|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 1
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 1;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 3
> # Begin Function number 4
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 1
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (min_size < 1.0) then # if number 1
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 4
> # Begin Function number 5
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms;
> max_value3 := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (value3 > max_value3) then # if number 1
> max_value3 := value3;
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> fi;# end if 1;
> omniout_float(ALWAYS,"max_value3",32,max_value3,32,"");
> max_value3;
> end;
test_suggested_h := proc()
local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
max_value3 := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
value3 := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, "");
max_value3
end proc
> # End Function number 5
> # Begin Function number 6
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 6
> # Begin Function number 7
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> 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_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[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 > 0.0000000000000000000000000000000001) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> 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," ");
> fi;# end if 2;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, 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_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 2
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, " ")
end if
end if
end proc
> # End Function number 7
> # Begin Function number 8
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y_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;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_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
> # End Function number 8
> # Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> 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));
> glob_total_exp_sec := glob_optimal_expect_sec + total_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));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_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;
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, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, 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));
glob_total_exp_sec := glob_optimal_expect_sec + total_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));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_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
> # End Function number 9
> # Begin Function number 10
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
> #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_y_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> 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
> #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_y_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
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> elif
> (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_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
> rad_c := glob_large_float;
> ord_no := 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
> found_sing := 0;
> #TOP WHICH RADII EQ = 1
> if (1 <> found_sing 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 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing 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] > -1.0 * glob_smallish_float) 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 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing 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 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found_sing := 1;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing 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] > -1.0 * glob_smallish_float))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing 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 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found_sing := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing ) then # if number 2
> 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 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> #BOTTOM WHICH RADII EQ = 1
> 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 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2;
> #BOTTOM WHICH RADIUS EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 2;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 2
> display_pole();
> fi;# end if 2
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no,
rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (
omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or
omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float
or
omniabs(array_y_higher[1, m - 2]) < glob_small_float*glob_small_float)
do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if glob_small_float*glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
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 - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
elif glob_large_float <= omniabs(array_y_higher[1, m]) or
glob_large_float <= omniabs(array_y_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y_higher[1, m - 5]) or
omniabs(array_y_higher[1, m]) <= glob_small_float or
omniabs(array_y_higher[1, m - 1]) <= glob_small_float or
omniabs(array_y_higher[1, m - 2]) <= glob_small_float or
omniabs(array_y_higher[1, m - 3]) <= glob_small_float or
omniabs(array_y_higher[1, m - 4]) <= glob_small_float or
omniabs(array_y_higher[1, m - 5]) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_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
rad_c := glob_large_float; ord_no := 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;
found_sing := 0;
if 1 <> found_sing 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_sing := 1;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing 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
-1.0*glob_smallish_float < 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_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing 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_sing := 1;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1]
and 0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < 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_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing 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_sing := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing 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 for equation 1")
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_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_pole() end if
end proc
> # End Function number 10
> # Begin Function number 11
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 2
> 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_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 3;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 2;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, 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_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 11
> # Begin Function number 12
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult FULL CONST $eq_no = 1 i = 1
> array_tmp1[1] := array_m1[1] * array_const_2D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) 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_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult FULL CONST $eq_no = 1 i = 2
> array_tmp1[2] := array_m1[2] * array_const_2D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp2[2] := (array_tmp1[2] - array_tmp2[1] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := (array_tmp2[2] - array_tmp3[1] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp4[2] := (array_tmp3[2] - array_tmp4[1] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) 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_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult FULL CONST $eq_no = 1 i = 3
> array_tmp1[3] := array_m1[3] * array_const_2D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp2[3] := (array_tmp1[3] - array_tmp2[2] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp3[3] := (array_tmp2[3] - array_tmp3[2] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp4[3] := (array_tmp3[3] - array_tmp4[2] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) 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_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre mult FULL CONST $eq_no = 1 i = 4
> array_tmp1[4] := array_m1[4] * array_const_2D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp2[4] := (array_tmp1[4] - array_tmp2[3] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp3[4] := (array_tmp2[4] - array_tmp3[3] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp4[4] := (array_tmp3[4] - array_tmp4[3] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) 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_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre mult FULL CONST $eq_no = 1 i = 5
> array_tmp1[5] := array_m1[5] * array_const_2D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp2[5] := (array_tmp1[5] - array_tmp2[4] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp3[5] := (array_tmp2[5] - array_tmp3[4] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp4[5] := (array_tmp3[5] - array_tmp4[4] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) 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_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_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 CONST $eq_no = 1 i = 1
> array_tmp1[kkk] := array_m1[kkk] * array_const_2D0[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp2[kkk] := -ats(kkk,array_x,array_tmp2,2) / array_x[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp3[kkk] := -ats(kkk,array_x,array_tmp3,2) / array_x[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp4[kkk] := -ats(kkk,array_x,array_tmp4,2) / array_x[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,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_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 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;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
array_tmp1[1] := array_m1[1]*array_const_2D0[1];
array_tmp2[1] := array_tmp1[1]/array_x[1];
array_tmp3[1] := array_tmp2[1]/array_x[1];
array_tmp4[1] := array_tmp3[1]/array_x[1];
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_m1[2]*array_const_2D0[1];
array_tmp2[2] := (array_tmp1[2] - array_tmp2[1]*array_x[2])/array_x[1];
array_tmp3[2] := (array_tmp2[2] - array_tmp3[1]*array_x[2])/array_x[1];
array_tmp4[2] := (array_tmp3[2] - array_tmp4[1]*array_x[2])/array_x[1];
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_m1[3]*array_const_2D0[1];
array_tmp2[3] := (array_tmp1[3] - array_tmp2[2]*array_x[2])/array_x[1];
array_tmp3[3] := (array_tmp2[3] - array_tmp3[2]*array_x[2])/array_x[1];
array_tmp4[3] := (array_tmp3[3] - array_tmp4[2]*array_x[2])/array_x[1];
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_m1[4]*array_const_2D0[1];
array_tmp2[4] := (array_tmp1[4] - array_tmp2[3]*array_x[2])/array_x[1];
array_tmp3[4] := (array_tmp2[4] - array_tmp3[3]*array_x[2])/array_x[1];
array_tmp4[4] := (array_tmp3[4] - array_tmp4[3]*array_x[2])/array_x[1];
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_m1[5]*array_const_2D0[1];
array_tmp2[5] := (array_tmp1[5] - array_tmp2[4]*array_x[2])/array_x[1];
array_tmp3[5] := (array_tmp2[5] - array_tmp3[4]*array_x[2])/array_x[1];
array_tmp4[5] := (array_tmp3[5] - array_tmp4[4]*array_x[2])/array_x[1];
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_m1[kkk]*array_const_2D0[1];
array_tmp2[kkk] := -ats(kkk, array_x, array_tmp2, 2)/array_x[1];
array_tmp3[kkk] := -ats(kkk, array_x, array_tmp3, 2)/array_x[1];
array_tmp4[kkk] := -ats(kkk, array_x, array_tmp4, 2)/array_x[1];
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 12
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> 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
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> 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
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> 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
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_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,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> 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 if 0;
> 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
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> 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 2
> 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 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 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, " | \n")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> 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 5
> 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 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 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
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> 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 + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_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 + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_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 6
> 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 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_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 + arr_aa[iii_att]*arr_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
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> 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 6
> 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 6
> 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
> # End Function number 16
> # Begin Function number 17
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
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
> # End Function number 20
> # Begin Function number 21
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 21
> # Begin Function number 22
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 8
> fprintf(file," | ");
> 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
> # End Function number 23
> # Begin Function number 24
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 24
> # Begin Function number 25
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # End Function number 25
> # Begin Function number 26
> 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 8
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 8;
> if (glob_max_iter < 2) then # if number 8
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 8;
> if (errflag) then # if number 8
> quit;
> fi;# end if 8
> 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
> # End Function number 26
> # Begin Function number 27
> 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 8
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 9
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 9
> fi;# end if 8;
> sec_left;
> 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
> # End Function number 27
> # Begin Function number 28
> 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 8
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 8;
> rrr;
> 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
> # End Function number 28
> # Begin Function number 29
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 29
> # Begin Function number 30
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 8
> if (array_fact_1[nnn] = 0) then # if number 9
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 9;
> else
> ret := factorial_2(nnn);
> fi;# end if 8;
> ret;
> 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
> # End Function number 30
> # Begin Function number 31
> 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 8
> if (array_fact_2[mmm,nnn] = 0) then # if number 9
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 9;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 8;
> ret;
> 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
> # End Function number 31
> # Begin Function number 32
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 33
> # Begin Function number 34
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 34
> # Begin Function number 35
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 35
> # Begin Function number 36
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 36
> # Begin Function number 37
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 37
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(1.0/x/x);
> end;
exact_soln_y := proc(x) return 1.0/(x*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, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_value3 := 0.0;
> glob_ratio_of_radius := 0.01;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.1e-200;
> glob_smallish_float := 0.1e-100;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 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 := 1;
> 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/sing3postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=20;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -1.0;");
> omniout_str(ALWAYS,"x_end := -0.7;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.001;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(1.0/x/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;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=20;
> #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_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= 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_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_init[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_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_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_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y[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_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_m1[term] := 0.0;
> term := term + 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_y_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_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_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_y_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 <=1) 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 <=1) 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 <=1) 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 <=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;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[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_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_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_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_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_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_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_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_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_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_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_2D0[1] := 2.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3;
> iiif := iiif + 1;
> od;# end do number 2;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -1.0;
> x_end := -0.7;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.001;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #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);
> 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_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> if (glob_display_interval < glob_h) then # if number 2
> glob_h := glob_display_interval;
> fi;# end if 2;
> if (glob_max_h < glob_h) then # if number 2
> glob_h := glob_max_h;
> fi;# end if 2;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> atomall();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 2;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 2
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 2;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 2
> 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_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_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_y_higher[r_order,term_no] := array_y_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();
> 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 ((glob_check_sign * array_x[1]) < (glob_check_sign * 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;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3;#was right paren 0004C
> if (reached_interval()) then # if number 3
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 3;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_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_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_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
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 3;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 3;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-01-28T19:06:53-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing3")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;")
> ;
> 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 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 4
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 4;
> log_revs(html_log_file," 165 | ")
> ;
> logitem_str(html_log_file,"sing3 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing3 maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3;
> if (glob_html_log) then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> fi;# end if 2
> #END OUTFILEMAIN
> 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, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, value3, min_value, est_answer, best_h,
found_h, repeat_it;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_y_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole,
array_complex_pole, array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_value3 := 0.;
glob_ratio_of_radius := 0.01;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.1*10^(-200);
glob_smallish_float := 0.1*10^(-100);
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
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/sing3postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=20;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -1.0;");
omniout_str(ALWAYS, "x_end := -0.7;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.001;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(1.0/x/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;
Digits := 32;
max_terms := 20;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := 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_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[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_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[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_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_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_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_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_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_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 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 <= 1 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 <= 1 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 <= 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;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[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_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[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_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[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_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
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_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_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := -1.0;
x_end := -0.7;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 100;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
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);
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_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
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_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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;
atomall();
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < found_h then
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_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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();
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
glob_check_sign*array_x[1] < glob_check_sign*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;
atomall();
display_alot(current_iter);
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 := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
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 ( y , x , 1 ) = m1 * 2.0 / x / x / x ;");
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, "2013-01-28T19:06:53-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing3");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;");
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_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 165 | ");
logitem_str(html_log_file,
"sing3 diffeq.mxt");
logitem_str(html_log_file,
"sing3 maple results")
;
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/sing3postode.ode#################
diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.0;
x_end := -0.7;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.001;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(1.0/x/x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 0.3
estimated_steps = 300
step_error = 3.3333333333333333333333333333333e-13
est_needed_step_err = 3.3333333333333333333333333333333e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 1.8758827696078431372549019607843e-48
max_value3 = 1.8758827696078431372549019607843e-48
value3 = 1.8758827696078431372549019607843e-48
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (analytic) = 1
y[1] (numeric) = 1
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9963
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.999
y[1] (analytic) = 1.002003004005006007008009010011
y[1] (numeric) = 1.0020030040050060050042894676221
absolute error = 2.0037195423889e-18
relative error = 1.9997141070236645889000000000000e-16 %
Correct digits = 17
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9953
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.998
y[1] (analytic) = 1.0040120320801924490263091312887
y[1] (numeric) = 1.0040120320801924450027641566564
absolute error = 4.0235449746323e-18
relative error = 4.0074668889136693291999999999997e-16 %
Correct digits = 17
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9943
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.997
y[1] (analytic) = 1.0060271084064631205552464816717
y[1] (numeric) = 1.0060271084064631144956243970799
absolute error = 6.0596220845918e-18
relative error = 6.0233188886830105262000000000000e-16 %
Correct digits = 17
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9933
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.996
y[1] (analytic) = 1.0080482572861728036644570248866
y[1] (numeric) = 1.0080482572861727955523588970067
absolute error = 8.1120981278799e-18
relative error = 8.0473311364269068784000000000008e-16 %
Correct digits = 17
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9924
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.995
y[1] (analytic) = 1.0100755031438600035352642610035
y[1] (numeric) = 1.0100755031438599933541424168727
absolute error = 1.01811218441308e-17
relative error = 1.0079565153735595270000000000000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9914
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.994
y[1] (analytic) = 1.0121088705269848467059904699829
y[1] (numeric) = 1.0121088705269848344391469965151
absolute error = 1.22668434734678e-17
relative error = 1.2120082958151231240800000000000e-15 %
Correct digits = 16
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.4899
Order of pole = 4.944e-28
TOP MAIN SOLVE Loop
x[1] = -0.993
y[1] (analytic) = 1.0141483841066721836338762069633
y[1] (numeric) = 1.014148384106672169264461433792
absolute error = 1.43694147731713e-17
relative error = 1.4168947067670787193700000000001e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9894
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.992
y[1] (analytic) = 1.0161940686784599375650364203955
y[1] (numeric) = 1.0161940686784599210760473858469
absolute error = 1.64889890345486e-17
relative error = 1.6226220505294033510399999999999e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9884
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.991
y[1] (analytic) = 1.0182459491630527420854287986429
y[1] (numeric) = 1.0182459491630527234597076986353
absolute error = 1.86257211000076e-17
relative error = 1.8291966803616563815600000000000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9874
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (analytic) = 1.0203040506070809101112131415162
y[1] (numeric) = 1.0203040506070808893314457611764
absolute error = 2.07797673803398e-17
relative error = 2.0366250009471037979999999999999e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9864
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.989
y[1] (analytic) = 1.0223683981838647774661826093091
y[1] (numeric) = 1.0223683981838647545148967370972
absolute error = 2.29512858722119e-17
relative error = 2.2449134688613775839899999999999e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9854
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.988
y[1] (analytic) = 1.0244390171941844645871920536315
y[1] (numeric) = 1.0244390171941844394467558777599
absolute error = 2.51404361758716e-17
relative error = 2.4540685930460007110399999999998e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9844
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.987
y[1] (analytic) = 1.0265159330670551002957392403166
y[1] (numeric) = 1.0265159330670550729483597272483
absolute error = 2.73473795130683e-17
relative error = 2.6640969352866232742700000000000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9834
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.986
y[1] (analytic) = 1.0285991713605075519751161288464
y[1] (numeric) = 1.0285991713605075224028373836527
absolute error = 2.95722787451937e-17
relative error = 2.8750051106962334365200000000001e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9824
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.985
y[1] (analytic) = 1.0306887577623747068978845113247
y[1] (numeric) = 1.030688757762374675082586119682
absolute error = 3.18152983916427e-17
relative error = 3.0867997882031538607500000000000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9814
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.984
y[1] (analytic) = 1.0327847180910833498578888227906
y[1] (numeric) = 1.032784718091083315781284174391
absolute error = 3.40766046483996e-17
relative error = 3.2994876910440803097600000000002e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9804
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.983
y[1] (analytic) = 1.0348870782964516826746449561156
y[1] (numeric) = 1.0348870782964516463182795492634
absolute error = 3.63563654068522e-17
relative error = 3.5130755972621805485800000000000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9794
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.982
y[1] (analytic) = 1.0369958644604925315557841555328
y[1] (numeric) = 1.0369958644604924929010338826977
absolute error = 3.86547502728351e-17
relative error = 3.7275703402101434972400000000000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9784
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.981
y[1] (analytic) = 1.0391111027982222887253328013085
y[1] (numeric) = 1.0391111027982222477534022154004
absolute error = 4.09719305859081e-17
relative error = 3.9429788090585105024099999999998e-15 %
Correct digits = 16
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.9691
Order of pole = 4.446e-28
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.9MB, time=0.18
x[1] = -0.98
y[1] (analytic) = 1.0412328196584756351520199916701
y[1] (numeric) = 1.0412328196584755918439405527999
absolute error = 4.33080794388702e-17
relative error = 4.1593079493090940080000000000001e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9764
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.979
y[1] (analytic) = 1.0433610415247260916425737212828
y[1] (numeric) = 1.0433610415247260459792020237682
absolute error = 4.56633716975146e-17
relative error = 4.3765647633137590738600000000000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9754
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.978
y[1] (analytic) = 1.0454957950159124460001421874281
y[1] (numeric) = 1.0454957950159123979621581668031
absolute error = 4.80379840206250e-17
relative error = 4.5947563107983482500000000000001e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9744
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.977
y[1] (analytic) = 1.0476371068872711043876089673546
y[1] (numeric) = 1.0476371068872710539555140871343
absolute error = 5.04320948802203e-17
relative error = 4.8138897093921802738699999999999e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9734
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.976
y[1] (analytic) = 1.0497850040311744154797097554421
y[1] (numeric) = 1.049785004031174362633825173395
absolute error = 5.28458845820471e-17
relative error = 5.0339721351628098329599999999999e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9724
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.975
y[1] (analytic) = 1.0519395134779750164365548980933
y[1] (numeric) = 1.0519395134779749611570196117669
absolute error = 5.52795352863264e-17
relative error = 5.2550108231564034000000000000003e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9714
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.974
y[1] (analytic) = 1.0541006623968562501844676159194
y[1] (numeric) = 1.0541006623968561924512365871633
absolute error = 5.77332310287561e-17
relative error = 5.4770130679436221923600000000003e-15 %
Correct digits = 16
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.7873
Order of pole = 3.363e-28
TOP MAIN SOLVE Loop
x[1] = -0.973
y[1] (analytic) = 1.056268478096688703948014690582
y[1] (numeric) = 1.0562684780966886437408569488092
absolute error = 6.02071577417728e-17
relative error = 5.6999862241710821171200000000000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9694
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.972
y[1] (analytic) = 1.0584429880268929194397872952971
y[1] (numeric) = 1.0584429880268928567382840192193
absolute error = 6.27015032760778e-17
relative error = 5.9239377071185888195200000000001e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9684
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.971
y[1] (analytic) = 1.0606242197783083255819379937868
y[1] (numeric) = 1.0606242197783082603654805713576
absolute error = 6.52164574224292e-17
relative error = 6.1488749932620569357200000000004e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9674
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.97
y[1] (analytic) = 1.0628122010840684451057498140078
y[1] (numeric) = 1.0628122010840683773535378803033
absolute error = 6.77522119337045e-17
relative error = 6.3748056208422564050000000000004e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9664
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.969
y[1] (analytic) = 1.0650069598204824268526594821297
y[1] (numeric) = 1.0650069598204823565436989348924
absolute error = 7.03089605472373e-17
relative error = 6.6017371904394482445300000000001e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9655
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.968
y[1] (analytic) = 1.0672085240079229560822348200259
y[1] (numeric) = 1.0672085240079228831953358125945
absolute error = 7.28868990074314e-17
relative error = 6.8296773655539400153600000000003e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9645
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.967
y[1] (analytic) = 1.0694169218117205955796720953835
y[1] (numeric) = 1.0694169218117205200934470067265
absolute error = 7.54862250886570e-17
relative error = 7.0586338731927185472999999999996e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9635
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.966
y[1] (analytic) = 1.0716321815430646108474895944516
y[1] (numeric) = 1.0716321815430645327403509760207
absolute error = 7.81071386184309e-17
relative error = 7.2886145044620504920399999999994e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9625
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.965
y[1] (analytic) = 1.0738543316599103331633063974872
y[1] (numeric) = 1.0738543316599102524134648966001
absolute error = 8.07498415008871e-17
relative error = 7.5196271151663589697499999999999e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9615
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.964
y[1] (analytic) = 1.0760834007678931147879685267127
y[1] (numeric) = 1.0760834007678930313734307861728
absolute error = 8.34145377405399e-17
relative error = 7.7516796264132766910400000000000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9605
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.963
y[1] (analytic) = 1.078319417621248931115877282937
y[1] (numeric) = 1.0783194176212488450144438165935
absolute error = 8.61014334663435e-17
relative error = 7.9847800252249505251500000000000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9595
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.962
y[1] (analytic) = 1.0805624111237416850722464028077
y[1] (numeric) = 1.0805624111237415962615094467548
absolute error = 8.88107369560529e-17
relative error = 8.2189363651557419987600000000003e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9585
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.961
y[1] (analytic) = 1.0828124103295972695802261128875
y[1] (numeric) = 1.0828124103295971780375674519971
absolute error = 9.15426586608904e-17
relative error = 8.4541567669164163098400000000002e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9575
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (analytic) = 1.0850694444444444444444444444445
y[1] (numeric) = 1.0850694444444443501470332139242
absolute error = 9.42974112305203e-17
relative error = 8.6904494190047508479999999999996e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9565
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.959
y[1] (analytic) = 1.0873335428262625845265912854566
y[1] (numeric) = 1.0873335428262624874513817471191
absolute error = 9.70752095383375e-17
relative error = 8.9278225783427770337499999999999e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9555
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.958
y[1] (analytic) = 1.0896047349863363566232713420879
y[1] (numeric) = 1.0896047349863362567470006350136
absolute error = 9.98762707070743e-17
relative error = 9.1662845709207337865200000000004e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9545
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.957
y[1] (analytic) = 1.0918830505902173829965420063788
y[1] (numeric) = 1.0918830505902172802957278716504
absolute error = 1.027008141347284e-16
relative error = 9.4058437924476870411599999999998e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9535
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.956
y[1] (analytic) = 1.0941685194586929500533954237496
y[1] (numeric) = 1.0941685194586928445043339029325
absolute error = 1.055490615208171e-16
relative error = 9.6465087090089497105599999999999e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9525
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.955
y[1] (analytic) = 1.0964611715687618212220059757134
y[1] (numeric) = 1.0964611715687617128007690827497
absolute error = 1.084212368929637e-16
relative error = 9.8882878577305218492499999999999e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9515
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.954
y[1] (analytic) = 1.0987610370546172136299109124551
y[1] (numeric) = 1.0987610370546171023123442786374
absolute error = 1.113175666338177e-16
relative error = 1.0131189847450362985320000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9505
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.953
y[1] (analytic) = 1.1010681462086369987524897903456
y[1] (numeric) = 1.1010681462086368845142102820296
absolute error = 1.142382795083160e-16
relative error = 1.0375223359396816604400000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9495
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.952
y[1] (analytic) = 1.1033825294823811877692253371937
y[1] (numeric) = 1.1033825294823810705856186459057
absolute error = 1.171836066912880e-16
relative error = 1.0620397147874107955200000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9485
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.951
y[1] (analytic) = 1.1057042174875967629403328833117
y[1] (numeric) = 1.1057042174875966427865510879009
absolute error = 1.201537817954108e-16
relative error = 1.0866720040955132293080000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9475
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (analytic) = 1.1080332409972299168975069252078
y[1] (numeric) = 1.1080332409972297937484660256899
absolute error = 1.231490408995179e-16
relative error = 1.1114200941181490475000000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9465
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.949
y[1] (analytic) = 1.1103696309464457623298219744371
y[1] (numeric) = 1.1103696309464456361601993971702
absolute error = 1.261696225772669e-16
relative error = 1.1362848826270914740690000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9455
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.948
y[1] (analytic) = 1.1127134184336555751393117199879
y[1] (numeric) = 1.1127134184336554459235437938161
absolute error = 1.292157679261718e-16
relative error = 1.1612672749832230134720000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9445
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.947
y[1] (analytic) = 1.1150646347215516347405077335307
y[1] (numeric) = 1.1150646347215515024527871365274
absolute error = 1.322877205970033e-16
relative error = 1.1863681842087793246970000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9435
Order of pole = 225.1
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.0MB, time=0.39
x[1] = -0.946
y[1] (analytic) = 1.117423311238149725784319422158
y[1] (numeric) = 1.1174233112381495903985925985938
absolute error = 1.353857268235642e-16
relative error = 1.2115885310603677960720000000001e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.5675
Order of pole = 7.373e-28
TOP MAIN SOLVE Loop
x[1] = -0.945
y[1] (analytic) = 1.119789479577839366199154558943
y[1] (numeric) = 1.1197894795778392276891191061003
absolute error = 1.385100354528427e-16
relative error = 1.2369292441027485216749999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9415
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.944
y[1] (analytic) = 1.1221631715024418270611893134157
y[1] (numeric) = 1.1221631715024416854002913378649
absolute error = 1.416608979755508e-16
relative error = 1.2623912597834043770880000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9405
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.943
y[1] (analytic) = 1.1245444189422760104312740301086
y[1] (numeric) = 1.1245444189422758655927054730551
absolute error = 1.448385685570535e-16
relative error = 1.2879755225079126782149999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9395
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.942
y[1] (analytic) = 1.1269332539972322519281827975893
y[1] (numeric) = 1.1269332539972321038848787288984
absolute error = 1.480433040686909e-16
relative error = 1.3136829847160983178760000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9385
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.941
y[1] (analytic) = 1.1293297089378541154468588258811
y[1] (numeric) = 1.1293297089378539641714947063784
absolute error = 1.512753641195027e-16
relative error = 1.3395146069590137029870000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9376
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (analytic) = 1.131733816206428248076052512449
y[1] (numeric) = 1.1317338162064280935410414240911
absolute error = 1.545350110883579e-16
relative error = 1.3654713579767304044000000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9366
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.939
y[1] (analytic) = 1.1341456084180823639223745379774
y[1] (numeric) = 1.1341456084180822060998643814802
absolute error = 1.578225101564972e-16
relative error = 1.3915542147769686768120000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9356
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.938
y[1] (analytic) = 1.1365651183618914262073731252358
y[1] (numeric) = 1.1365651183618912650692437847442
absolute error = 1.611381293404916e-16
relative error = 1.4177641627145549131040000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9346
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.937
y[1] (analytic) = 1.1389923790019920976708744841789
y[1] (numeric) = 1.138992379001991933188734958553
absolute error = 1.644821395256259e-16
relative error = 1.4441021955717424579709999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9336
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.936
y[1] (analytic) = 1.1414274234787055299875812696326
y[1] (numeric) = 1.1414274234787053621327667699228
absolute error = 1.678548144997098e-16
relative error = 1.4705693156393775694079999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9326
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.935
y[1] (analytic) = 1.1438702851096685635848894735337
y[1] (numeric) = 1.1438702851096683923284584862076
absolute error = 1.712564309873261e-16
relative error = 1.4971665337989515977250000000000e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.6058
Order of pole = 3.898e-28
TOP MAIN SOLVE Loop
x[1] = -0.934
y[1] (analytic) = 1.1463209973909734099381445189808
y[1] (numeric) = 1.1463209973909732352508758344625
absolute error = 1.746872686845183e-16
relative error = 1.5238948696055164611480000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9306
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.933
y[1] (analytic) = 1.1487795939983158891151984689065
y[1] (numeric) = 1.1487795939983157109675881749796
absolute error = 1.781476102939269e-16
relative error = 1.5507553513715013325410000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9296
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.932
y[1] (analytic) = 1.151246108788152296045239367091
y[1] (numeric) = 1.1512461087881521144074978067119
absolute error = 1.816377415603791e-16
relative error = 1.5777490162514273535839999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9286
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.931
y[1] (analytic) = 1.1537205757988649696975290766429
y[1] (numeric) = 1.1537205757988647845395777697049
absolute error = 1.851579513069380e-16
relative error = 1.6048769103275288781799999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9276
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (analytic) = 1.1562030292519366400739969938722
y[1] (numeric) = 1.1562030292519364513654655224526
absolute error = 1.887085314714196e-16
relative error = 1.6321400886963081203999999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9266
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.929
y[1] (analytic) = 1.158693503553133628645684272242
y[1] (numeric) = 1.1586935035531334363559071288605
absolute error = 1.922897771433815e-16
relative error = 1.6595396155560111314150000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9256
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.928
y[1] (analytic) = 1.1611920332936979785969084423306
y[1] (numeric) = 1.1611920332936977826949218407382
absolute error = 1.959019866015924e-16
relative error = 1.6870765642950574940159999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9246
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.927
y[1] (analytic) = 1.1636986532515485919828144982888
y[1] (numeric) = 1.1636986532515483924373531463017
absolute error = 1.995454613519871e-16
relative error = 1.7147520175814172265590000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9236
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.926
y[1] (analytic) = 1.1662133983924914516557897830377
y[1] (numeric) = 1.166213398392491248435283616922
absolute error = 2.032205061661157e-16
relative error = 1.7425670674529622597319999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9226
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.925
y[1] (analytic) = 1.1687363038714390065741417092769
y[1] (numeric) = 1.1687363038714387996467125891844
absolute error = 2.069274291200925e-16
relative error = 1.7705228154087914531249999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9216
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.924
y[1] (analytic) = 1.1712674050336387998725661063324
y[1] (numeric) = 1.17126740503363858920602447228
absolute error = 2.106665416340524e-16
relative error = 1.7986203725015472186239999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9206
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.923
y[1] (analytic) = 1.1738067374159114198483676456606
y[1] (numeric) = 1.1738067374159112054102091335387
absolute error = 2.144381585121219e-16
relative error = 1.8268608594307349814510000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9196
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.922
y[1] (analytic) = 1.1763543367478978548002315065335
y[1] (numeric) = 1.1763543367478976365576335236216
absolute error = 2.182425979829119e-16
relative error = 1.8552454066370567959960000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9186
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.921
y[1] (analytic) = 1.1789102389533163334476876265118
y[1] (numeric) = 1.1789102389533161113675058859729
absolute error = 2.220801817405389e-16
relative error = 1.8837751543977645707490000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9176
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (analytic) = 1.1814744801512287334593572778828
y[1] (numeric) = 1.1814744801512285075081222916985
absolute error = 2.259512349861843e-16
relative error = 1.9124512529230639152000000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9166
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.919
y[1] (analytic) = 1.1840470966573166414267293895882
y[1] (numeric) = 1.1840470966573164115706429193915
absolute error = 2.298560864701967e-16
relative error = 1.9412748624535579514870000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9156
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.918
y[1] (analytic) = 1.1866281249851671484376854106446
y[1] (numeric) = 1.1866281249851669146426168758979
absolute error = 2.337950685347467e-16
relative error = 1.9702471533587587801079999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9146
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.917
y[1] (analytic) = 1.1892176018475684662303823691356
y[1] (numeric) = 1.1892176018475682284618652120942
absolute error = 2.377685171570414e-16
relative error = 1.9993693062366738580459999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9136
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.916
y[1] (analytic) = 1.1918155641578154497435212905932
y[1] (numeric) = 1.1918155641578152079667492974862
absolute error = 2.417767719931070e-16
relative error = 2.0286425120144838699200000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9126
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.915
y[1] (analytic) = 1.194422049031025112723580877303
y[1] (numeric) = 1.1944220490310248669034044551554
absolute error = 2.458201764221476e-16
relative error = 2.0580679720503252441000000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9116
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.914
y[1] (analytic) = 1.1970370937854622239033943183832
y[1] (numeric) = 1.1970370937854619740043167268966
absolute error = 2.498990775914866e-16
relative error = 2.0876468982361753969359999999999e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.4967
Order of pole = 5.877e-28
TOP MAIN SOLVE Loop
x[1] = -0.913
y[1] (analytic) = 1.1996607359438750721296017486255
y[1] (numeric) = 1.1996607359438748181157752865233
absolute error = 2.540138264621022e-16
relative error = 2.1173805131018806875180000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9097
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.912
y[1] (analytic) = 1.202293013234841489689135118498
y[1] (numeric) = 1.2022930132348412315243572637345
absolute error = 2.581647778547635e-16
relative error = 2.1472700499203241254400000000000e-14 %
memory used=11.4MB, alloc=4.1MB, time=0.61
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9087
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.911
y[1] (analytic) = 1.2049339635941252239671004830581
y[1] (numeric) = 1.2049339635941249616148099862824
absolute error = 2.623522904967757e-16
relative error = 2.1773167528137458571969999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9077
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (analytic) = 1.2075836251660427484603308779133
y[1] (numeric) = 1.20758362516604248188360380857
absolute error = 2.665767270693433e-16
relative error = 2.2075218768612318673000000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9067
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.909
y[1] (analytic) = 1.2102420363048406050726084709681
y[1] (numeric) = 1.2102420363048403342341542154061
absolute error = 2.708384542555620e-16
relative error = 2.2378866882074002492200000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9057
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.908
y[1] (analytic) = 1.2129092355760833705292165576665
y[1] (numeric) = 1.212909235576083095391373768622
absolute error = 2.751378427890445e-16
relative error = 2.2684124641722678464800000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9047
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.907
y[1] (analytic) = 1.2155852617580523406702007782176
y[1] (numeric) = 1.2155852617580520611949332750239
absolute error = 2.794752675031937e-16
relative error = 2.2991004933623479411130000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9037
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.906
y[1] (analytic) = 1.2182701538431550273136168491636
y[1] (numeric) = 1.2182701538431547434625094680346
absolute error = 2.838511073811290e-16
relative error = 2.3299520757829640384399999999999e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.8576
Order of pole = 1.175e-28
TOP MAIN SOLVE Loop
x[1] = -0.905
y[1] (analytic) = 1.220963951039345563322242910778
y[1] (numeric) = 1.2209639510393452750564973045011
absolute error = 2.882657456062769e-16
relative error = 2.3609685229518093802250000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9017
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.904
y[1] (analytic) = 1.2236666927715561124598637324771
y[1] (numeric) = 1.2236666927715558197402941188403
absolute error = 2.927195696136368e-16
relative error = 2.3921511580137781114880000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9007
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.903
y[1] (analytic) = 1.2263784186831393815864185948401
y[1] (numeric) = 1.2263784186831390843734474531133
absolute error = 2.972129711417268e-16
relative error = 2.4235013158570430826120000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8997
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.902
y[1] (analytic) = 1.2290991686373223337151734750567
y[1] (numeric) = 1.2290991686373220319688271898302
absolute error = 3.017463462852265e-16
relative error = 2.4550203432304542130599999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8987
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.901
y[1] (analytic) = 1.2318289827186712014397617150016
y[1] (numeric) = 1.2318289827186708951196661666818
absolute error = 3.063200955483198e-16
relative error = 2.4867095988622156195980000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8977
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (analytic) = 1.2345679012345679012345679012346
y[1] (numeric) = 1.2345679012345675902999440024812
absolute error = 3.109346238987534e-16
relative error = 2.5185704535799025399999999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8967
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.899
y[1] (analytic) = 1.2373159647166979501386412538465
y[1] (numeric) = 1.2373159647166976345483004312289
absolute error = 3.155903408226176e-16
relative error = 2.5506042904318036693760000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8957
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.898
y[1] (analytic) = 1.24007321392254998735125321799
y[1] (numeric) = 1.2400732139225496670635928381276
absolute error = 3.202876603798624e-16
relative error = 2.5828125048096255880960000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8947
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.897
y[1] (analytic) = 1.2428396898369270042964968077662
y[1] (numeric) = 1.2428396898369266792694955472085
absolute error = 3.250270012605577e-16
relative error = 2.6151965045725607043930000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8937
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.896
y[1] (analytic) = 1.2456154336734693877551020408163
y[1] (numeric) = 1.2456154336734690579463151989063
absolute error = 3.298087868419100e-16
relative error = 2.6477577101727481856000000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8927
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.895
y[1] (analytic) = 1.248400486876189881714053868481
y[1] (numeric) = 1.2484004868761895470806086224358
absolute error = 3.346334452460452e-16
relative error = 2.6804975547821335633000000000000e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.8683
Order of pole = 6.467e-28
TOP MAIN SOLVE Loop
x[1] = -0.894
y[1] (analytic) = 1.2511948911210205746487895940623
y[1] (numeric) = 1.2511948911210202351473801954923
absolute error = 3.395014093985700e-16
relative error = 2.7134174844207549252000000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8907
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.893
y[1] (analytic) = 1.253998688317372020028867049805
y[1] (numeric) = 1.2539986883173716756157499618826
absolute error = 3.444131170879224e-16
relative error = 2.7465189580864662995760000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8897
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.892
y[1] (analytic) = 1.2568119206097045989261798950311
y[1] (numeric) = 1.256811920609704249557168869508
absolute error = 3.493690110255231e-16
relative error = 2.7798034478861181183839999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8887
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.891
y[1] (analytic) = 1.2596346303791122347052014092792
y[1] (numeric) = 1.2596346303791118803356625025402
absolute error = 3.543695389067390e-16
relative error = 2.8132724391682086405900000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8877
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (analytic) = 1.2624668602449185708875142027521
y[1] (numeric) = 1.2624668602449182114723607300795
absolute error = 3.594151534726726e-16
relative error = 2.8469274306570396646000000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8867
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.889
y[1] (analytic) = 1.2653086530662857244081835102445
y[1] (numeric) = 1.2653086530662853599018709374581
absolute error = 3.645063125727864e-16
relative error = 2.8807699345883712043440000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8857
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.888
y[1] (analytic) = 1.2681600519438357276195114032952
y[1] (numeric) = 1.2681600519438353579760321749181
absolute error = 3.696434792283771e-16
relative error = 2.9148014768466139194240000000000e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.2889
Order of pole = 9.300e-28
TOP MAIN SOLVE Loop
x[1] = -0.887
y[1] (analytic) = 1.2710211002212847735485256790747
y[1] (numeric) = 1.271021100221284398721403982164
absolute error = 3.748271216969107e-16
relative error = 2.9490235971035673452830000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8838
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.886
y[1] (analytic) = 1.2738918414870903800783698260883
y[1] (numeric) = 1.2738918414870900000206562888556
absolute error = 3.800577135372327e-16
relative error = 2.9834378489587352056920000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8828
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.885
y[1] (analytic) = 1.276772319576111589900730952153
y[1] (numeric) = 1.2767723195761112045649972764897
absolute error = 3.853357336756633e-16
relative error = 3.0180458000812138814249999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8818
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.884
y[1] (analytic) = 1.2796625785712823242767347105915
y[1] (numeric) = 1.2796625785712819336150682375971
absolute error = 3.906616664729944e-16
relative error = 3.0528490323532031184640000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8808
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.883
y[1] (analytic) = 1.282562662805298009847516125019
y[1] (numeric) = 1.2825626628052976138115143326196
absolute error = 3.960360017923994e-16
relative error = 3.0878491420151409578660000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8798
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.882
y[1] (analytic) = 1.2854726168623155989531111008273
y[1] (numeric) = 1.2854726168623151974938760325579
absolute error = 4.014592350682694e-16
relative error = 3.1230477398124840472560000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8788
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.881
y[1] (analytic) = 1.2883924855796671051495759256134
y[1] (numeric) = 1.2883924855796666982177085496236
absolute error = 4.069318673759898e-16
relative error = 3.1584464511441561915779999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8778
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (analytic) = 1.2913223140495867768595041322314
y[1] (numeric) = 1.2913223140495863644050986295592
absolute error = 4.124544055026722e-16
relative error = 3.1940469162126935168000000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8768
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.879
y[1] (analytic) = 1.2942621476209520333505470198967
y[1] (numeric) = 1.2942621476209516153231850010424
absolute error = 4.180273620188543e-16
relative error = 3.2298507901760960520630000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8758
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.878
y[1] (analytic) = 1.2972120319010382885103335910461
y[1] (numeric) = 1.2972120319010378648590782398632
absolute error = 4.236512553511829e-16
relative error = 3.2658597433014127868360000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8748
Order of pole = 225.1
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.82
x[1] = -0.877
y[1] (analytic) = 1.3001720127572877891745077873803
y[1] (numeric) = 1.3001720127572873598478979312856
absolute error = 4.293266098560947e-16
relative error = 3.3020754611200826051629999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8738
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.876
y[1] (analytic) = 1.3031421363190925960676382894435
y[1] (numeric) = 1.3031421363190921610136823949344
absolute error = 4.350539558945091e-16
relative error = 3.3384996445850481512160000000000e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.555
Order of pole = 5.360e-28
TOP MAIN SOLVE Loop
x[1] = -0.875
y[1] (analytic) = 1.306122448979591836734693877551
y[1] (numeric) = 1.3061224489795913959008639700017
absolute error = 4.408338299075493e-16
relative error = 3.3751340102296743281250000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8718
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.874
y[1] (analytic) = 1.3091129973974833611738030779865
y[1] (numeric) = 1.3091129973974829145070285846809
absolute error = 4.466667744933056e-16
relative error = 3.4119802903284830850559999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8708
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.873
y[1] (analytic) = 1.3121138284988499322293207580344
y[1] (numeric) = 1.3121138284988494796759822733769
absolute error = 4.525533384846575e-16
relative error = 3.4490402330597353581750000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8698
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.872
y[1] (analytic) = 1.315124989479000084167999326656
y[1] (numeric) = 1.3151249894789996256739222984857
absolute error = 4.584940770281703e-16
relative error = 3.4863156026698824539520000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8688
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.871
y[1] (analytic) = 1.318146527804323784240503742877
y[1] (numeric) = 1.3181465278043233197509520787955
absolute error = 4.644895516640815e-16
relative error = 3.5238081796399045324150000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8678
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (analytic) = 1.3211784912141630334258158277183
y[1] (numeric) = 1.3211784912141625628854854203237
absolute error = 4.705403304073946e-16
relative error = 3.5615197608535697274000000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8668
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.869
y[1] (analytic) = 1.3242209277226975439674453527129
y[1] (numeric) = 1.3242209277226970673204575226173
absolute error = 4.766469878300956e-16
relative error = 3.5994521597676282339159999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8658
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.868
y[1] (analytic) = 1.3272738856208456327380067531696
y[1] (numeric) = 1.3272738856208451499279016086593
absolute error = 4.828101051445103e-16
relative error = 3.6376072065839752826719999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8648
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.867
y[1] (analytic) = 1.3303374134781804709128376230063
y[1] (numeric) = 1.3303374134781799818825673351879
absolute error = 4.890302702878184e-16
relative error = 3.6759867484237992527760000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8638
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.866
y[1] (analytic) = 1.333411560144861831894137789417
y[1] (numeric) = 1.3334115601448613365860597816737
absolute error = 4.953080780077433e-16
relative error = 3.7145926495037513429479999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8628
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.865
y[1] (analytic) = 1.3364963747535834809048080457082
y[1] (numeric) = 1.3364963747535829792606780962752
absolute error = 5.016441299494330e-16
relative error = 3.7534267913141450642499999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8618
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.864
y[1] (analytic) = 1.3395919067215363511659807956104
y[1] (numeric) = 1.3395919067215358431269460520576
absolute error = 5.080390347435528e-16
relative error = 3.7924910727992319098880000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8608
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.863
y[1] (analytic) = 1.3426982057523876530843791833441
y[1] (numeric) = 1.3426982057523871385909710877377
absolute error = 5.144934080956064e-16
relative error = 3.8317874105395668292160000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8598
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.862
y[1] (analytic) = 1.3458153218382760644053380418926
y[1] (numeric) = 1.3458153218382755433974651653888
absolute error = 5.210078728765038e-16
relative error = 3.8713177389364888956719999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8588
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.861
y[1] (analytic) = 1.3489433052618231508347935644613
y[1] (numeric) = 1.3489433052618226232517343500649
absolute error = 5.275830592143964e-16
relative error = 3.9110840103987555364439999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8578
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (analytic) = 1.3520822065981611681990265008113
y[1] (numeric) = 1.3520822065981606339794219130141
absolute error = 5.342196045877972e-16
relative error = 3.9510881955313480911999999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8568
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.859
y[1] (analytic) = 1.3552320767169773987946565909679
y[1] (numeric) = 1.3552320767169768578765026709625
absolute error = 5.409181539200054e-16
relative error = 3.9913322833264750455740000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8559
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.858
y[1] (analytic) = 1.3583929667845751761835677919594
y[1] (numeric) = 1.3583929667845746285042081171021
absolute error = 5.476793596748573e-16
relative error = 4.0318182813568164939720000000000e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.1826
Order of pole = 6.045e-28
TOP MAIN SOLVE Loop
x[1] = -0.857
y[1] (analytic) = 1.3615649282659517543083318242656
y[1] (numeric) = 1.3615649282659511998044498704451
absolute error = 5.545038819538205e-16
relative error = 4.0725482159710151240449999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8539
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.856
y[1] (analytic) = 1.3647480129268931784435321862172
y[1] (numeric) = 1.3647480129268926170511435917625
absolute error = 5.613923885944547e-16
relative error = 4.1135241324914635905919999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8529
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.855
y[1] (analytic) = 1.3679422728360863171574159570467
y[1] (numeric) = 1.367942272836085748811860686788
absolute error = 5.683455552702587e-16
relative error = 4.1547480954144086616749999999997e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8519
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.854
y[1] (analytic) = 1.3711477603672482161367637622101
y[1] (numeric) = 1.3711477603672476407726981702859
absolute error = 5.753640655919242e-16
relative error = 4.1962221886123978984719999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8509
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.853
y[1] (analytic) = 1.3743645282012729364260200189937
y[1] (numeric) = 1.374364528201272353977408808974
absolute error = 5.824486112100197e-16
relative error = 4.2379485155391122389730000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8499
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.852
y[1] (analytic) = 1.3775926293283960413498203619211
y[1] (numeric) = 1.3775926293283954517499284427968
absolute error = 5.895998919191243e-16
relative error = 4.2799291994366000586720000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8489
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.851
y[1] (analytic) = 1.3808321170503768981263489003744
y[1] (numeric) = 1.3808321170503763013077331369392
absolute error = 5.968186157634352e-16
relative error = 4.3221663835449553527519999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8479
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (analytic) = 1.3840830449826989619377162629758
y[1] (numeric) = 1.3840830449826983578322171191057
absolute error = 6.041054991438701e-16
relative error = 4.3646622313144614724999999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8469
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.849
y[1] (analytic) = 1.387345467056788212003035511882
y[1] (numeric) = 1.3873454670567876005417685851918
absolute error = 6.114612669266902e-16
relative error = 4.4074189266202522285019999999997e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8459
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.848
y[1] (analytic) = 1.3906194375222499110003559985761
y[1] (numeric) = 1.3906194375222492921137034449135
absolute error = 6.188866525536626e-16
relative error = 4.4504386739794899031039999999997e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8449
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.847
y[1] (analytic) = 1.3939050109491238610053679281972
y[1] (numeric) = 1.3939050109491232346229697744066
absolute error = 6.263823981537906e-16
relative error = 4.4937236987711276055539999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8439
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.846
y[1] (analytic) = 1.3972022422301583309580895215421
y[1] (numeric) = 1.3972022422301576970088348649087
absolute error = 6.339492546566334e-16
relative error = 4.5372762474582703051439999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8429
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.845
y[1] (analytic) = 1.4005111865831028325338748643254
y[1] (numeric) = 1.4005111865831021909458929570862
absolute error = 6.415879819072392e-16
relative error = 4.5810985878131646978000000000003e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8419
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.844
y[1] (analytic) = 1.4038318995530199231823184564588
y[1] (numeric) = 1.4038318995530192738829696737389
absolute error = 6.492993487827199e-16
relative error = 4.6251930091448756268639999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8409
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.843
y[1] (analytic) = 1.407164437014616217007270818646
y[1] (numeric) = 1.4071644370146155599231375081584
absolute error = 6.570841333104876e-16
relative error = 4.6695618225296470245240000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8399
Order of pole = 225.1
memory used=19.0MB, alloc=4.1MB, time=1.03
TOP MAIN SOLVE Loop
x[1] = -0.842
y[1] (analytic) = 1.4105088551745927860935110950627
y[1] (numeric) = 1.4105088551745921211503883068776
absolute error = 6.649431227881851e-16
relative error = 4.7142073610440286123639999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8389
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.841
y[1] (analytic) = 1.4138652105740151368409444054061
y[1] (numeric) = 1.4138652105740144639638305000761
absolute error = 6.728771139053300e-16
relative error = 4.7591319800007570772999999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8379
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (analytic) = 1.4172335600907029478458049886621
y[1] (numeric) = 1.4172335600907022669588921219575
absolute error = 6.808869128667046e-16
relative error = 4.8043380571874676576000000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8369
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.839
y[1] (analytic) = 1.4206139609416397578705564971069
y[1] (numeric) = 1.4206139609416390688972209795915
absolute error = 6.889733355175154e-16
relative error = 4.8498279931082495788340000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8359
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.838
y[1] (analytic) = 1.4240064706854027944702980730345
y[1] (numeric) = 1.4240064706854020973330906026843
absolute error = 6.971372074703502e-16
relative error = 4.8956042112280860584879999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8349
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.837
y[1] (analytic) = 1.4274111472246131358938234492248
y[1] (numeric) = 1.4274111472246124305144592152628
absolute error = 7.053793642339620e-16
relative error = 4.9416691582202252437800000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8339
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.836
y[1] (analytic) = 1.4308280488084064009523591492868
y[1] (numeric) = 1.4308280488084056872517078053787
absolute error = 7.137006513439081e-16
relative error = 4.9880253042165199545760000000003e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8329
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.835
y[1] (analytic) = 1.4342572340349241636487504033848
y[1] (numeric) = 1.4342572340349234415468259083136
absolute error = 7.221019244950712e-16
relative error = 5.0346751430607601742000000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8319
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.834
y[1] (analytic) = 1.4376987618538262914847977732922
y[1] (numeric) = 1.4376987618538255609007480971973
absolute error = 7.305840496760949e-16
relative error = 5.0816211925650586426439999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8309
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.833
y[1] (analytic) = 1.4411526915688244085149065628652
y[1] (numeric) = 1.4411526915688236693670032571042
absolute error = 7.391479033057610e-16
relative error = 5.1288659947693119452900000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8299
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.832
y[1] (analytic) = 1.4446190828402366863905325443787
y[1] (numeric) = 1.4446190828402359385961601730364
absolute error = 7.477943723713423e-16
relative error = 5.1764121162038005227520000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.829
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.831
y[1] (analytic) = 1.4480979956875641688424339051872
y[1] (numeric) = 1.4480979956875634123180793362303
absolute error = 7.565243545689569e-16
relative error = 5.2242621481549344582090000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.828
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (analytic) = 1.4515894904920888372768181158369
y[1] (numeric) = 1.4515894904920880719380596698757
absolute error = 7.653387584459612e-16
relative error = 5.2724187069342267067999999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.827
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.829
y[1] (analytic) = 1.4550936279994936274174561762176
y[1] (numeric) = 1.455093627999492853178952630809
absolute error = 7.742385035454086e-16
relative error = 5.3208844341505015167260000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.826
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.828
y[1] (analytic) = 1.4586104693225046092090830591146
y[1] (numeric) = 1.4586104693225038259845625065035
absolute error = 7.832245205526111e-16
relative error = 5.3696619969854132838239999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.825
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.827
y[1] (analytic) = 1.4621400759435555445082749817599
y[1] (numeric) = 1.4621400759435547522105235379281
absolute error = 7.922977514438318e-16
relative error = 5.4187540884722843914219999999996e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.824
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.826
y[1] (analytic) = 1.4656825097174750394268595114001
y[1] (numeric) = 1.4656825097174742379677098742531
absolute error = 8.014591496371470e-16
relative error = 5.4681634277783410657199999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.823
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.825
y[1] (analytic) = 1.4692378328741965105601469237833
y[1] (numeric) = 1.4692378328741956998504667782743
absolute error = 8.107096801455090e-16
relative error = 5.5178927604903706312500000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.822
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.824
y[1] (analytic) = 1.4728061080214911867282495993967
y[1] (numeric) = 1.4728061080214903666779298673514
absolute error = 8.200503197320453e-16
relative error = 5.5679448589038518961280000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.821
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.823
y[1] (analytic) = 1.4763873981477243702838650050419
y[1] (numeric) = 1.4763873981477235408018079374119
absolute error = 8.294820570676300e-16
relative error = 5.6183225223156076026999999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.82
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.822
y[1] (analytic) = 1.479981766624635184494527027427
y[1] (numeric) = 1.4799817666246343454886341366644
absolute error = 8.390058928907626e-16
relative error = 5.6690285773200203661840000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.819
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.821
y[1] (analytic) = 1.483589277210140035991875865118
y[1] (numeric) = 1.4835892772101391873690356953254
absolute error = 8.486228401697926e-16
relative error = 5.7200658781088717389660000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.818
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (analytic) = 1.4872099940511600237953599048185
y[1] (numeric) = 1.4872099940511591654614356372941
absolute error = 8.583339242675244e-16
relative error = 5.7714373067748340656000000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.817
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.819
y[1] (analytic) = 1.4908439816864725289633714542139
y[1] (numeric) = 1.4908439816864716608231883459703
absolute error = 8.681401831082436e-16
relative error = 5.8231457736186858537960000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.816
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.818
y[1] (analytic) = 1.4944913050495872215015453040094
y[1] (numeric) = 1.4944913050495863434588779568088
absolute error = 8.780426673472006e-16
relative error = 5.8751942174602825427440000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.815
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.817
y[1] (analytic) = 1.4981520294716467237662343499294
y[1] (numeric) = 1.4981520294716458357237938073368
absolute error = 8.880424405425926e-16
relative error = 5.9275856059533459198139999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.814
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.816
y[1] (analytic) = 1.5018262206843521722414455978469
y[1] (numeric) = 1.5018262206843512741008662677644
absolute error = 8.981405793300825e-16
relative error = 5.9803229359041141312000000000003e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.813
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.815
y[1] (analytic) = 1.5055139448229139222402047498964
y[1] (numeric) = 1.5055139448229130139020311499991
absolute error = 9.083381735998973e-16
relative error = 6.0334092335939178409250000000004e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.812
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.814
y[1] (analytic) = 1.5092152684290276427868565460703
y[1] (numeric) = 1.5092152684290267241505298695259
absolute error = 9.186363266765444e-16
relative error = 6.0868475551057161326240000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.811
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.813
y[1] (analytic) = 1.5129302584538760516756459077506
y[1] (numeric) = 1.5129302584538751226394904065602
absolute error = 9.290361555011904e-16
relative error = 6.1406409866546631749760000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.81
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.812
y[1] (analytic) = 1.5166589822611565434735130675337
y[1] (numeric) = 1.5166589822611556039347222507893
absolute error = 9.395387908167444e-16
relative error = 6.1947926449227551967360000000004e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.809
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.811
y[1] (analytic) = 1.5204015076301349660418323270809
y[1] (numeric) = 1.5204015076301340158964549713919
absolute error = 9.501453773556890e-16
relative error = 6.2493056773976112476900000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.808
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (analytic) = 1.5241579027587258039932937052279
y[1] (numeric) = 1.5241579027587248431362196745255
absolute error = 9.608570740307024e-16
relative error = 6.3041832627154384463999999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.807
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.809
y[1] (analytic) = 1.5279282362665990303767412652163
y[1] (numeric) = 1.5279282362665980587016871370976
absolute error = 9.716750541281187e-16
relative error = 6.3594286110082525489469999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.806
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.808
y[1] (analytic) = 1.5317125771983138907950200960691
y[1] (numeric) = 1.5317125771983129081945145917979
absolute error = 9.826005055042712e-16
relative error = 6.4150449642554051271679999999996e-14 %
Correct digits = 15
h = 0.001
memory used=22.8MB, alloc=4.1MB, time=1.25
Real estimate of pole used for equation 1
Radius of convergence = 0.805
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.807
y[1] (analytic) = 1.5355109950264798871092316456532
y[1] (numeric) = 1.5355109950264788934746008608893
absolute error = 9.936346307847639e-16
relative error = 6.4710355966394670511110000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.804
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.806
y[1] (analytic) = 1.5393235596549452308677474770486
y[1] (numeric) = 1.539323559654944226089099910327
absolute error = 1.0047786475667216e-15
relative error = 6.5274038149065475333760000000004e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.803
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.805
y[1] (analytic) = 1.5431503414220130396203850160102
y[1] (numeric) = 1.5431503414220120235865963919465
absolute error = 1.0160337886240637e-15
relative error = 6.5841529587310887919249999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8021
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.804
y[1] (analytic) = 1.54699141110368555233781342046
y[1] (numeric) = 1.5469914111036845249365113046074
absolute error = 1.0274013021158526e-15
relative error = 6.6412864010852097428159999999995e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8011
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.803
y[1] (analytic) = 1.5508468399169366432540488733873
y[1] (numeric) = 1.5508468399169356043715970756209
absolute error = 1.0388824517977664e-15
relative error = 6.6988075486126595461760000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8001
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.802
y[1] (analytic) = 1.5547166995230129165863396371913
y[1] (numeric) = 1.5547166995230118661078224004437
absolute error = 1.0504785172367476e-15
relative error = 6.7567198420074500331040000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7991
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.801
y[1] (analytic) = 1.5586010620307636677623632132743
y[1] (numeric) = 1.5586010620307626055715691843985
absolute error = 1.0621907940288758e-15
relative error = 6.8150267563972074215580000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7981
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (analytic) = 1.5625
y[1] (numeric) = 1.5624999999999989259794059794775
absolute error = 1.0740205940205225e-15
relative error = 6.8737318017313440000000000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7971
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.799
y[1] (analytic) = 1.5664135864448833883405571106562
y[1] (numeric) = 1.5664135864448823023713115778193
absolute error = 1.0859692455328369e-15
relative error = 6.9328385231740860979689999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7961
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.798
y[1] (analytic) = 1.5703418948373439865327479098749
y[1] (numeric) = 1.5703418948373428884946543202551
absolute error = 1.0980380935896198e-15
relative error = 6.9923505015024424711920000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7951
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.797
y[1] (analytic) = 1.574284999110528975502551128841
y[1] (numeric) = 1.5742849991105278652740509802008
absolute error = 1.1102285001486402e-15
relative error = 7.0522713535091759280180000000003e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7941
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.796
y[1] (analytic) = 1.578242973662281255523850407818
y[1] (numeric) = 1.5782429736622801329820060713674
absolute error = 1.1225418443364506e-15
relative error = 7.1126047324108448336959999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7931
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.795
y[1] (analytic) = 1.5822158933586487876270717139353
y[1] (numeric) = 1.5822158933586476526475490271762
absolute error = 1.1349795226867591e-15
relative error = 7.1733543282609892017750000000003e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7921
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.794
y[1] (analytic) = 1.5862038335374248932484820029314
y[1] (numeric) = 1.5862038335374237457055326205142
absolute error = 1.1475429493824172e-15
relative error = 7.2345238683685356989919999999996e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7911
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.793
y[1] (analytic) = 1.5902068700117198246319863751076
y[1] (numeric) = 1.5902068700117186643984298740273
absolute error = 1.1602335565010803e-15
relative error = 7.2961171177214784557469999999997e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7901
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.792
y[1] (analytic) = 1.5942250790735639220487705336191
y[1] (numeric) = 1.5942250790735627489959762690137
absolute error = 1.1730527942646054e-15
relative error = 7.3581378794159344162559999999996e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7891
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.791
y[1] (analytic) = 1.5982585374975426774985975281334
y[1] (numeric) = 1.5982585374975414914964662358897
absolute error = 1.1860021312922437e-15
relative error = 7.4205899950906233045969999999997e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7881
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (analytic) = 1.6023073225444640282006088767825
y[1] (numeric) = 1.6023073225444628291175540190894
absolute error = 1.1990830548576931e-15
relative error = 7.4834773453668626371000000000003e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7871
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.789
y[1] (analytic) = 1.6063715119650582068717360538842
y[1] (numeric) = 1.6063715119650569945746649038098
absolute error = 1.2122970711500744e-15
relative error = 7.5468038502941546556239999999997e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7861
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.788
y[1] (analytic) = 1.6104511840037104795279445489448
y[1] (numeric) = 1.6104511840037092538822390100514
absolute error = 1.2256457055388934e-15
relative error = 7.6105734698014262336960000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7851
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.787
y[1] (analytic) = 1.6145464174022271053281646320691
y[1] (numeric) = 1.6145464174022258661976617890088
absolute error = 1.2391305028430603e-15
relative error = 7.6747902041540341495070000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7841
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.786
y[1] (analytic) = 1.6186572914036348568135760024345
y[1] (numeric) = 1.6186572914036336040605483984069
absolute error = 1.2527530276040276e-15
relative error = 7.7394580944165783516959999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7831
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.785
y[1] (analytic) = 1.6227838857560144427765832285285
y[1] (numeric) = 1.6227838857560131762617188654088
absolute error = 1.2665148643631197e-15
relative error = 7.8045812229216343713250000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7821
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.784
y[1] (analytic) = 1.6269262807163681799250312369846
y[1] (numeric) = 1.6269262807163668995074132938629
absolute error = 1.2804176179431217e-15
relative error = 7.8701637137444741163520000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7811
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.783
y[1] (analytic) = 1.6310845570545222634886615157017
y[1] (numeric) = 1.6310845570545209690257477815037
absolute error = 1.2944629137341980e-15
relative error = 7.9362097331838571762199999999997e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7801
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.782
y[1] (analytic) = 1.6352587960570639909472073050281
y[1] (numeric) = 1.6352587960570626822948093208133
absolute error = 1.3086523979842148e-15
relative error = 8.0027234902489897135520000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7791
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.781
y[1] (analytic) = 1.6394490795313142971435878687326
y[1] (numeric) = 1.6394490795313129741558497751938
absolute error = 1.3229877380935388e-15
relative error = 8.0697092371527301998680000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7781
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (analytic) = 1.6436554898093359631821170282709
y[1] (numeric) = 1.6436554898093346257114941138844
absolute error = 1.3374706229143865e-15
relative error = 8.1371712698111274659999999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7771
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.779
y[1] (analytic) = 1.6478781097519778657012298114332
y[1] (numeric) = 1.6478781097519765135984667566319
absolute error = 1.3521027630548013e-15
relative error = 8.2051139283493867569330000000005e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7761
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.778
y[1] (analytic) = 1.6521170227529556373537050376352
y[1] (numeric) = 1.6521170227529542704678138502985
absolute error = 1.3668858911873367e-15
relative error = 8.2735415976143590712280000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7752
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.777
y[1] (analytic) = 1.656372312742969113625484281855
y[1] (numeric) = 1.6563723127429677318037219193338
absolute error = 1.3818217623625212e-15
relative error = 8.3424587076936256155479999999997e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7742
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.776
y[1] (analytic) = 1.6606440641938569454777340843872
y[1] (numeric) = 1.6606440641938555485655797571975
absolute error = 1.3969121543271897e-15
relative error = 8.4118697344412978478720000000004e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7732
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.775
y[1] (analytic) = 1.6649323621227887617065556711759
y[1] (numeric) = 1.6649323621227873495476878234144
absolute error = 1.4121588678477615e-15
relative error = 8.4817792000106175093749999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7722
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.774
y[1] (analytic) = 1.6692372920964952693815141985324
y[1] (numeric) = 1.6692372920964938418177871599869
absolute error = 1.4275637270385455e-15
relative error = 8.5521916733934368395800000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7712
Order of pole = 225.1
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.2MB, time=1.47
x[1] = -0.773
y[1] (analytic) = 1.6735589402355366852487494330819
y[1] (numeric) = 1.6735589402355352421201697379185
absolute error = 1.4431285796951634e-15
relative error = 8.6231117709667129123860000000000e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.5888
Order of pole = 1.095e-27
TOP MAIN SOLVE Loop
x[1] = -0.772
y[1] (analytic) = 1.6778973932186098955676662460737
y[1] (numeric) = 1.6778973932186084367123686129026
absolute error = 1.4588552976331711e-15
relative error = 8.6945441570460784486240000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7692
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.771
y[1] (analytic) = 1.6822527382868947464929236038564
y[1] (numeric) = 1.6822527382868932717471465718854
absolute error = 1.4747457770319710e-15
relative error = 8.7664935444466187321100000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7682
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (analytic) = 1.6866250632484398718164951931186
y[1] (numeric) = 1.6866250632484383810145564090166
absolute error = 1.4908019387841020e-15
relative error = 8.8389646950509407579999999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7672
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.769
y[1] (analytic) = 1.6910144564825884696488270278222
y[1] (numeric) = 1.6910144564825869626230981778224
absolute error = 1.5070257288499998e-15
relative error = 8.9119624203846473172780000000003e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7662
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.768
y[1] (analytic) = 1.6954210069444444444444444444444
y[1] (numeric) = 1.6954210069444429210253258261238
absolute error = 1.5234191186183206e-15
relative error = 8.9854915821993232957440000000002e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7652
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.767
y[1] (analytic) = 1.6998448041693793356666536345232
y[1] (numeric) = 1.6998448041693777956825483626025
absolute error = 1.5399841052719207e-15
relative error = 9.0595570930631295668229999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7642
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.766
y[1] (analytic) = 1.7042859382775804593391460845735
y[1] (numeric) = 1.7042859382775789026164339249819
absolute error = 1.5567227121595916e-15
relative error = 9.1341639169591332884959999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7632
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.765
y[1] (analytic) = 1.7087444999786406937502669913281
y[1] (numeric) = 1.7087444999786391201132778176819
absolute error = 1.5736369891736462e-15
relative error = 9.2093170698914709739500000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7622
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.764
y[1] (analytic) = 1.7132205805761903456593843370522
y[1] (numeric) = 1.713220580576188754930371203595
absolute error = 1.5907290131334572e-15
relative error = 9.2850216204994643381119999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7612
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.763
y[1] (analytic) = 1.7177142719725715385051419776731
y[1] (numeric) = 1.7177142719725699305042538026246
absolute error = 1.6080008881750485e-15
relative error = 9.3612826906797981019650000000003e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7602
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.762
y[1] (analytic) = 1.722225666673555569333360888944
y[1] (numeric) = 1.7222256666735539438786147420986
absolute error = 1.6254547461468454e-15
relative error = 9.4381054562168890043760000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7592
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.761
y[1] (analytic) = 1.7267548577931036864489459024971
y[1] (numeric) = 1.7267548577931020433561988908116
absolute error = 1.6430927470116855e-15
relative error = 9.5154951474215431844549999999998e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7582
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (analytic) = 1.7313019390581717451523545706371
y[1] (numeric) = 1.7313019390581700842352753154352
absolute error = 1.6609170792552019e-15
relative error = 9.5934570497780461744000000000001e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.2564
Order of pole = 1.536e-28
TOP MAIN SOLVE Loop
x[1] = -0.759
y[1] (analytic) = 1.735867004813559204347999673657
y[1] (numeric) = 1.7358670048135575254180393729714
absolute error = 1.6789299603006856e-15
relative error = 9.6719965045997926113360000000000e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7562
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.758
y[1] (analytic) = 1.7404501500268029323104127651575
y[1] (numeric) = 1.7404501500268012351767758346187
absolute error = 1.6971336369305388e-15
relative error = 9.7511189096935809508320000000004e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7552
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.757
y[1] (analytic) = 1.7450514702931162954651347441493
y[1] (numeric) = 1.745051470293114579934749029715
absolute error = 1.7155303857144343e-15
relative error = 9.8308297200327086118069999999999e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7542
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.756
y[1] (analytic) = 1.7496710618403740096861789983483
y[1] (numeric) = 1.749671061840372275563665554054
absolute error = 1.7341225134442943e-15
relative error = 9.9111344484389818704480000000001e-14 %
Correct digits = 15
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7532
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.755
y[1] (analytic) = 1.7543090215341432393316082627955
y[1] (numeric) = 1.7543090215341414864192506865864
absolute error = 1.7529123575762091e-15
relative error = 9.9920386662737859222750000000000e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.1886
Order of pole = 7.63e-29
TOP MAIN SOLVE Loop
x[1] = -0.754
y[1] (analytic) = 1.7589654468827614350343701848321
y[1] (numeric) = 1.7589654468827596631320835054184
absolute error = 1.7719022866794137e-15
relative error = 1.0073548004138335590692000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7512
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.753
y[1] (analytic) = 1.7636404360424614071381583008382
y[1] (numeric) = 1.7636404360424596160434574083928
absolute error = 1.7910947008924454e-15
relative error = 1.0155668152583245738086000000000e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.4195
Order of pole = 4.858e-28
TOP MAIN SOLVE Loop
x[1] = -0.752
y[1] (analytic) = 1.7683340878225441376188320507017
y[1] (numeric) = 1.7683340878225423271267996640942
absolute error = 1.8104920323866075e-15
relative error = 1.0238404862827560876800000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7492
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.751
y[1] (analytic) = 1.7730465016905998393619869468317
y[1] (numeric) = 1.7730465016905980092652411099671
absolute error = 1.8300967458368646e-15
relative error = 1.0321763947487374712646000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7482
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (analytic) = 1.7777777777777777777777777777777
y[1] (numeric) = 1.7777777777777759278664388774772
absolute error = 1.8499113389003005e-15
relative error = 1.0405751281314190312500000000000e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.4637
Order of pole = 2.366e-28
TOP MAIN SOLVE Loop
x[1] = -0.749
y[1] (analytic) = 1.7825280168841053759262461207734
y[1] (numeric) = 1.7825280168841035059879034185038
absolute error = 1.8699383427022696e-15
relative error = 1.0490372801943159478696000000000e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.233
Order of pole = 2.083e-28
TOP MAIN SOLVE Loop
x[1] = -0.748
y[1] (analytic) = 1.7872973204838571306013898023964
y[1] (numeric) = 1.7872973204838552404210674720216
absolute error = 1.8901803223303748e-15
relative error = 1.0575634510651340220992000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7453
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.747
y[1] (analytic) = 1.7920857907309738731812569331319
y[1] (numeric) = 1.7920857907309719625413795967204
absolute error = 1.9106398773364115e-15
relative error = 1.0661542473126136447035000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7443
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.746
y[1] (analytic) = 1.7968935304645329154956910493139
y[1] (numeric) = 1.7968935304645309841760488028995
absolute error = 1.9313196422464144e-15
relative error = 1.0748102820244055562304000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7433
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.745
y[1] (analytic) = 1.8017206432142696274942570154498
y[1] (numeric) = 1.8017206432142676752719699364998
absolute error = 1.9522222870789500e-15
relative error = 1.0835321748859942237500000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7423
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.744
y[1] (analytic) = 1.8065672332061510001156203029251
y[1] (numeric) = 1.8065672332061490267651024311261
absolute error = 1.9733505178717990e-15
relative error = 1.0923205522606841312640000000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7413
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.743
y[1] (analytic) = 1.8114334053680017534675363962257
y[1] (numeric) = 1.8114334053679997587604591790477
absolute error = 1.9947070772171780e-15
relative error = 1.1011760472706658977220000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7403
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.742
y[1] (analytic) = 1.8163192653351835572249547736503
y[1] (numeric) = 1.8163192653351815409302099680041
absolute error = 2.0162947448056462e-15
relative error = 1.1100992998791757944568000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7393
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.741
y[1] (analytic) = 1.8212249194563279370438969842336
y[1] (numeric) = 1.8212249194563258989275590053782
absolute error = 2.0381163379788554e-15
relative error = 1.1190909569737679018874000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7383
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (analytic) = 1.8261504747991234477720964207451
y[1] (numeric) = 1.82615047479912138759738412945
absolute error = 2.0601747122912951e-15
relative error = 1.1281516724507131967600000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7373
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.739
y[1] (analytic) = 1.8310960391561577013152762849258
y[1] (numeric) = 1.8310960391561556188425142037327
absolute error = 2.0824727620811931e-15
relative error = 1.1372821073005432569651000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7363
Order of pole = 225.1
memory used=30.5MB, alloc=4.2MB, time=1.69
TOP MAIN SOLVE Loop
x[1] = -0.738
y[1] (analytic) = 1.8360617210508148441918023516279
y[1] (numeric) = 1.8360617210508127391783813008933
absolute error = 2.1050134210507346e-15
relative error = 1.1464829296947562954824000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7353
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.737
y[1] (analytic) = 1.841047629743229087079711839225
y[1] (numeric) = 1.8410476297432269592800489834635
absolute error = 2.1277996628557615e-15
relative error = 1.1557548150737011181935000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7343
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.736
y[1] (analytic) = 1.8460538752362948960302457466918
y[1] (numeric) = 1.8460538752362927451957440415674
absolute error = 2.1508345017051244e-15
relative error = 1.1650984462356590669824000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7333
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.735
y[1] (analytic) = 1.8510805682817344624924799851913
y[1] (numeric) = 1.8510805682817322883714870153365
absolute error = 2.1741209929698548e-15
relative error = 1.1745145134271398093300000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7323
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.734
y[1] (analytic) = 1.8561278203862230768659652978343
y[1] (numeric) = 1.8561278203862208792037314955007
absolute error = 2.1976622338023336e-15
relative error = 1.1840037144344100410016000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7313
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.733
y[1] (analytic) = 1.86119574381757303797397676111
y[1] (numeric) = 1.8611957438175708165126129954753
absolute error = 2.2214613637656347e-15
relative error = 1.1935667546762741023283000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7303
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.732
y[1] (analytic) = 1.8662844516109767386305951207859
y[1] (numeric) = 1.8662844516109744931090296475625
absolute error = 2.2455215654732234e-15
relative error = 1.2032043472981244550816000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7293
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.731
y[1] (analytic) = 1.8713940575753095753619743955865
y[1] (numeric) = 1.8713940575753073055159091563903
absolute error = 2.2698460652391962e-15
relative error = 1.2129172132672821206282000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7283
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (analytic) = 1.8765246762994933383373991367986
y[1] (numeric) = 1.8765246762994910438992653975507
absolute error = 2.2944381337392479e-15
relative error = 1.2227060814696452059100000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7273
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.729
y[1] (analytic) = 1.8816764231589207456707329694171
y[1] (numeric) = 1.8816764231589184263696462868556
absolute error = 2.3193010866825615e-15
relative error = 1.2325716888076671661215000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7263
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.728
y[1] (analytic) = 1.8868494143219417944692669967396
y[1] (numeric) = 1.8868494143219394500309815019263
absolute error = 2.3444382854948133e-15
relative error = 1.2425147802996831319872000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7253
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.727
y[1] (analytic) = 1.8920437667564126093364791714362
y[1] (numeric) = 1.8920437667564102394833411589415
absolute error = 2.3698531380124947e-15
relative error = 1.2525361091806058112963000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7243
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.726
y[1] (analytic) = 1.897259598236307477479528568935
y[1] (numeric) = 1.8972595982363050819304293801809
absolute error = 2.3955490991887541e-15
relative error = 1.2626364370040117560116000000000e-13 %
Correct digits = 14
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.6403
Order of pole = 3.008e-28
TOP MAIN SOLVE Loop
x[1] = -0.725
y[1] (analytic) = 1.9024970273483947681331747919143
y[1] (numeric) = 1.9024970273483923466035029809494
absolute error = 2.4215296718109649e-15
relative error = 1.2728165337456384255625000000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7223
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.724
y[1] (analytic) = 1.9077561734989774426910045480907
y[1] (numeric) = 1.9077561734989749948925973178585
absolute error = 2.4477984072302322e-15
relative error = 1.2830771779083141936672000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7213
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.723
y[1] (analytic) = 1.9130371569206988707341662697115
y[1] (numeric) = 1.9130371569206963963752601666586
absolute error = 2.4743589061030529e-15
relative error = 1.2934191566283427393641000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7204
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.722
y[1] (analytic) = 1.918340098679414676069090936994
y[1] (numeric) = 1.9183400986794121748542717916442
absolute error = 2.5012148191453498e-15
relative error = 1.3038432657833645251432000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7194
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.721
y[1] (analytic) = 1.9236651206811313459307749869671
y[1] (numeric) = 1.9236651206811288175609270878642
absolute error = 2.5283698478991029e-15
relative error = 1.3143503101017175506389000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7184
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (analytic) = 1.929012345679012345679012345679
y[1] (numeric) = 1.9290123456790097898512668338731
absolute error = 2.5558277455118059e-15
relative error = 1.3249411032733201785600000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7174
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.719
y[1] (analytic) = 1.9343818972804524906134118434466
y[1] (numeric) = 1.9343818972804499070210943144653
absolute error = 2.5835923175289813e-15
relative error = 1.3356164680620997018293000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7164
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.718
y[1] (analytic) = 1.9397738999542213359610803764713
y[1] (numeric) = 1.9397738999542187242936576764792
absolute error = 2.6116674226999921e-15
relative error = 1.3463772364199907273604000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7154
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.717
y[1] (analytic) = 1.9451884790376763556504807533326
y[1] (numeric) = 1.9451884790376737155935069559425
absolute error = 2.6400569737973901e-15
relative error = 1.3572242496025264791189000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7144
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.716
y[1] (analytic) = 1.9506257607440466901782091695015
y[1] (numeric) = 1.9506257607440440214132707194523
absolute error = 2.6687649384500492e-15
relative error = 1.3681583582860484226752000000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7134
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.715
y[1] (analytic) = 1.9560858721697882537043376204215
y[1] (numeric) = 1.9560858721697855559089976300859
absolute error = 2.6977953399903356e-15
relative error = 1.3791804226865593171100000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7124
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.714
y[1] (analytic) = 1.9615689413020110004786228216777
y[1] (numeric) = 1.961568941302008273326364506109
absolute error = 2.7271522583155687e-15
relative error = 1.3902913126802436609852000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7114
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.713
y[1] (analytic) = 1.9670750970259791608064221067767
y[1] (numeric) = 1.9670750970259764039665913427386
absolute error = 2.7568398307640381e-15
relative error = 1.4014919079256832848589000000001e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7104
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.712
y[1] (analytic) = 1.9726044691326852670117409418003
y[1] (numeric) = 1.9726044691326824801494879359593
absolute error = 2.7868622530058410e-15
relative error = 1.4127830979877930599040000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7094
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.711
y[1] (analytic) = 1.9781571883264988002476652799785
y[1] (numeric) = 1.9781571883264959830238853311667
absolute error = 2.8172237799488118e-15
relative error = 1.4241657824635032899478000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7084
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (analytic) = 1.9837333862328902995437413211665
y[1] (numeric) = 1.9837333862328874516150146613432
absolute error = 2.8479287266598233e-15
relative error = 1.4356408711092169255300000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7074
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.709
y[1] (analytic) = 1.9893331954062317851679295616903
y[1] (numeric) = 1.9893331954062289061864602599496
absolute error = 2.8789814693017407e-15
relative error = 1.4472092839700683168166999999999e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7064
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.708
y[1] (analytic) = 1.994956749337674359219892112739
y[1] (numeric) = 1.9949567493376714488334460264219
absolute error = 2.9103864460863171e-15
relative error = 1.4588719515110116548144000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7054
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.707
y[1] (analytic) = 2.0006041824631038573649242071106
y[1] (numeric) = 2.0006041824631009152167659637845
absolute error = 2.9421481582433261e-15
relative error = 1.4706298147497683077589000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7044
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.706
y[1] (analytic) = 2.0062756301711754367662046882649
y[1] (numeric) = 2.0062756301711724624950336820355
absolute error = 2.9742711710062294e-15
relative error = 1.4824838253916609572184000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7034
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.705
y[1] (analytic) = 2.0119712288114279965796489110206
y[1] (numeric) = 2.0119712288114249898195342963325
absolute error = 3.0067601146146881e-15
relative error = 1.4944349459663653529025000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7024
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.704
y[1] (analytic) = 2.0176911157024793388429752066115
y[1] (numeric) = 2.0176911157024762992232898723844
absolute error = 3.0396196853342271e-15
relative error = 1.5064841499666082983936000000001e-13 %
Correct digits = 14
h = 0.001
memory used=34.3MB, alloc=4.2MB, time=1.91
Real estimate of pole used for equation 1
Radius of convergence = 0.7014
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.703
y[1] (analytic) = 2.0234354291403029892211594689696
y[1] (numeric) = 2.0234354291402999163665129755953
absolute error = 3.0728546464933743e-15
relative error = 1.5186324219888440194287000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7004
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.702
y[1] (analytic) = 2.0292043084065876088668111460134
y[1] (numeric) = 2.0292043084065845023969816074179
absolute error = 3.1064698295385955e-15
relative error = 1.5308807578759380167820000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.6994
Order of pole = 225.1
TOP MAIN SOLVE Loop
x[1] = -0.701
y[1] (analytic) = 2.0349978937771799406187614595819
y[1] (numeric) = 2.0349978937771768001486263522211
absolute error = 3.1404701351073608e-15
relative error = 1.5432301648618922044808000000000e-13 %
Correct digits = 14
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.6984
Order of pole = 225.1
Finished!
diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;
Iterations = 300
Total Elapsed Time = 1 Seconds
Elapsed Time(since restart) = 1 Seconds
Time to Timeout = 2 Minutes 58 Seconds
Percent Done = 100.3 %
> quit
memory used=34.7MB, alloc=4.2MB, time=1.93