MB, time=381.67
memory used=3311.2MB, alloc=4.5MB, time=381.90
memory used=3315.0MB, alloc=4.5MB, time=382.13
memory used=3318.8MB, alloc=4.5MB, time=382.37
memory used=3322.6MB, alloc=4.5MB, time=382.60
memory used=3326.4MB, alloc=4.5MB, time=382.83
x[1] = 8.5
y1[1] (analytic) = 0.397988097315176384651573477043
y1[1] (numeric) = 0.39798809731597510780876612689928
absolute error = 7.9872315719264985628e-13
relative error = 2.0069021224022227503746119472407e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.7984871126234902866669131603391
y2[1] (numeric) = 1.7984871126224964313371643967097
absolute error = 9.938553297487636294e-13
relative error = 5.5260631158985973415910295272860e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=3330.2MB, alloc=4.5MB, time=383.07
NO POLE
NO POLE
memory used=3334.1MB, alloc=4.5MB, time=383.30
memory used=3337.9MB, alloc=4.5MB, time=383.54
memory used=3341.7MB, alloc=4.5MB, time=383.77
memory used=3345.5MB, alloc=4.5MB, time=384.00
memory used=3349.3MB, alloc=4.5MB, time=384.24
memory used=3353.1MB, alloc=4.5MB, time=384.47
memory used=3356.9MB, alloc=4.5MB, time=384.71
memory used=3360.8MB, alloc=4.5MB, time=384.94
memory used=3364.6MB, alloc=4.5MB, time=385.18
memory used=3368.4MB, alloc=4.5MB, time=385.41
x[1] = 8.6
y1[1] (analytic) = 0.32127995267998729913553021483952
y1[1] (numeric) = 0.32127995268089189427279491475957
absolute error = 9.0459513726469992005e-13
relative error = 2.8155978289928565379681238678331e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.7343970978741131437171641875634
y2[1] (numeric) = 1.734397097873193169560748293724
absolute error = 9.199741564158938394e-13
relative error = 5.3042879139011788892534578529303e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3372.2MB, alloc=4.5MB, time=385.64
memory used=3376.0MB, alloc=4.5MB, time=385.87
memory used=3379.8MB, alloc=4.5MB, time=386.11
memory used=3383.7MB, alloc=4.5MB, time=386.35
memory used=3387.5MB, alloc=4.5MB, time=386.58
memory used=3391.3MB, alloc=4.5MB, time=386.82
memory used=3395.1MB, alloc=4.5MB, time=387.05
memory used=3398.9MB, alloc=4.5MB, time=387.29
memory used=3402.7MB, alloc=4.5MB, time=387.52
memory used=3406.5MB, alloc=4.5MB, time=387.75
x[1] = 8.7
y1[1] (analytic) = 0.25135335440260084268120821911072
y1[1] (numeric) = 0.25135335440360443242208838685113
absolute error = 1.00358974088016774041e-12
relative error = 3.9927445697529280314145043191336e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.6629692300821827922023461866156
y2[1] (numeric) = 1.6629692300813480162104189323011
absolute error = 8.347759919272543145e-13
relative error = 5.0197921694919169419843572458500e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3410.4MB, alloc=4.5MB, time=387.99
memory used=3414.2MB, alloc=4.5MB, time=388.22
memory used=3418.0MB, alloc=4.5MB, time=388.45
memory used=3421.8MB, alloc=4.5MB, time=388.68
memory used=3425.6MB, alloc=4.5MB, time=388.92
memory used=3429.4MB, alloc=4.5MB, time=389.15
memory used=3433.2MB, alloc=4.5MB, time=389.39
memory used=3437.1MB, alloc=4.5MB, time=389.63
memory used=3440.9MB, alloc=4.5MB, time=389.86
memory used=3444.7MB, alloc=4.5MB, time=390.09
x[1] = 8.8
y1[1] (analytic) = 0.18890698593834443711091449578068
y1[1] (numeric) = 0.18890698593943893202402956491869
absolute error = 1.09449491311506913801e-12
relative error = 5.7938297394268466698096904926224e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.5849171928917622535309313118124
y2[1] (numeric) = 1.5849171928910233465509554925544
absolute error = 7.389069799758192580e-13
relative error = 4.6621172594364112282905543625710e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=3448.5MB, alloc=4.5MB, time=390.33
NO POLE
NO POLE
memory used=3452.3MB, alloc=4.5MB, time=390.56
memory used=3456.1MB, alloc=4.5MB, time=390.80
memory used=3459.9MB, alloc=4.5MB, time=391.03
memory used=3463.8MB, alloc=4.5MB, time=391.26
memory used=3467.6MB, alloc=4.5MB, time=391.49
memory used=3471.4MB, alloc=4.5MB, time=391.73
memory used=3475.2MB, alloc=4.5MB, time=391.97
memory used=3479.0MB, alloc=4.5MB, time=392.21
memory used=3482.8MB, alloc=4.5MB, time=392.44
memory used=3486.6MB, alloc=4.5MB, time=392.67
x[1] = 8.9
y1[1] (analytic) = 0.13456479075888794036017232177465
y1[1] (numeric) = 0.13456479076006410042123190644279
absolute error = 1.17616006105958466814e-12
relative error = 8.7404740454508517571071890978498e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 1.5010208564578849820161746471113
y2[1] (numeric) = 1.5010208564572518388513331749565
absolute error = 6.331431648414721548e-13
relative error = 4.2180837269347870783680477306296e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3490.5MB, alloc=4.5MB, time=392.90
memory used=3494.3MB, alloc=4.5MB, time=393.14
memory used=3498.1MB, alloc=4.5MB, time=393.38
memory used=3501.9MB, alloc=4.5MB, time=393.61
memory used=3505.7MB, alloc=4.5MB, time=393.84
memory used=3509.5MB, alloc=4.5MB, time=394.07
memory used=3513.4MB, alloc=4.5MB, time=394.30
memory used=3517.2MB, alloc=4.5MB, time=394.53
memory used=3521.0MB, alloc=4.5MB, time=394.77
memory used=3524.8MB, alloc=4.5MB, time=395.00
x[1] = 9
y1[1] (analytic) = 0.08886973811532301163170528881883
y1[1] (numeric) = 0.088869738116570521602833667884728
absolute error = 1.247509971128379065898e-12
relative error = 1.4037511503741925777611419239454e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 1.4121184852417565697562725663524
y2[1] (numeric) = 1.4121184852412381852019023927835
absolute error = 5.183845543701735689e-13
relative error = 3.6709706712848917998791605127582e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3528.6MB, alloc=4.5MB, time=395.23
memory used=3532.4MB, alloc=4.5MB, time=395.46
memory used=3536.2MB, alloc=4.5MB, time=395.69
memory used=3540.1MB, alloc=4.5MB, time=395.92
memory used=3543.9MB, alloc=4.5MB, time=396.16
memory used=3547.7MB, alloc=4.5MB, time=396.39
memory used=3551.5MB, alloc=4.5MB, time=396.62
memory used=3555.3MB, alloc=4.5MB, time=396.86
memory used=3559.1MB, alloc=4.5MB, time=397.09
memory used=3562.9MB, alloc=4.5MB, time=397.32
x[1] = 9.1
y1[1] (analytic) = 0.05227839786888797528093341042463
y1[1] (numeric) = 0.052278397870195533423437324281944
absolute error = 1.307558142503913857314e-12
relative error = 2.5011442504095376548655254702270e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 1.3190983623493517707939976839854
y2[1] (numeric) = 1.3190983623489561231004180849937
absolute error = 3.956476935795989917e-13
relative error = 2.9993797647882692806251349624088e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=3566.8MB, alloc=4.5MB, time=397.55
NO POLE
NO POLE
memory used=3570.6MB, alloc=4.5MB, time=397.79
memory used=3574.4MB, alloc=4.5MB, time=398.03
memory used=3578.2MB, alloc=4.5MB, time=398.26
memory used=3582.0MB, alloc=4.5MB, time=398.49
memory used=3585.8MB, alloc=4.5MB, time=398.72
memory used=3589.6MB, alloc=4.5MB, time=398.95
memory used=3593.5MB, alloc=4.5MB, time=399.19
memory used=3597.3MB, alloc=4.5MB, time=399.43
memory used=3601.1MB, alloc=4.5MB, time=399.66
memory used=3604.9MB, alloc=4.5MB, time=399.89
x[1] = 9.2
y1[1] (analytic) = 0.0251563785958362580585546615242
y1[1] (numeric) = 0.025156378597191677436162989012362
absolute error = 1.355419377608327488162e-12
relative error = 5.3879749521366674813785948709255e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 1.2228899141002469575280690577583
y2[1] (numeric) = 1.2228899140999809007206245515018
absolute error = 2.660568074445062565e-13
relative error = 2.1756398869334049357922940465300e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3608.7MB, alloc=4.5MB, time=400.12
memory used=3612.5MB, alloc=4.5MB, time=400.35
memory used=3616.4MB, alloc=4.5MB, time=400.58
memory used=3620.2MB, alloc=4.5MB, time=400.81
memory used=3624.0MB, alloc=4.5MB, time=401.04
memory used=3627.8MB, alloc=4.5MB, time=401.28
memory used=3631.6MB, alloc=4.5MB, time=401.51
memory used=3635.4MB, alloc=4.5MB, time=401.74
memory used=3639.2MB, alloc=4.5MB, time=401.97
memory used=3643.1MB, alloc=4.5MB, time=402.20
x[1] = 9.3
y1[1] (analytic) = 0.00777467454739659224309076536484
y1[1] (numeric) = 0.0077746745487869137195807702044418
absolute error = 1.3903214764900048396018e-12
relative error = 1.7882696799900959908797482250745e-08 %
Correct digits = 9
h = 0.005
y2[1] (analytic) = 1.1244544235070624079894062785863
y2[1] (numeric) = 1.1244544235069315744010329290693
absolute error = 1.308335883733495170e-13
relative error = 1.1635294916204114608318495182002e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=3646.9MB, alloc=4.5MB, time=402.43
NO POLE
NO POLE
memory used=3650.7MB, alloc=4.5MB, time=402.66
memory used=3654.5MB, alloc=4.5MB, time=402.90
memory used=3658.3MB, alloc=4.5MB, time=403.13
memory used=3662.1MB, alloc=4.5MB, time=403.37
memory used=3665.9MB, alloc=4.5MB, time=403.60
memory used=3669.8MB, alloc=4.5MB, time=403.84
memory used=3673.6MB, alloc=4.5MB, time=404.08
memory used=3677.4MB, alloc=4.5MB, time=404.32
memory used=3681.2MB, alloc=4.5MB, time=404.55
memory used=3685.0MB, alloc=4.5MB, time=404.78
x[1] = 9.4
y1[1] (analytic) = 0.00030695796479352782205257932708
y1[1] (numeric) = 0.00030695796620514371185686100940899
absolute error = 1.41161588980428168232899e-12
relative error = 4.5987270301123831988590599731501e-07 %
Correct digits = 8
h = 0.005
y2[1] (analytic) = 1.0247754254533581210797730773676
y2[1] (numeric) = 1.0247754254533668353595518889669
absolute error = 8.7142797788115993e-15
relative error = 8.5035994837175407632817573911865e-13 %
Correct digits = 14
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3688.8MB, alloc=4.5MB, time=405.01
memory used=3692.6MB, alloc=4.5MB, time=405.24
memory used=3696.5MB, alloc=4.5MB, time=405.47
memory used=3700.3MB, alloc=4.5MB, time=405.71
memory used=3704.1MB, alloc=4.5MB, time=405.93
memory used=3707.9MB, alloc=4.5MB, time=406.17
memory used=3711.7MB, alloc=4.5MB, time=406.40
memory used=3715.5MB, alloc=4.5MB, time=406.63
memory used=3719.3MB, alloc=4.5MB, time=406.86
memory used=3723.2MB, alloc=4.5MB, time=407.10
x[1] = 9.5
y1[1] (analytic) = 0.00282784380362152710839835982201
y1[1] (numeric) = 0.0028278438050403143029959119591906
absolute error = 1.4187871945975521371806e-12
relative error = 5.0172049558768336552773707426823e-08 %
Correct digits = 9
h = 0.005
y2[1] (analytic) = 0.92484887953819069271651749546599
y2[1] (numeric) = 0.92484887953834189847031584210668
absolute error = 1.5120575379834664069e-13
relative error = 1.6349239010144981535672231245323e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=3727.0MB, alloc=4.5MB, time=407.33
NO POLE
NO POLE
memory used=3730.8MB, alloc=4.5MB, time=407.56
memory used=3734.6MB, alloc=4.5MB, time=407.79
memory used=3738.4MB, alloc=4.5MB, time=408.02
memory used=3742.2MB, alloc=4.5MB, time=408.25
memory used=3746.1MB, alloc=4.5MB, time=408.49
memory used=3749.9MB, alloc=4.5MB, time=408.72
memory used=3753.7MB, alloc=4.5MB, time=408.95
memory used=3757.5MB, alloc=4.5MB, time=409.19
memory used=3761.3MB, alloc=4.5MB, time=409.42
x[1] = 9.6
y1[1] (analytic) = 0.01531214420587308997965792011627
y1[1] (numeric) = 0.015312144207284551247941818151541
absolute error = 1.411461268283898035271e-12
relative error = 9.2179204251650221165484605290024e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 0.82567321877702001487589827347958
y2[1] (numeric) = 0.82567321877731521497331961178684
absolute error = 2.9520009742133830726e-13
relative error = 3.5752655010245593551619970262008e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=3765.1MB, alloc=4.5MB, time=409.65
NO POLE
NO POLE
memory used=3768.9MB, alloc=4.5MB, time=409.89
memory used=3772.8MB, alloc=4.5MB, time=410.13
memory used=3776.6MB, alloc=4.5MB, time=410.36
memory used=3780.4MB, alloc=4.5MB, time=410.59
memory used=3784.2MB, alloc=4.5MB, time=410.82
memory used=3788.0MB, alloc=4.5MB, time=411.06
memory used=3791.8MB, alloc=4.5MB, time=411.29
memory used=3795.6MB, alloc=4.5MB, time=411.52
memory used=3799.5MB, alloc=4.5MB, time=411.75
memory used=3803.3MB, alloc=4.5MB, time=411.98
x[1] = 9.7
y1[1] (analytic) = 0.03763512016868996592964362910856
y1[1] (numeric) = 0.037635120170079377978570980174038
absolute error = 1.389412048927351065478e-12
relative error = 3.6917964993858417575717770210470e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 0.72823937358905687566225910317516
y2[1] (numeric) = 0.72823937358949608710889706919287
absolute error = 4.3921144663796601771e-13
relative error = 6.0311411682309231635898722296841e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3807.1MB, alloc=4.5MB, time=412.22
memory used=3810.9MB, alloc=4.5MB, time=412.45
memory used=3814.7MB, alloc=4.5MB, time=412.68
memory used=3818.5MB, alloc=4.5MB, time=412.91
memory used=3822.3MB, alloc=4.5MB, time=413.15
memory used=3826.2MB, alloc=4.5MB, time=413.38
memory used=3830.0MB, alloc=4.5MB, time=413.61
memory used=3833.8MB, alloc=4.5MB, time=413.85
memory used=3837.6MB, alloc=4.5MB, time=414.08
memory used=3841.4MB, alloc=4.5MB, time=414.31
x[1] = 9.8
y1[1] (analytic) = 0.06957372789524648145062224791078
y1[1] (numeric) = 0.069573727896599048234708975769367
absolute error = 1.352566784086727858587e-12
relative error = 1.9440769166821373034916193749910e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 0.63352087074807225183074705127114
y2[1] (numeric) = 0.63352087074865397595751031052615
absolute error = 5.8172412676325925501e-13
relative error = 9.1823987752187150852887326075173e-11 %
Correct digits = 12
h = 0.005
TOP MAIN SOLVE Loop
memory used=3845.2MB, alloc=4.5MB, time=414.54
NO POLE
NO POLE
memory used=3849.1MB, alloc=4.5MB, time=414.77
memory used=3852.9MB, alloc=4.5MB, time=415.01
memory used=3856.7MB, alloc=4.5MB, time=415.24
memory used=3860.5MB, alloc=4.5MB, time=415.47
memory used=3864.3MB, alloc=4.5MB, time=415.71
memory used=3868.1MB, alloc=4.5MB, time=415.94
memory used=3871.9MB, alloc=4.5MB, time=416.18
memory used=3875.8MB, alloc=4.5MB, time=416.41
memory used=3879.6MB, alloc=4.5MB, time=416.64
memory used=3883.4MB, alloc=4.5MB, time=416.87
x[1] = 9.9
y1[1] (analytic) = 0.11080884737463894536556130131089
y1[1] (numeric) = 0.11080884737593995505146343906222
absolute error = 1.30100968590213775133e-12
relative error = 1.1741027153756881171573819248723e-09 %
Correct digits = 10
h = 0.005
y2[1] (analytic) = 0.54246410622467895558618189249464
y2[1] (numeric) = 0.54246410622540016414970884018233
absolute error = 7.2120856352694768769e-13
relative error = 1.3295046718321229655254077069926e-10 %
Correct digits = 11
h = 0.005
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3887.2MB, alloc=4.5MB, time=417.11
memory used=3891.0MB, alloc=4.5MB, time=417.34
memory used=3894.8MB, alloc=4.5MB, time=417.57
memory used=3898.6MB, alloc=4.5MB, time=417.80
memory used=3902.5MB, alloc=4.5MB, time=418.03
memory used=3906.3MB, alloc=4.5MB, time=418.26
memory used=3910.1MB, alloc=4.5MB, time=418.49
memory used=3913.9MB, alloc=4.5MB, time=418.72
memory used=3917.7MB, alloc=4.5MB, time=418.96
memory used=3921.5MB, alloc=4.5MB, time=419.20
x[1] = 10
y1[1] (analytic) = 0.16092847092354754774113605217594
y1[1] (numeric) = 0.16092847092478253166778151085831
absolute error = 1.23498392664545868237e-12
relative error = 7.6741170754810921661720803770323e-10 %
Correct digits = 11
h = 0.005
y2[1] (analytic) = 0.45597888911063018659525233814862
y2[1] (numeric) = 0.4559788891114863242167930910881
absolute error = 8.5613762154075293948e-13
relative error = 1.8775817082466634211849202297960e-10 %
Correct digits = 11
h = 0.005
Finished!
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
diff ( y2 , x , 1 ) = y1 - 1.0;
Iterations = 1980
Total Elapsed Time = 6 Minutes 59 Seconds
Elapsed Time(since restart) = 6 Minutes 59 Seconds
Time to Timeout = 3 Minutes 0 Seconds
Percent Done = 100.1 %
> quit
memory used=3923.9MB, alloc=4.5MB, time=419.34