|\^/| 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.
| Type ? for help.
> #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_0D1,
> array_const_0D2,
> #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_0D1, array_const_0D2, 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_0D1,
> array_const_0D2,
> #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_0D1, array_const_0D2, 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_0D1,
> array_const_0D2,
> #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_0D1, array_const_0D2, 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_0D1,
> array_const_0D2,
> #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_0D1, array_const_0D2, 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_0D1,
> array_const_0D2,
> #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_0D1, array_const_0D2, 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_0D1,
> array_const_0D2,
> #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_0D1, array_const_0D2, 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_0D1,
> array_const_0D2,
> #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_0D1, array_const_0D2, 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_0D1,
> array_const_0D2,
> #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_0D1, array_const_0D2, 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_0D1,
> array_const_0D2,
> #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 CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> #emit pre ln 1 FULL $eq_no = 1
> array_tmp4[1] := ln(array_tmp3[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 CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0;
> #emit pre ln 2 FULL $eq_no = 1
> array_tmp4[2] := array_tmp3[2] / array_tmp3[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 sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0.0;
> array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre ln ID_FULL iii = 3 $eq_no = 1
> #emit pre ln 3 $eq_no = 1
> array_tmp4[3] := ( array_tmp3[3] - att(2,array_tmp3,array_tmp4,2) ) / array_tmp3[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 sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0.0;
> array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre ln ID_FULL iii = 4 $eq_no = 1
> #emit pre ln 4 $eq_no = 1
> array_tmp4[4] := ( array_tmp3[4] - att(3,array_tmp3,array_tmp4,2) ) / array_tmp3[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 sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0.0;
> array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre ln ID_FULL iii = 5 $eq_no = 1
> #emit pre ln 5 $eq_no = 1
> array_tmp4[5] := ( array_tmp3[5] - att(4,array_tmp3,array_tmp4,2) ) / array_tmp3[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 sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0.0;
> array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0;
> #emit ln FULL $eq_no = 1
> array_tmp4[kkk] := (array_tmp3[kkk] - att(kkk-1,array_tmp3,array_tmp4,2))/array_tmp3[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_0D1, array_const_0D2, 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_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4[1] := ln(array_tmp3[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_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0);
array_tmp4[2] := array_tmp3[2]/array_tmp3[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_tmp3[3] := 0.;
array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4[3] :=
(array_tmp3[3] - att(2, array_tmp3, array_tmp4, 2))/array_tmp3[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_tmp3[4] := 0.;
array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4[4] :=
(array_tmp3[4] - att(3, array_tmp3, array_tmp4, 2))/array_tmp3[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_tmp3[5] := 0.;
array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4[5] :=
(array_tmp3[5] - att(4, array_tmp3, array_tmp4, 2))/array_tmp3[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_tmp3[kkk] := 0.;
array_tmp3[kkk] :=
-ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0);
array_tmp4[kkk] := (
array_tmp3[kkk] - att(kkk - 1, array_tmp3, array_tmp4, 2))/
array_tmp3[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(5.0 * ln(0.1 * x + 0.2) * ( 0.1 * x + 0.2) - 0.5 * x - 1.0);
> end;
exact_soln_y :=
proc(x) return 5.0*ln(0.1*x + 0.2)*(0.1*x + 0.2) - 0.5*x - 1.0 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_0D1,
> array_const_0D2,
> #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/ln_sqrtpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 0.5 ;");
> 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 := 1000000;");
> 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(5.0 * ln(0.1 * x + 0.2) * ( 0.1 * x + 0.2) - 0.5 * x - 1.0);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_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_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_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_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_0D1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D1[1] := 0.1;
> array_const_0D2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D2[1] := 0.2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3;
> iiif := iiif + 1;
> od;# end do number 2;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 0.5 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #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;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := 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 ) = ln(sqrt(0.1 * x + 0.2));");
> 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,"2013-01-28T16:19:24-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"ln_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));")
> ;
> 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,"ln_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"ln_sqrt 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_0D1, array_const_0D2, 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/ln_sqrtpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 0.5 ;");
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 := 1000000;");
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(5.0 * ln(0.1 * x + 0.2) * ( 0.1 * x + 0.2\
) - 0.5 * x - 1.0);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
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_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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[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_0D1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D1[term] := 0.; term := term + 1
end do;
array_const_0D1[1] := 0.1;
array_const_0D2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D2[term] := 0.; term := term + 1
end do;
array_const_0D2[1] := 0.2;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 0.5;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
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;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := 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 ) = ln(sqrt(0.1 * x + 0.2));");
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, "2013-01-28T16:19:24-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"ln_sqrt");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));");
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,
"ln_sqrt diffeq.mxt")
;
logitem_str(html_log_file, "ln_sqrt 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/ln_sqrtpostode.ode#################
diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 0.5 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
#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(5.0 * ln(0.1 * x + 0.2) * ( 0.1 * x + 0.2) - 0.5 * x - 1.0);
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 = 0.4
estimated_steps = 400
step_error = 2.5000000000000000000000000000000e-13
est_needed_step_err = 2.5000000000000000000000000000000e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 6.7682835704795934185673433857193e-90
max_value3 = 6.7682835704795934185673433857193e-90
value3 = 6.7682835704795934185673433857193e-90
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = -2.6886801356779017901121541754532
y[1] (numeric) = -2.6886801356779017901121541754532
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.101
y[1] (analytic) = -2.6894603405233070262776559391428
y[1] (numeric) = -2.6894603405233070262776559391428
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.102
y[1] (analytic) = -2.6902403073867899023929870640188
y[1] (numeric) = -2.6902403073867899023929870640188
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.13
x[1] = 0.103
y[1] (analytic) = -2.6910200363815673263164553239129
y[1] (numeric) = -2.691020036381567326316455323913
absolute error = 1e-31
relative error = 3.7160630039181439135042762581851e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.104
y[1] (analytic) = -2.6917995276207485340845290360461
y[1] (numeric) = -2.6917995276207485340845290360461
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.105
y[1] (analytic) = -2.6925787812173352434363209956127
y[1] (numeric) = -2.6925787812173352434363209956127
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.106
y[1] (analytic) = -2.6933577972842218070463393693492
y[1] (numeric) = -2.6933577972842218070463393693492
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.107
y[1] (analytic) = -2.6941365759341953654661981717953
y[1] (numeric) = -2.6941365759341953654661981717954
absolute error = 1e-31
relative error = 3.7117643141504387096700316713965e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.108
y[1] (analytic) = -2.6949151172799359997759779756095
y[1] (numeric) = -2.6949151172799359997759779756096
absolute error = 1e-31
relative error = 3.7106920124791610353439975575064e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.109
y[1] (analytic) = -2.6956934214340168839459255414954
y[1] (numeric) = -2.6956934214340168839459255414955
absolute error = 1e-31
relative error = 3.7096206565954155667329572843530e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = -2.6964714885089044369091790940217
y[1] (numeric) = -2.6964714885089044369091790940218
absolute error = 1e-31
relative error = 3.7085502452428313329509601272512e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.9MB, time=0.28
x[1] = 0.111
y[1] (analytic) = -2.6972493186169584743462040168404
y[1] (numeric) = -2.6972493186169584743462040168404
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.112
y[1] (analytic) = -2.6980269118704323601816217945063
y[1] (numeric) = -2.6980269118704323601816217945064
absolute error = 1e-31
relative error = 3.7064122511170233603552560992387e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.113
y[1] (analytic) = -2.6988042683814731577941130882528
y[1] (numeric) = -2.6988042683814731577941130882529
absolute error = 1e-31
relative error = 3.7053446658424027916964617187099e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.114
y[1] (analytic) = -2.6995813882621217809400738996496
y[1] (numeric) = -2.6995813882621217809400738996497
absolute error = 1e-31
relative error = 3.7042780200961394568168615150909e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.115
y[1] (analytic) = -2.7003582716243131443917018490529
y[1] (numeric) = -2.700358271624313144391701849053
absolute error = 1e-31
relative error = 3.7032123126331764725858910176439e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.116
y[1] (analytic) = -2.7011349185798763142901876751083
y[1] (numeric) = -2.7011349185798763142901876751084
absolute error = 1e-31
relative error = 3.7021475422107043111662813225366e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.117
y[1] (analytic) = -2.7019113292405346582146851472798
y[1] (numeric) = -2.7019113292405346582146851472799
absolute error = 1e-31
relative error = 3.7010837075881556790242627788459e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.118
y[1] (analytic) = -2.7026875037179059949677306754158
y[1] (numeric) = -2.7026875037179059949677306754158
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=0.42
x[1] = 0.119
y[1] (analytic) = -2.703463442123502744077781998709
y[1] (numeric) = -2.703463442123502744077781998709
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = -2.7042391445687320750195434410342
y[1] (numeric) = -2.7042391445687320750195434410342
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.121
y[1] (analytic) = -2.7050146111648960561527433305321
y[1] (numeric) = -2.7050146111648960561527433305321
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.122
y[1] (analytic) = -2.7057898420231918033800272984291
y[1] (numeric) = -2.7057898420231918033800272984291
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.123
y[1] (analytic) = -2.7065648372547116285246292954137
y[1] (numeric) = -2.7065648372547116285246292954137
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.124
y[1] (analytic) = -2.7073395969704431874284802934083
y[1] (numeric) = -2.7073395969704431874284802934082
absolute error = 1e-31
relative error = 3.6936629638890377090458638350857e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.125
y[1] (analytic) = -2.7081141212812696277714127762599
y[1] (numeric) = -2.7081141212812696277714127762598
absolute error = 1e-31
relative error = 3.6926065712728440531593883857443e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.126
y[1] (analytic) = -2.7088884102979697366121172646987
y[1] (numeric) = -2.7088884102979697366121172646987
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.57
x[1] = 0.127
y[1] (analytic) = -2.7096624641312180876515052688542
y[1] (numeric) = -2.7096624641312180876515052688542
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.128
y[1] (analytic) = -2.7104362828915851882191312156584
y[1] (numeric) = -2.7104362828915851882191312156584
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.129
y[1] (analytic) = -2.7112098666895376259833240585772
y[1] (numeric) = -2.7112098666895376259833240585772
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = -2.7119832156354382153856774432676
y[1] (numeric) = -2.7119832156354382153856774432676
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.131
y[1] (analytic) = -2.7127563298395461438005454749481
y[1] (numeric) = -2.7127563298395461438005454749481
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.132
y[1] (analytic) = -2.7135292094120171174201893114588
y[1] (numeric) = -2.7135292094120171174201893114587
absolute error = 1e-31
relative error = 3.6852376474572229332823500690593e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.133
y[1] (analytic) = -2.71430185446290350686621799016
y[1] (numeric) = -2.7143018544629035068662179901599
absolute error = 1e-31
relative error = 3.6841886187263298271449267513262e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.134
y[1] (analytic) = -2.7150742651021544925279650869501
y[1] (numeric) = -2.71507426510215449252796508695
absolute error = 1e-31
relative error = 3.6831405050438834500160713104698e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.2MB, time=0.72
x[1] = 0.135
y[1] (analytic) = -2.7158464414396162096284410017509
y[1] (numeric) = -2.7158464414396162096284410017508
absolute error = 1e-31
relative error = 3.6820933052088168845279133963314e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.136
y[1] (analytic) = -2.716618383585031893018498866791
y[1] (numeric) = -2.7166183835850318930184988667909
absolute error = 1e-31
relative error = 3.6810470180222107754014877089139e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.137
y[1] (analytic) = -2.7173900916480420216998502818944
y[1] (numeric) = -2.7173900916480420216998502818944
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.138
y[1] (analytic) = -2.7181615657381844630775652947251
y[1] (numeric) = -2.7181615657381844630775652947251
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.139
y[1] (analytic) = -2.718932805964894616942689263532
y[1] (numeric) = -2.718932805964894616942689263532
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = -2.7197038124375055591856074653616
y[1] (numeric) = -2.7197038124375055591856074653616
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.141
y[1] (analytic) = -2.7204745852652481852407865439264
y[1] (numeric) = -2.7204745852652481852407865439264
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.142
y[1] (analytic) = -2.7212451245572513532635201283283
y[1] (numeric) = -2.7212451245572513532635201283282
absolute error = 1e-31
relative error = 3.6747883936501338108346705543632e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.143
y[1] (analytic) = -2.7220154304225420270393041966038
y[1] (numeric) = -2.7220154304225420270393041966037
absolute error = 1e-31
relative error = 3.6737484616123894926627126149864e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
memory used=22.8MB, alloc=4.2MB, time=0.87
TOP MAIN SOLVE Loop
x[1] = 0.144
y[1] (analytic) = -2.7227855029700454186264660065689
y[1] (numeric) = -2.7227855029700454186264660065687
absolute error = 2e-31
relative error = 7.3454188654169681566454352881304e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.145
y[1] (analytic) = -2.723555342308585130732668670665
y[1] (numeric) = -2.7235553423085851307326686706649
absolute error = 1e-31
relative error = 3.6716713057586097070411911388377e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.146
y[1] (analytic) = -2.7243249485468832988259117114396
y[1] (numeric) = -2.7243249485468832988259117114395
absolute error = 1e-31
relative error = 3.6706340795850581939367495850716e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.147
y[1] (analytic) = -2.7250943217935607329806461998863
y[1] (numeric) = -2.7250943217935607329806461998862
absolute error = 1e-31
relative error = 3.6695977530122163127048303464373e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.148
y[1] (analytic) = -2.7258634621571370594596213501341
y[1] (numeric) = -2.725863462157137059459621350134
absolute error = 1e-31
relative error = 3.6685623248665610911021178851306e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.149
y[1] (analytic) = -2.7266323697460308620320777208587
y[1] (numeric) = -2.7266323697460308620320777208586
absolute error = 1e-31
relative error = 3.6675277939766551191899943445354e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = -2.7274010446685598230289004562922
y[1] (numeric) = -2.7274010446685598230289004562921
absolute error = 1e-31
relative error = 3.6664941591731418702964708151105e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.151
y[1] (analytic) = -2.7281694870329408641353442878031
y[1] (numeric) = -2.7281694870329408641353442878031
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.2MB, time=1.03
x[1] = 0.152
y[1] (analytic) = -2.7289376969472902869219403106816
y[1] (numeric) = -2.7289376969472902869219403106816
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.153
y[1] (analytic) = -2.7297056745196239131141928499805
y[1] (numeric) = -2.7297056745196239131141928499804
absolute error = 1e-31
relative error = 3.6633986196185085388721282691734e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.154
y[1] (analytic) = -2.730473419857857224601673034008
y[1] (numeric) = -2.7304734198578572246016730340079
absolute error = 1e-31
relative error = 3.6623685575084555231802326462075e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.155
y[1] (analytic) = -2.7312409330698055031871140043231
y[1] (numeric) = -2.7312409330698055031871140043231
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.156
y[1] (analytic) = -2.7320082142631839700761110068252
y[1] (numeric) = -2.7320082142631839700761110068252
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.157
y[1] (analytic) = -2.7327752635456079251080279297426
y[1] (numeric) = -2.7327752635456079251080279297426
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.158
y[1] (analytic) = -2.733542081024592885728710180984
y[1] (numeric) = -2.733542081024592885728710180984
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.159
y[1] (analytic) = -2.7343086668075547257056021294033
y[1] (numeric) = -2.7343086668075547257056021294033
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.3MB, time=1.18
x[1] = 0.16
y[1] (analytic) = -2.7350750210018098135858656720239
y[1] (numeric) = -2.7350750210018098135858656720239
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.161
y[1] (analytic) = -2.7358411437145751508980948321504
y[1] (numeric) = -2.7358411437145751508980948321504
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.162
y[1] (analytic) = -2.7366070350529685100982196415483
y[1] (numeric) = -2.7366070350529685100982196415484
absolute error = 1e-31
relative error = 3.6541600134439633158464722751048e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.163
y[1] (analytic) = -2.7373726951240085722601909134687
y[1] (numeric) = -2.7373726951240085722601909134688
absolute error = 1e-31
relative error = 3.6531379222904755327762184268268e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.164
y[1] (analytic) = -2.7381381240346150645120358722219
y[1] (numeric) = -2.7381381240346150645120358722219
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.165
y[1] (analytic) = -2.7389033218916088972178729692406
y[1] (numeric) = -2.7389033218916088972178729692407
absolute error = 1e-31
relative error = 3.6510963786387150042109010041251e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.166
y[1] (analytic) = -2.7396682888017123009064725850972
y[1] (numeric) = -2.7396682888017123009064725850973
absolute error = 1e-31
relative error = 3.6500769238650575024951798818145e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.167
y[1] (analytic) = -2.7404330248715489629469486917289
y[1] (numeric) = -2.7404330248715489629469486917289
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.3MB, time=1.34
x[1] = 0.168
y[1] (analytic) = -2.7411975302076441639721649291743
y[1] (numeric) = -2.7411975302076441639721649291743
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.169
y[1] (analytic) = -2.7419618049164249140504369363939
y[1] (numeric) = -2.741961804916424914050436936394
absolute error = 1e-31
relative error = 3.6470238141427357806419489679950e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = -2.7427258491042200886061111662333
y[1] (numeric) = -2.7427258491042200886061111662334
absolute error = 1e-31
relative error = 3.6460078586658672417358566551207e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.171
y[1] (analytic) = -2.7434896628772605640895988102639
y[1] (numeric) = -2.743489662877260564089598810264
absolute error = 1e-31
relative error = 3.6449927751914348500042022900972e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.172
y[1] (analytic) = -2.7442532463416793533974418600884
y[1] (numeric) = -2.7442532463416793533974418600885
absolute error = 1e-31
relative error = 3.6439785625947029529134434248863e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.173
y[1] (analytic) = -2.745016599603511741042986737698
y[1] (numeric) = -2.7450165996035117410429867376981
absolute error = 1e-31
relative error = 3.6429652197529125825398598790572e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.174
y[1] (analytic) = -2.7457797227686954180782393386095
y[1] (numeric) = -2.7457797227686954180782393386096
absolute error = 1e-31
relative error = 3.6419527455452770699870008110949e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.175
y[1] (analytic) = -2.7465426159430706167674737477632
y[1] (numeric) = -2.7465426159430706167674737477633
absolute error = 1e-31
relative error = 3.6409411388529776715544805310192e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.176
y[1] (analytic) = -2.7473052792323802450131653095149
y[1] (numeric) = -2.747305279232380245013165309515
absolute error = 1e-31
relative error = 3.6399303985591592066212289785585e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=1.49
x[1] = 0.177
y[1] (analytic) = -2.7480677127422700205348171594844
y[1] (numeric) = -2.7480677127422700205348171594844
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.178
y[1] (analytic) = -2.7488299165782886048012477575119
y[1] (numeric) = -2.7488299165782886048012477575119
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.179
y[1] (analytic) = -2.7495918908458877367169053975064
y[1] (numeric) = -2.7495918908458877367169053975064
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = -2.7503536356504223660627741115204
y[1] (numeric) = -2.7503536356504223660627741115205
absolute error = 1e-31
relative error = 3.6358960791000724783063642512075e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.181
y[1] (analytic) = -2.7511151510971507866924338319456
y[1] (numeric) = -2.7511151510971507866924338319457
absolute error = 1e-31
relative error = 3.6348896541142517994742459007967e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.182
y[1] (analytic) = -2.7518764372912347694838361272643
y[1] (numeric) = -2.7518764372912347694838361272644
absolute error = 1e-31
relative error = 3.6338840888667729833277777704016e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.183
y[1] (analytic) = -2.752637494337739695047355283306
y[1] (numeric) = -2.7526374943377396950473552833062
absolute error = 2e-31
relative error = 7.2657587645088092557192879217658e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.184
y[1] (analytic) = -2.7533983223416346861906729634156
y[1] (numeric) = -2.7533983223416346861906729634158
absolute error = 2e-31
relative error = 7.2637510663516888290889917524872e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=1.64
x[1] = 0.185
y[1] (analytic) = -2.7541589214077927401410531473309
y[1] (numeric) = -2.7541589214077927401410531473311
absolute error = 2e-31
relative error = 7.2617450810634297000275859862154e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.186
y[1] (analytic) = -2.7549192916409908605255625198752
y[1] (numeric) = -2.7549192916409908605255625198754
absolute error = 2e-31
relative error = 7.2597408064491180381667444683757e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.187
y[1] (analytic) = -2.755679433145910189109789956766
y[1] (numeric) = -2.7556794331459101891097899567661
absolute error = 1e-31
relative error = 3.6288691201588363490982831944195e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.188
y[1] (analytic) = -2.7564393460271361372956172359204
y[1] (numeric) = -2.7564393460271361372956172359206
absolute error = 2e-31
relative error = 7.2557373804818367711191069039344e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.189
y[1] (analytic) = -2.7571990303891585173785915885752
y[1] (numeric) = -2.7571990303891585173785915885754
absolute error = 2e-31
relative error = 7.2537382247581691579953493343640e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = -2.7579584863363716735654491953127
y[1] (numeric) = -2.757958486336371673565449195313
absolute error = 3e-31
relative error = 1.0877611156450554249173178399354e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.191
y[1] (analytic) = -2.7587177139730746127523372276936
y[1] (numeric) = -2.7587177139730746127523372276938
absolute error = 2e-31
relative error = 7.2497450169326031275223557873359e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.192
y[1] (analytic) = -2.7594767134034711350642805365977
y[1] (numeric) = -2.7594767134034711350642805365979
absolute error = 2e-31
relative error = 7.2477509604828260398190809841563e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.3MB, time=1.79
x[1] = 0.193
y[1] (analytic) = -2.7602354847316699641564375935785
y[1] (numeric) = -2.7602354847316699641564375935787
absolute error = 2e-31
relative error = 7.2457585994494432291903057115143e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.194
y[1] (analytic) = -2.7609940280616848772776888015007
y[1] (numeric) = -2.760994028061684877277688801501
absolute error = 3e-31
relative error = 1.0865651897501950553353571295706e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.195
y[1] (analytic) = -2.7617523434974348350970988054559
y[1] (numeric) = -2.7617523434974348350970988054562
absolute error = 3e-31
relative error = 1.0862668432466513279819297394101e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.196
y[1] (analytic) = -2.7625104311427441112937929544083
y[1] (numeric) = -2.7625104311427441112937929544086
absolute error = 3e-31
relative error = 1.0859687500832406289931350753091e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.197
y[1] (analytic) = -2.7632682911013424219107865882046
y[1] (numeric) = -2.7632682911013424219107865882048
absolute error = 2e-31
relative error = 7.2378060662465377683900013263389e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.198
y[1] (analytic) = -2.7640259234768650544733043534584
y[1] (numeric) = -2.7640259234768650544733043534587
absolute error = 3e-31
relative error = 1.0853733224854502898412593558952e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.199
y[1] (analytic) = -2.7647833283728529968721252853913
y[1] (numeric) = -2.7647833283728529968721252853915
absolute error = 2e-31
relative error = 7.2338399160452551413856483757320e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = -2.7655405058927530660124879309399
y[1] (numeric) = -2.7655405058927530660124879309402
absolute error = 3e-31
relative error = 1.0847789043796920657176787349754e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.201
y[1] (analytic) = -2.7662974561399180362290883313312
y[1] (numeric) = -2.7662974561399180362290883313313
absolute error = 1e-31
relative error = 3.6149402436113886445436518253270e-30 %
Correct digits = 31
memory used=49.5MB, alloc=4.3MB, time=1.95
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.202
y[1] (analytic) = -2.7670541792176067674677022298393
y[1] (numeric) = -2.7670541792176067674677022298395
absolute error = 2e-31
relative error = 7.2279032879851534449959804455213e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.203
y[1] (analytic) = -2.7678106752289843332339614225834
y[1] (numeric) = -2.7678106752289843332339614225835
absolute error = 1e-31
relative error = 3.6129638813437584110163583233953e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.204
y[1] (analytic) = -2.7685669442771221483098127269516
y[1] (numeric) = -2.7685669442771221483098127269517
absolute error = 1e-31
relative error = 3.6119769546013337023702264830418e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.205
y[1] (analytic) = -2.7693229864649980962381866035698
y[1] (numeric) = -2.7693229864649980962381866035699
absolute error = 1e-31
relative error = 3.6109908627035445851419241808687e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.206
y[1] (analytic) = -2.7700788018954966565764010336116
y[1] (numeric) = -2.7700788018954966565764010336117
absolute error = 1e-31
relative error = 3.6100056045904710170254698082718e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.207
y[1] (analytic) = -2.7708343906714090319188248236919
y[1] (numeric) = -2.770834390671409031918824823692
absolute error = 1e-31
relative error = 3.6090211792040269082614095509129e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.208
y[1] (analytic) = -2.7715897528954332746893230855561
y[1] (numeric) = -2.7715897528954332746893230855562
absolute error = 1e-31
relative error = 3.6080375854879561156727646056558e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.209
y[1] (analytic) = -2.7723448886701744137040062172688
y[1] (numeric) = -2.7723448886701744137040062172689
absolute error = 1e-31
relative error = 3.6070548223878284472693026608081e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.3MB, time=2.10
x[1] = 0.21
y[1] (analytic) = -2.7730997980981445805048022965991
y[1] (numeric) = -2.7730997980981445805048022965993
absolute error = 2e-31
relative error = 7.2121457777020713547749315763226e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.211
y[1] (analytic) = -2.7738544812817631354643713857759
y[1] (numeric) = -2.773854481281763135464371385776
absolute error = 1e-31
relative error = 3.6050917838267875723334026508853e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.212
y[1] (analytic) = -2.7746089383233567936628788397315
y[1] (numeric) = -2.7746089383233567936628788397317
absolute error = 2e-31
relative error = 7.2082230125322158529933364488856e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.213
y[1] (analytic) = -2.7753631693251597505371433073566
y[1] (numeric) = -2.7753631693251597505371433073568
absolute error = 2e-31
relative error = 7.2062641102436612178045381207812e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.214
y[1] (analytic) = -2.7761171743893138073026737171161
y[1] (numeric) = -2.7761171743893138073026737171162
absolute error = 1e-31
relative error = 3.6021534293485956201688464973003e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.215
y[1] (analytic) = -2.7768709536178684961491081446401
y[1] (numeric) = -2.7768709536178684961491081446402
absolute error = 1e-31
relative error = 3.6011756279028451598409041410606e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.216
y[1] (analytic) = -2.7776245071127812052095660705608
y[1] (numeric) = -2.777624507112781205209566070561
absolute error = 2e-31
relative error = 7.2003972994856394081261988011493e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.217
y[1] (analytic) = -2.7783778349759173033044241519151
y[1] (numeric) = -2.7783778349759173033044241519152
absolute error = 1e-31
relative error = 3.5992224938285540935647318763418e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.3MB, time=2.26
x[1] = 0.218
y[1] (analytic) = -2.7791309373090502644600242498567
y[1] (numeric) = -2.7791309373090502644600242498569
absolute error = 2e-31
relative error = 7.1964943182437472638453479212272e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.219
y[1] (analytic) = -2.7798838142138617922028210802022
y[1] (numeric) = -2.7798838142138617922028210802024
absolute error = 2e-31
relative error = 7.1945452891727803881422022414983e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = -2.7806364657919419436294754814514
y[1] (numeric) = -2.7806364657919419436294754814517
absolute error = 3e-31
relative error = 1.0788896847562495035079473012141e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.221
y[1] (analytic) = -2.7813888921447892532533979273756
y[1] (numeric) = -2.7813888921447892532533979273759
absolute error = 3e-31
relative error = 1.0785978215677114406389415173997e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.222
y[1] (analytic) = -2.7821410933738108566282455480177
y[1] (numeric) = -2.782141093373810856628245548018
absolute error = 3e-31
relative error = 1.0783062035009873722323631419764e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.223
y[1] (analytic) = -2.7828930695803226137488745640047
y[1] (numeric) = -2.782893069580322613748874564005
absolute error = 3e-31
relative error = 1.0780148302472931330768431788580e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.224
y[1] (analytic) = -2.7836448208655492322302486844005
y[1] (numeric) = -2.7836448208655492322302486844008
absolute error = 3e-31
relative error = 1.0777237014983747379134885577584e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.225
y[1] (analytic) = -2.7843963473306243902648026679219
y[1] (numeric) = -2.7843963473306243902648026679223
absolute error = 4e-31
relative error = 1.4365770892620096429807458965551e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=2.41
x[1] = 0.226
y[1] (analytic) = -2.7851476490765908593587589011854
y[1] (numeric) = -2.7851476490765908593587589011858
absolute error = 4e-31
relative error = 1.4361895683793247281288901211093e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.227
y[1] (analytic) = -2.7858987262044006268478935057252
y[1] (numeric) = -2.7858987262044006268478935057255
absolute error = 3e-31
relative error = 1.0768517792056633509182677296324e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.228
y[1] (analytic) = -2.7866495788149150181932471478196
y[1] (numeric) = -2.78664957881491501819324714782
absolute error = 4e-31
relative error = 1.4354155005384958923829936462685e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.229
y[1] (analytic) = -2.7874002070089048190572743916601
y[1] (numeric) = -2.7874002070089048190572743916605
absolute error = 4e-31
relative error = 1.4350289527646653169792495087780e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = -2.788150610887050397160924107078
y[1] (numeric) = -2.7881506108870503971609241070783
absolute error = 3e-31
relative error = 1.0759820464094476224849545024663e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.231
y[1] (analytic) = -2.7889007905499418239221421179066
y[1] (numeric) = -2.788900790549941823922142117907
absolute error = 4e-31
relative error = 1.4342568274761907842282760164139e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.232
y[1] (analytic) = -2.7896507460980789958762859560687
y[1] (numeric) = -2.7896507460980789958762859560691
absolute error = 4e-31
relative error = 1.4338712491500422926660827273634e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.233
y[1] (analytic) = -2.7904004776318717558789402696359
y[1] (numeric) = -2.7904004776318717558789402696363
absolute error = 4e-31
relative error = 1.4334859931627730611488037026434e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.234
y[1] (analytic) = -2.7911499852516400140916201203974
y[1] (numeric) = -2.7911499852516400140916201203977
absolute error = 3e-31
relative error = 1.0748257943327724188809811878207e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=64.8MB, alloc=4.3MB, time=2.57
TOP MAIN SOLVE Loop
x[1] = 0.235
y[1] (analytic) = -2.791899269057613868750848097869
y[1] (numeric) = -2.7918992690576138687508480978694
absolute error = 4e-31
relative error = 1.4327164465894831905158581301832e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.236
y[1] (analytic) = -2.7926483291499337267210898721773
y[1] (numeric) = -2.7926483291499337267210898721776
absolute error = 3e-31
relative error = 1.0742491163981191083052377214195e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.237
y[1] (analytic) = -2.7933971656286504238320315078285
y[1] (numeric) = -2.7933971656286504238320315078288
absolute error = 3e-31
relative error = 1.0739611383993274279585415717878e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.238
y[1] (analytic) = -2.7941457785937253450006805640305
y[1] (numeric) = -2.7941457785937253450006805640307
absolute error = 2e-31
relative error = 7.1578226709652438417719047729615e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.239
y[1] (analytic) = -2.7948941681450305441387717149349
y[1] (numeric) = -2.7948941681450305441387717149351
absolute error = 2e-31
relative error = 7.1559060188937268755551430822178e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = -2.7956423343823488638459563349173
y[1] (numeric) = -2.7956423343823488638459563349176
absolute error = 3e-31
relative error = 1.0730986446672194199277184951127e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.241
y[1] (analytic) = -2.7963902774053740548892542097823
y[1] (numeric) = -2.7963902774053740548892542097826
absolute error = 3e-31
relative error = 1.0728116258448534153228062956138e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.242
y[1] (analytic) = -2.797137997313710895469244254564
y[1] (numeric) = -2.7971379973137108954692442545643
absolute error = 3e-31
relative error = 1.0725248460680566380104043895280e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.3MB, time=2.72
x[1] = 0.243
y[1] (analytic) = -2.7978854942068753102734698423747
y[1] (numeric) = -2.797885494206875310273469842375
absolute error = 3e-31
relative error = 1.0722383050384335592677670372328e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.244
y[1] (analytic) = -2.7986327681842944893175330765137
y[1] (numeric) = -2.798632768184294489317533076514
absolute error = 3e-31
relative error = 1.0719520024580964075719984428619e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.245
y[1] (analytic) = -2.7993798193453070065743510697841
y[1] (numeric) = -2.7993798193453070065743510697844
absolute error = 3e-31
relative error = 1.0716659380296640778531248960655e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.246
y[1] (analytic) = -2.8001266477891629383920460306488
y[1] (numeric) = -2.8001266477891629383920460306491
absolute error = 3e-31
relative error = 1.0713801114562610435771404793689e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.247
y[1] (analytic) = -2.800873253615023981700939695485
y[1] (numeric) = -2.8008732536150239817009396954853
absolute error = 3e-31
relative error = 1.0710945224415162716504230741560e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.248
y[1] (analytic) = -2.8016196369219635720101213897489
y[1] (numeric) = -2.8016196369219635720101213897491
absolute error = 2e-31
relative error = 7.1387278045970809342463158673648e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.249
y[1] (analytic) = -2.8023657978089670011940577483281
y[1] (numeric) = -2.8023657978089670011940577483285
absolute error = 4e-31
relative error = 1.4273654078733778117063353691904e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = -2.8031117363749315350697108767252
y[1] (numeric) = -2.8031117363749315350697108767254
absolute error = 2e-31
relative error = 7.1349278519537726154542906912919e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.3MB, time=2.88
x[1] = 0.251
y[1] (analytic) = -2.8038574527186665307646304899576
y[1] (numeric) = -2.8038574527186665307646304899579
absolute error = 3e-31
relative error = 1.0699545360592958865921640619126e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.252
y[1] (analytic) = -2.804602946938893553876484325191
y[1] (numeric) = -2.8046029469388935538764843251913
absolute error = 3e-31
relative error = 1.0696701304098585974258494602630e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.253
y[1] (analytic) = -2.8053482191342464954244898870849
y[1] (numeric) = -2.8053482191342464954244898870852
absolute error = 3e-31
relative error = 1.0693859605513873222808724191939e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.254
y[1] (analytic) = -2.8060932694032716885932093516627
y[1] (numeric) = -2.806093269403271688593209351663
absolute error = 3e-31
relative error = 1.0691020261910123346721619343116e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.255
y[1] (analytic) = -2.8068380978444280252691682251586
y[1] (numeric) = -2.8068380978444280252691682251589
absolute error = 3e-31
relative error = 1.0688183270363598213371373663429e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.256
y[1] (analytic) = -2.807582704556087072370757128765
y[1] (numeric) = -2.8075827045560870723707571287652
absolute error = 2e-31
relative error = 7.1235657519703388143347898588278e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.257
y[1] (analytic) = -2.8083270896365331879718748584704
y[1] (numeric) = -2.8083270896365331879718748584707
absolute error = 3e-31
relative error = 1.0682516331772001727743028345948e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.258
y[1] (analytic) = -2.8090712531839636372197696512368
y[1] (numeric) = -2.8090712531839636372197696512371
absolute error = 3e-31
relative error = 1.0679686378904154500409306888053e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=3.03
x[1] = 0.259
y[1] (analytic) = -2.8098151952964887080475343745962
y[1] (numeric) = -2.8098151952964887080475343745965
absolute error = 3e-31
relative error = 1.0676858766447959200508862300209e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = -2.8105589160721318266817101463462
y[1] (numeric) = -2.8105589160721318266817101463465
absolute error = 3e-31
relative error = 1.0674033491504314889870126225995e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.261
y[1] (analytic) = -2.8113024156088296729454516843654
y[1] (numeric) = -2.8113024156088296729454516843657
absolute error = 3e-31
relative error = 1.0671210551179016566310467933355e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.262
y[1] (analytic) = -2.8120456940044322953577064836518
y[1] (numeric) = -2.8120456940044322953577064836521
absolute error = 3e-31
relative error = 1.0668389942582744725763082838752e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.263
y[1] (analytic) = -2.8127887513567032260288587184901
y[1] (numeric) = -2.8127887513567032260288587184904
absolute error = 3e-31
relative error = 1.0665571662831054951281047581145e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.264
y[1] (analytic) = -2.8135315877633195953532875721667
y[1] (numeric) = -2.8135315877633195953532875721671
absolute error = 4e-31
relative error = 1.4217007612059156705116598815377e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.265
y[1] (analytic) = -2.8142742033218722464992885048606
y[1] (numeric) = -2.8142742033218722464992885048609
absolute error = 3e-31
relative error = 1.0659942078347957089840775739002e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.266
y[1] (analytic) = -2.8150165981298658496968047822274
y[1] (numeric) = -2.8150165981298658496968047822277
absolute error = 3e-31
relative error = 1.0657130767871942280285037455618e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.267
y[1] (analytic) = -2.8157587722847190163234154027616
y[1] (numeric) = -2.8157587722847190163234154027619
absolute error = 3e-31
relative error = 1.0654321774751275456454361154827e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=80.1MB, alloc=4.3MB, time=3.18
TOP MAIN SOLVE Loop
x[1] = 0.268
y[1] (analytic) = -2.816500725883764412789024381236
y[1] (numeric) = -2.8165007258837644127890243812363
absolute error = 3e-31
relative error = 1.0651515096125732407102083566203e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.269
y[1] (analytic) = -2.8172424590242488742196951683853
y[1] (numeric) = -2.8172424590242488742196951683856
absolute error = 3e-31
relative error = 1.0648710729139902102024640857804e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = -2.8179839718033335179410728134942
y[1] (numeric) = -2.8179839718033335179410728134946
absolute error = 4e-31
relative error = 1.4194544894590901955934438548059e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.271
y[1] (analytic) = -2.8187252643180938567618353066664
y[1] (numeric) = -2.8187252643180938567618353066668
absolute error = 4e-31
relative error = 1.4190811891586320246223043008407e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.272
y[1] (analytic) = -2.8194663366655199120576143712685
y[1] (numeric) = -2.8194663366655199120576143712689
absolute error = 4e-31
relative error = 1.4187081959384747363068390100319e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.273
y[1] (analytic) = -2.82020718894251632665582481436
y[1] (numeric) = -2.8202071889425163266558248143604
absolute error = 4e-31
relative error = 1.4183355094204502912909812709906e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.274
y[1] (analytic) = -2.8209478212459024775218403838114
y[1] (numeric) = -2.8209478212459024775218403838119
absolute error = 5e-31
relative error = 1.7724539115337820322840229165658e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.275
y[1] (analytic) = -2.8216882336724125882469529252771
y[1] (numeric) = -2.8216882336724125882469529252776
absolute error = 5e-31
relative error = 1.7719888187266266322681185803932e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.3MB, time=3.34
x[1] = 0.276
y[1] (analytic) = -2.8224284263186958413385504802053
y[1] (numeric) = -2.8224284263186958413385504802058
absolute error = 5e-31
relative error = 1.7715241078837627303525673777304e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.277
y[1] (analytic) = -2.8231683992813164903129488176308
y[1] (numeric) = -2.8231683992813164903129488176313
absolute error = 5e-31
relative error = 1.7710597785356450778860974078072e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.278
y[1] (analytic) = -2.8239081526567539715913097475853
y[1] (numeric) = -2.8239081526567539715913097475858
absolute error = 5e-31
relative error = 1.7705958302135154417105352732264e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.279
y[1] (analytic) = -2.8246476865414030161990784225702
y[1] (numeric) = -2.8246476865414030161990784225706
absolute error = 4e-31
relative error = 1.4161058099595207510884160994112e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = -2.8253870010315737612693706956521
y[1] (numeric) = -2.8253870010315737612693706956525
absolute error = 4e-31
relative error = 1.4157352598208899004153748945771e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.281
y[1] (analytic) = -2.8261260962234918613507404693517
y[1] (numeric) = -2.8261260962234918613507404693522
absolute error = 5e-31
relative error = 1.7692062667272425902172957882563e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.282
y[1] (analytic) = -2.8268649722132985995197558385833
y[1] (numeric) = -2.8268649722132985995197558385837
absolute error = 4e-31
relative error = 1.4149950702697318410099524544491e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.283
y[1] (analytic) = -2.8276036290970509982988117034633
y[1] (numeric) = -2.8276036290970509982988117034637
absolute error = 4e-31
relative error = 1.4146254301128247667094306410855e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.3MB, time=3.50
x[1] = 0.284
y[1] (analytic) = -2.8283420669707219303796054038247
y[1] (numeric) = -2.8283420669707219303796054038251
absolute error = 4e-31
relative error = 1.4142560925398160788797007833156e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.285
y[1] (analytic) = -2.8290802859302002291527008067288
y[1] (numeric) = -2.8290802859302002291527008067292
absolute error = 4e-31
relative error = 1.4138870571800693649862473550124e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.286
y[1] (analytic) = -2.8298182860712907990436051611656
y[1] (numeric) = -2.829818286071290799043605161166
absolute error = 4e-31
relative error = 1.4135183236635672617330903021831e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.287
y[1] (analytic) = -2.8305560674897147256557819204444
y[1] (numeric) = -2.8305560674897147256557819204447
absolute error = 3e-31
relative error = 1.0598624187156826123330684846533e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.288
y[1] (analytic) = -2.8312936302811093857210216225002
y[1] (numeric) = -2.8312936302811093857210216225006
absolute error = 4e-31
relative error = 1.4127817606833148517684652809859e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.289
y[1] (analytic) = -2.832030974541028556857591811463
y[1] (numeric) = -2.8320309745410285568575918114634
absolute error = 4e-31
relative error = 1.4124139304826133337005772111952e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = -2.832768100364942527136585880338
y[1] (numeric) = -2.8327681003649425271365858803383
absolute error = 3e-31
relative error = 1.0590348004884385571781040594625e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.291
y[1] (analytic) = -2.8335050078482382044568896145262
y[1] (numeric) = -2.8335050078482382044568896145266
absolute error = 4e-31
relative error = 1.4116791708222874493309522987605e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.4MB, time=3.65
x[1] = 0.292
y[1] (analytic) = -2.8342416970862192257291831191538
y[1] (numeric) = -2.8342416970862192257291831191542
absolute error = 4e-31
relative error = 1.4113122406293910901243844505706e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.293
y[1] (analytic) = -2.834978168174106065869394719764
y[1] (numeric) = -2.8349781681741060658693947197643
absolute error = 3e-31
relative error = 1.0582092072801314630983378567811e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.294
y[1] (analytic) = -2.8357144212070361466020223358562
y[1] (numeric) = -2.8357144212070361466020223358565
absolute error = 3e-31
relative error = 1.0579344582671462622585689582368e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.295
y[1] (analytic) = -2.836450456280063945073736740009
y[1] (numeric) = -2.8364504562800639450737367400093
absolute error = 3e-31
relative error = 1.0576599331597095192036969749520e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.296
y[1] (analytic) = -2.8371862734881611022776800318889
y[1] (numeric) = -2.8371862734881611022776800318893
absolute error = 4e-31
relative error = 1.4098475089131968622088044679355e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.297
y[1] (analytic) = -2.8379218729262165312888715763216
y[1] (numeric) = -2.837921872926216531288871576322
absolute error = 4e-31
relative error = 1.4094820714269876154254615798988e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.298
y[1] (analytic) = -2.8386572546890365253111325777617
y[1] (numeric) = -2.8386572546890365253111325777621
absolute error = 4e-31
relative error = 1.4091169313916286442367468015753e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.299
y[1] (analytic) = -2.8393924188713448655359393899417
y[1] (numeric) = -2.8393924188713448655359393899422
absolute error = 5e-31
relative error = 1.7609401105562908057855096182611e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = -2.8401273655677829288136145891923
y[1] (numeric) = -2.8401273655677829288136145891927
absolute error = 4e-31
relative error = 1.4083875422257133867552718590097e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.4MB, time=3.81
x[1] = 0.301
y[1] (analytic) = -2.8408620948729097951372637728926
y[1] (numeric) = -2.8408620948729097951372637728931
absolute error = 5e-31
relative error = 1.7600291154659805691303547433432e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.302
y[1] (analytic) = -2.841596606881202354939864980729
y[1] (numeric) = -2.8415966068812023549398649807294
absolute error = 4e-31
relative error = 1.4076593385259579930459113200905e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.303
y[1] (analytic) = -2.8423309016870554162049165758839
y[1] (numeric) = -2.8423309016870554162049165758843
absolute error = 4e-31
relative error = 1.4072956803255434475644651618763e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.304
y[1] (analytic) = -2.8430649793847818113910483659575
y[1] (numeric) = -2.8430649793847818113910483659579
absolute error = 4e-31
relative error = 1.4069323174124463211579074805478e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.305
y[1] (analytic) = -2.8437988400686125041709996893028
y[1] (numeric) = -2.8437988400686125041709996893033
absolute error = 5e-31
relative error = 1.7582115617852086548721964079685e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.306
y[1] (analytic) = -2.8445324838326966959853671415481
y[1] (numeric) = -2.8445324838326966959853671415486
absolute error = 5e-31
relative error = 1.7577580950184989122996641561803e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.307
y[1] (analytic) = -2.8452659107711019324115235693536
y[1] (numeric) = -2.845265910771101932411523569354
absolute error = 4e-31
relative error = 1.4058439968150291363757952755919e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.308
y[1] (analytic) = -2.8459991209778142093481089139072
y[1] (numeric) = -2.8459991209778142093481089139076
absolute error = 4e-31
relative error = 1.4054818114721342267183228077216e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=3.96
x[1] = 0.309
y[1] (analytic) = -2.8467321145467380790154924452885
y[1] (numeric) = -2.8467321145467380790154924452889
absolute error = 4e-31
relative error = 1.4051199196299815355071027807265e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = -2.8474648915716967557726048906093
y[1] (numeric) = -2.8474648915716967557726048906096
absolute error = 3e-31
relative error = 1.0535687406997701131474679999522e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.311
y[1] (analytic) = -2.8481974521464322217505379237684
y[1] (numeric) = -2.8481974521464322217505379237687
absolute error = 3e-31
relative error = 1.0532977612697349146608270406920e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.312
y[1] (analytic) = -2.8489297963646053323033074527209
y[1] (numeric) = -2.8489297963646053323033074527212
absolute error = 3e-31
relative error = 1.0530270011666025414110609960803e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.313
y[1] (analytic) = -2.8496619243197959212761761113467
y[1] (numeric) = -2.849661924319795921276176111347
absolute error = 3e-31
relative error = 1.0527564601250336873135933760882e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.314
y[1] (analytic) = -2.850393836105502906091929337306
y[1] (numeric) = -2.8503938361055029060919293373064
absolute error = 4e-31
relative error = 1.4033148505068357876948367942284e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.315
y[1] (analytic) = -2.8511255318151443926554983946724
y[1] (numeric) = -2.8511255318151443926554983946727
absolute error = 3e-31
relative error = 1.0522160341674173727870922769987e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.316
y[1] (analytic) = -2.8518570115420577800773226806269
y[1] (numeric) = -2.8518570115420577800773226806273
absolute error = 4e-31
relative error = 1.4025948649638355031643103484044e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.4MB, time=4.12
x[1] = 0.317
y[1] (analytic) = -2.8525882753794998652158426390788
y[1] (numeric) = -2.8525882753794998652158426390792
absolute error = 4e-31
relative error = 1.4022353083772146856594478178407e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.318
y[1] (analytic) = -2.8533193234206469470395135907184
y[1] (numeric) = -2.8533193234206469470395135907187
absolute error = 3e-31
relative error = 1.0514070315843611037950977566133e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.319
y[1] (analytic) = -2.8540501557585949308087297787226
y[1] (numeric) = -2.8540501557585949308087297787229
absolute error = 3e-31
relative error = 1.0511377993645007243471676441656e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = -2.8547807724863594320780469220874
y[1] (numeric) = -2.8547807724863594320780469220876
absolute error = 2e-31
relative error = 7.0057918957402404111228170202400e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.321
y[1] (analytic) = -2.8555111736968758805190905643565
y[1] (numeric) = -2.8555111736968758805190905643569
absolute error = 4e-31
relative error = 1.4007999817494730143320682431538e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.322
y[1] (analytic) = -2.8562413594829996235645365043456
y[1] (numeric) = -2.8562413594829996235645365043459
absolute error = 3e-31
relative error = 1.0503314049562750298330472461126e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.323
y[1] (analytic) = -2.8569713299375060298735485972966
y[1] (numeric) = -2.8569713299375060298735485972969
absolute error = 3e-31
relative error = 1.0500630400325447466967351733148e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.324
y[1] (analytic) = -2.8577010851530905926190582197586
y[1] (numeric) = -2.8577010851530905926190582197589
absolute error = 3e-31
relative error = 1.0497948912803405671679733669916e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.325
y[1] (analytic) = -2.8584306252223690325972686993285
y[1] (numeric) = -2.8584306252223690325972686993288
absolute error = 3e-31
relative error = 1.0495269584395170358794524757118e-29 %
Correct digits = 30
h = 0.001
memory used=106.8MB, alloc=4.4MB, time=4.27
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.326
y[1] (analytic) = -2.859159950237877401159767021229
y[1] (numeric) = -2.8591599502378774011597670212294
absolute error = 4e-31
relative error = 1.3990123216671409323327044003329e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.327
y[1] (analytic) = -2.8598890602920721829686241375098
y[1] (numeric) = -2.8598890602920721829686241375102
absolute error = 4e-31
relative error = 1.3986556526047522942454013893367e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.328
y[1] (analytic) = -2.8606179554773303985748642214372
y[1] (numeric) = -2.8606179554773303985748642214375
absolute error = 3e-31
relative error = 1.0487244527902754979926746002537e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.329
y[1] (analytic) = -2.861346635885949706820682229374
y[1] (numeric) = -2.8613466358859497068206822293742
absolute error = 2e-31
relative error = 6.9897158733469785534210102820972e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = -2.8620751016101485070657881551326
y[1] (numeric) = -2.8620751016101485070657881551328
absolute error = 2e-31
relative error = 6.9879368255390586895809413627373e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.331
y[1] (analytic) = -2.8628033527420660412382553874019
y[1] (numeric) = -2.8628033527420660412382553874021
absolute error = 2e-31
relative error = 6.9861592067940992455405342149518e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.332
y[1] (analytic) = -2.8635313893737624957102496093922
y[1] (numeric) = -2.8635313893737624957102496093924
absolute error = 2e-31
relative error = 6.9843830153976005789712382587256e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.333
y[1] (analytic) = -2.8642592115972191029990137113035
y[1] (numeric) = -2.8642592115972191029990137113036
absolute error = 1e-31
relative error = 3.4913041248189343720256188121646e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.4MB, time=4.43
x[1] = 0.334
y[1] (analytic) = -2.8649868195043382432934832205876
y[1] (numeric) = -2.8649868195043382432934832205878
absolute error = 2e-31
relative error = 6.9808349078060096952492444169684e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.335
y[1] (analytic) = -2.8657142131869435458069057922371
y[1] (numeric) = -2.8657142131869435458069057922374
absolute error = 3e-31
relative error = 1.0468594482293885258357188401757e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.336
y[1] (analytic) = -2.8664413927367799899558373414813
y[1] (numeric) = -2.8664413927367799899558373414816
absolute error = 3e-31
relative error = 1.0465938733656447898844112606935e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.337
y[1] (analytic) = -2.8671683582455140063658864442956
y[1] (numeric) = -2.8671683582455140063658864442958
absolute error = 2e-31
relative error = 6.9755234088306059986865175528339e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.338
y[1] (analytic) = -2.8678951098047335777045776770197
y[1] (numeric) = -2.86789510980473357770457767702
absolute error = 3e-31
relative error = 1.0460633618515640379062108283063e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.339
y[1] (analytic) = -2.8686216475059483393417036151307
y[1] (numeric) = -2.868621647505948339341703615131
absolute error = 3e-31
relative error = 1.0457984246923170568059066510392e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = -2.8693479714405896798375342628059
y[1] (numeric) = -2.8693479714405896798375342628062
absolute error = 3e-31
relative error = 1.0455336995930176229005581416662e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.341
y[1] (analytic) = -2.8700740817000108412592517393487
y[1] (numeric) = -2.8700740817000108412592517393491
absolute error = 4e-31
relative error = 1.3936922484003298159957102101410e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.4MB, time=4.58
x[1] = 0.342
y[1] (analytic) = -2.8707999783754870193259771058044
y[1] (numeric) = -2.8707999783754870193259771058047
absolute error = 3e-31
relative error = 1.0450048845610010070562648375441e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.343
y[1] (analytic) = -2.8715256615582154633827552751711
y[1] (numeric) = -2.8715256615582154633827552751713
absolute error = 2e-31
relative error = 6.9649386274845703204134622749316e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.344
y[1] (analytic) = -2.8722511313393155762038630124971
y[1] (numeric) = -2.8722511313393155762038630124974
absolute error = 3e-31
relative error = 1.0444769147331193839977979626117e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.345
y[1] (analytic) = -2.8729763878098290136258040968384
y[1] (numeric) = -2.8729763878098290136258040968387
absolute error = 3e-31
relative error = 1.0442132461405314769344863422753e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.346
y[1] (analytic) = -2.8737014310607197840103547855199
y[1] (numeric) = -2.8737014310607197840103547855203
absolute error = 4e-31
relative error = 1.3919330507914140109564747417217e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.347
y[1] (analytic) = -2.8744262611828743475380217924017
y[1] (numeric) = -2.8744262611828743475380217924022
absolute error = 5e-31
relative error = 1.7394775672354233945800972185319e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.348
y[1] (analytic) = -2.8751508782671017153322740658671
y[1] (numeric) = -2.8751508782671017153322740658676
absolute error = 5e-31
relative error = 1.7390391710551127655921100515975e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.349
y[1] (analytic) = -2.875875282404133548414908729036
y[1] (numeric) = -2.8758752824041335484149087290365
absolute error = 5e-31
relative error = 1.7386011245314402887464848052054e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.4MB, time=4.74
x[1] = 0.35
y[1] (analytic) = -2.8765994736846242564929106242393
y[1] (numeric) = -2.8765994736846242564929106242398
absolute error = 5e-31
relative error = 1.7381634272481879009080385835967e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.351
y[1] (analytic) = -2.8773234521991510965771639860651
y[1] (numeric) = -2.8773234521991510965771639860657
absolute error = 6e-31
relative error = 2.0852712945477761097503222487870e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.352
y[1] (analytic) = -2.8780472180382142714333738522968
y[1] (numeric) = -2.8780472180382142714333738522973
absolute error = 5e-31
relative error = 1.7372890787414491834048631864265e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.353
y[1] (analytic) = -2.8787707712922370278655539097913
y[1] (numeric) = -2.8787707712922370278655539097918
absolute error = 5e-31
relative error = 1.7368524266889006179170216470391e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.354
y[1] (analytic) = -2.8794941120515657548324365627964
y[1] (numeric) = -2.8794941120515657548324365627969
absolute error = 5e-31
relative error = 1.7364161222186449089549599169479e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.355
y[1] (analytic) = -2.8802172404064700813971601043482
y[1] (numeric) = -2.8802172404064700813971601043487
absolute error = 5e-31
relative error = 1.7359801649178296013053495854250e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.356
y[1] (analytic) = -2.8809401564471429745105869672425
y[1] (numeric) = -2.880940156447142974510586967243
absolute error = 5e-31
relative error = 1.7355445543742712320198008381330e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.357
y[1] (analytic) = -2.8816628602637008366286061296005
y[1] (numeric) = -2.881662860263700836628606129601
absolute error = 5e-31
relative error = 1.7351092901764539619108677298207e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.358
y[1] (analytic) = -2.8823853519461836031637718512601
y[1] (numeric) = -2.8823853519461836031637718512606
absolute error = 5e-31
relative error = 1.7346743719135282104294197962679e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=122.0MB, alloc=4.4MB, time=4.89
TOP MAIN SOLVE Loop
x[1] = 0.359
y[1] (analytic) = -2.8831076315845548397716300211017
y[1] (numeric) = -2.8831076315845548397716300211023
absolute error = 6e-31
relative error = 2.0810877590103711526963080276713e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = -2.8838296992687018394720825019521
y[1] (numeric) = -2.8838296992687018394720825019526
absolute error = 5e-31
relative error = 1.7338055715522760671995416827805e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.361
y[1] (analytic) = -2.8845515550884357196061389688967
y[1] (numeric) = -2.8845515550884357196061389688972
absolute error = 5e-31
relative error = 1.7333716886355695685843289246267e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.362
y[1] (analytic) = -2.88527319913349151862840484866
y[1] (numeric) = -2.8852731991334915186284048486604
absolute error = 4e-31
relative error = 1.3863505200135933345049266013798e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.363
y[1] (analytic) = -2.8859946314935282927356530821698
y[1] (numeric) = -2.8859946314935282927356530821702
absolute error = 4e-31
relative error = 1.3860039642312029754459121217390e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.364
y[1] (analytic) = -2.8867158522581292123318265495076
y[1] (numeric) = -2.8867158522581292123318265495081
absolute error = 5e-31
relative error = 1.7320721040447252139456521604275e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.365
y[1] (analytic) = -2.8874368615168016583298171161419
y[1] (numeric) = -2.8874368615168016583298171161423
absolute error = 4e-31
relative error = 1.3853116767023459524147732133336e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.366
y[1] (analytic) = -2.8881576593589773182903663816446
y[1] (numeric) = -2.888157659358977318290366381645
absolute error = 4e-31
relative error = 1.3849659443064457165734618909883e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.4MB, time=5.05
x[1] = 0.367
y[1] (analytic) = -2.8888782458740122823984323369934
y[1] (numeric) = -2.8888782458740122823984323369939
absolute error = 5e-31
relative error = 1.7307756071551851993231940745349e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.368
y[1] (analytic) = -2.8895986211511871392773652640451
y[1] (numeric) = -2.8895986211511871392773652640455
absolute error = 4e-31
relative error = 1.3842753006320442098955190704022e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.369
y[1] (analytic) = -2.8903187852797070716412353408345
y[1] (numeric) = -2.890318785279707071641235340835
absolute error = 5e-31
relative error = 1.7299129858840574585699980493848e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = -2.8910387383487019517856535489943
y[1] (numeric) = -2.8910387383487019517856535489947
absolute error = 4e-31
relative error = 1.3835857496273856392173026807927e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.371
y[1] (analytic) = -2.8917584804472264369174266147808
y[1] (numeric) = -2.8917584804472264369174266147812
absolute error = 4e-31
relative error = 1.3832413830706144881271674827594e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.372
y[1] (analytic) = -2.8924780116642600643233858529548
y[1] (numeric) = -2.8924780116642600643233858529552
absolute error = 4e-31
relative error = 1.3828972887156017719662929081105e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.373
y[1] (analytic) = -2.8931973320887073463787289230526
y[1] (numeric) = -2.8931973320887073463787289230531
absolute error = 5e-31
relative error = 1.7281918328019171173764755694653e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.374
y[1] (analytic) = -2.8939164418093978653952126504238
y[1] (numeric) = -2.8939164418093978653952126504243
absolute error = 5e-31
relative error = 1.7277623941601404400247713664533e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.4MB, time=5.20
x[1] = 0.375
y[1] (analytic) = -2.8946353409150863683095342097656
y[1] (numeric) = -2.894635340915086368309534209766
absolute error = 4e-31
relative error = 1.3818666356555546920427787497282e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.376
y[1] (analytic) = -2.8953540294944528612122371167687
y[1] (numeric) = -2.8953540294944528612122371167691
absolute error = 4e-31
relative error = 1.3815236269045914626023502378258e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.377
y[1] (analytic) = -2.8960725076361027037174776238757
y[1] (numeric) = -2.8960725076361027037174776238761
absolute error = 4e-31
relative error = 1.3811808887564661730822829762690e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.378
y[1] (analytic) = -2.8967907754285667031739862690453
y[1] (numeric) = -2.8967907754285667031739862690457
absolute error = 4e-31
relative error = 1.3808384208929340540108361852508e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.379
y[1] (analytic) = -2.8975088329603012087175584818021
y[1] (numeric) = -2.8975088329603012087175584818026
absolute error = 5e-31
relative error = 1.7256202787453262749997143016060e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = -2.8982266803196882051654073087215
y[1] (numeric) = -2.898226680319688205165407308722
absolute error = 5e-31
relative error = 1.7251928684365282940274932545501e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.381
y[1] (analytic) = -2.8989443175950354067527104808456
y[1] (numeric) = -2.8989443175950354067527104808461
absolute error = 5e-31
relative error = 1.7247657947938788517757039485672e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.382
y[1] (analytic) = -2.8996617448745763507116832083443
y[1] (numeric) = -2.8996617448745763507116832083447
absolute error = 4e-31
relative error = 1.3794712459376941284418009756669e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.383
y[1] (analytic) = -2.9003789622464704906935072530092
memory used=133.5MB, alloc=4.4MB, time=5.36
y[1] (numeric) = -2.9003789622464704906935072530096
absolute error = 4e-31
relative error = 1.3791301247412941072852863196957e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.384
y[1] (analytic) = -2.9010959697988032900334459968983
y[1] (numeric) = -2.9010959697988032900334459968988
absolute error = 5e-31
relative error = 1.7234865899133836070793784321350e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.385
y[1] (analytic) = -2.9018127676195863148594743956199
y[1] (numeric) = -2.9018127676195863148594743956203
absolute error = 4e-31
relative error = 1.3784486871912408460639661658723e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.386
y[1] (analytic) = -2.9025293557967573270447518773504
y[1] (numeric) = -2.9025293557967573270447518773508
absolute error = 4e-31
relative error = 1.3781083702087078663066649851534e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.387
y[1] (analytic) = -2.903245734418180377004265423721
y[1] (numeric) = -2.9032457344181803770042654237215
absolute error = 5e-31
relative error = 1.7222104008367778782370921256358e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.388
y[1] (analytic) = -2.9039619035716458963359692461538
y[1] (numeric) = -2.9039619035716458963359692461543
absolute error = 5e-31
relative error = 1.7217856728252499687697797238083e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.389
y[1] (analytic) = -2.9046778633448707903067466511004
y[1] (numeric) = -2.9046778633448707903067466511008
absolute error = 4e-31
relative error = 1.3770890226683571555933389622069e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = -2.9053936138254985301835188699005
y[1] (numeric) = -2.9053936138254985301835188699009
absolute error = 4e-31
relative error = 1.3767497735817095587033653886607e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.391
y[1] (analytic) = -2.906109155101099245409824813643
y[1] (numeric) = -2.9061091551010992454098248136434
absolute error = 4e-31
relative error = 1.3764107906885713340273500883731e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=5.51
x[1] = 0.392
y[1] (analytic) = -2.9068244872591698156281949004609
y[1] (numeric) = -2.9068244872591698156281949004614
absolute error = 5e-31
relative error = 1.7200900920971925774090555930784e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.393
y[1] (analytic) = -2.9075396103871339625486412921226
y[1] (numeric) = -2.907539610387133962548641292123
absolute error = 4e-31
relative error = 1.3757336222385657512715324484922e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.394
y[1] (analytic) = -2.9082545245723423416635860685795
y[1] (numeric) = -2.9082545245723423416635860685799
absolute error = 4e-31
relative error = 1.3753954360608098397001056389769e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.395
y[1] (analytic) = -2.9089692299020726338095480632988
y[1] (numeric) = -2.9089692299020726338095480632991
absolute error = 3e-31
relative error = 1.0312931361260881472407733344175e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.396
y[1] (analytic) = -2.9096837264635296365759082787216
y[1] (numeric) = -2.9096837264635296365759082787221
absolute error = 5e-31
relative error = 1.7183998228141001585403495409768e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.397
y[1] (analytic) = -2.9103980143438453555610730000623
y[1] (numeric) = -2.9103980143438453555610730000627
absolute error = 4e-31
relative error = 1.3743824660015813810615051931639e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.398
y[1] (analytic) = -2.9111120936300790954763529268588
y[1] (numeric) = -2.9111120936300790954763529268592
absolute error = 4e-31
relative error = 1.3740453377774631629169891193971e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.399
y[1] (analytic) = -2.9118259644092175510978758452352
y[1] (numeric) = -2.9118259644092175510978758452355
absolute error = 3e-31
relative error = 1.0302813549533933570571633905656e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=5.66
x[1] = 0.4
y[1] (analytic) = -2.912539626768174898066849569686
y[1] (numeric) = -2.9125396267681748980668495696864
absolute error = 4e-31
relative error = 1.3733718721755204720719192730377e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.401
y[1] (analytic) = -2.9132530807937928835384910913801
y[1] (numeric) = -2.9132530807937928835384910913806
absolute error = 5e-31
relative error = 1.7162944177296185009609225441887e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.402
y[1] (analytic) = -2.913966326572840916679937080461
y[1] (numeric) = -2.9139663265728409166799370804614
absolute error = 4e-31
relative error = 1.3726994589894452965570860407715e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.403
y[1] (analytic) = -2.914679364192016159017450102611
y[1] (numeric) = -2.9146793641920161590174501026115
absolute error = 5e-31
relative error = 1.7154545578587370836550744463111e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.404
y[1] (analytic) = -2.9153921937379436146332341252289
y[1] (numeric) = -2.9153921937379436146332341252293
absolute error = 4e-31
relative error = 1.3720280957710311833946699880608e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.405
y[1] (analytic) = -2.9161048152971762202121721059297
y[1] (numeric) = -2.9161048152971762202121721059302
absolute error = 5e-31
relative error = 1.7146160089209471352124882253467e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.406
y[1] (analytic) = -2.9168172289561949349387976757279
y[1] (numeric) = -2.9168172289561949349387976757284
absolute error = 5e-31
relative error = 1.7141972250998009039027207640371e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.407
y[1] (analytic) = -2.9175294348014088302448121511718
y[1] (numeric) = -2.9175294348014088302448121511723
absolute error = 5e-31
relative error = 1.7137787678705429514245897116249e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.4MB, time=5.82
x[1] = 0.408
y[1] (analytic) = -2.918241432919155179407457333879
y[1] (numeric) = -2.9182414329191551794074573338795
absolute error = 5e-31
relative error = 1.7133606368539680497699189829362e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.409
y[1] (analytic) = -2.9189532233956995469990537823524
y[1] (numeric) = -2.9189532233956995469990537823529
absolute error = 5e-31
relative error = 1.7129428316714718718438065714165e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = -2.9196648063172358781880134696375
y[1] (numeric) = -2.919664806317235878188013469638
absolute error = 5e-31
relative error = 1.7125253519450497894094474655395e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.411
y[1] (analytic) = -2.9203761817698865878916349713014
y[1] (numeric) = -2.920376181769886587891634971302
absolute error = 6e-31
relative error = 2.0545298367567548087250285099762e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.412
y[1] (analytic) = -2.9210873498397026497809885613684
y[1] (numeric) = -2.9210873498397026497809885613691
absolute error = 7e-31
relative error = 2.3963679142919609804927129124968e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.413
y[1] (analytic) = -2.9217983106126636851381978292243
y[1] (numeric) = -2.921798310612663685138197829225
absolute error = 7e-31
relative error = 2.3957848064236130151291672557647e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.414
y[1] (analytic) = -2.9225090641746780515664236681
y[1] (numeric) = -2.9225090641746780515664236681007
absolute error = 7e-31
relative error = 2.3952021520853051338786315307895e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.415
y[1] (analytic) = -2.9232196106115829315528557255525
y[1] (numeric) = -2.9232196106115829315528557255532
absolute error = 7e-31
relative error = 2.3946199507520036479791316823271e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.416
y[1] (analytic) = -2.9239299500091444208850156483717
y[1] (numeric) = -2.9239299500091444208850156483724
absolute error = 7e-31
relative error = 2.3940382018995044347991390362056e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=148.7MB, alloc=4.4MB, time=5.98
TOP MAIN SOLVE Loop
x[1] = 0.417
y[1] (analytic) = -2.9246400824530576169206756985501
y[1] (numeric) = -2.9246400824530576169206756985508
absolute error = 7e-31
relative error = 2.3934569050044312831845940232997e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.418
y[1] (analytic) = -2.9253500080289467067116955633472
y[1] (numeric) = -2.9253500080289467067116955633479
absolute error = 7e-31
relative error = 2.3928760595442342427925073375225e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.419
y[1] (analytic) = -2.9260597268223650549820794310603
y[1] (numeric) = -2.926059726822365054982079431061
absolute error = 7e-31
relative error = 2.3922956649971879773998834750747e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = -2.9267692389187952919605546548643
y[1] (numeric) = -2.926769238918795291960554654865
absolute error = 7e-31
relative error = 2.3917157208423901221767480302428e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.421
y[1] (analytic) = -2.9274785444036494010679725800028
y[1] (numeric) = -2.9274785444036494010679725800035
absolute error = 7e-31
relative error = 2.3911362265597596449120964181420e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.422
y[1] (analytic) = -2.9281876433622688064598313646935
y[1] (numeric) = -2.9281876433622688064598313646942
absolute error = 7e-31
relative error = 2.3905571816300352111816178575071e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.423
y[1] (analytic) = -2.9288965358799244604242198823421
y[1] (numeric) = -2.9288965358799244604242198823429
absolute error = 8e-31
relative error = 2.7314040977540269182240965456905e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.424
y[1] (analytic) = -2.9296052220418169306354810520392
y[1] (numeric) = -2.92960522204181693063548105204
absolute error = 8e-31
relative error = 2.7307433574358261075078072135338e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=6.13
x[1] = 0.425
y[1] (analytic) = -2.9303137019330764872638922058296
y[1] (numeric) = -2.9303137019330764872638922058304
absolute error = 8e-31
relative error = 2.7300831288890812254226156718722e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.426
y[1] (analytic) = -2.931021975638763189941659364895
y[1] (numeric) = -2.9310219756387631899416593648957
absolute error = 7e-31
relative error = 2.3882454850835694248195643555358e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.427
y[1] (analytic) = -2.9317300432438669745855215625622
y[1] (numeric) = -2.931730043243866974585521562563
absolute error = 8e-31
relative error = 2.7287642047520350525772657269030e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.428
y[1] (analytic) = -2.9324379048333077400762606199429
y[1] (numeric) = -2.9324379048333077400762606199437
absolute error = 8e-31
relative error = 2.7281055079850886296725984561545e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.429
y[1] (analytic) = -2.9331455604919354347954110500093
y[1] (numeric) = -2.93314556049193543479541105001
absolute error = 7e-31
relative error = 2.3865164055567661682586426782627e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = -2.9338530103045301430194640380202
y[1] (numeric) = -2.9338530103045301430194640380209
absolute error = 7e-31
relative error = 2.3859409368547093861609792561830e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.431
y[1] (analytic) = -2.9345602543558021711718587204114
y[1] (numeric) = -2.9345602543558021711718587204121
absolute error = 7e-31
relative error = 2.3853659128688252277957585982598e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.432
y[1] (analytic) = -2.9352672927303921339330532605572
y[1] (numeric) = -2.9352672927303921339330532605579
absolute error = 7e-31
relative error = 2.3847913330879602801232160785769e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.4MB, time=6.29
x[1] = 0.433
y[1] (analytic) = -2.9359741255128710402089674981866
y[1] (numeric) = -2.9359741255128710402089674981874
absolute error = 8e-31
relative error = 2.7248196537163006877033298974657e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.434
y[1] (analytic) = -2.936680752787740378958088229689
y[1] (numeric) = -2.9366807527877403789580882296897
absolute error = 7e-31
relative error = 2.3836435041006826344938508066989e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.435
y[1] (analytic) = -2.9373871746394322048775274590624
y[1] (numeric) = -2.9373871746394322048775274590632
absolute error = 8e-31
relative error = 2.7235088615725332787339223020268e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.436
y[1] (analytic) = -2.9380933911523092239483232438479
y[1] (numeric) = -2.9380933911523092239483232438486
absolute error = 7e-31
relative error = 2.3824974458196600133083874728915e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.437
y[1] (analytic) = -2.9387994024106648788402720470237
y[1] (numeric) = -2.9387994024106648788402720470244
absolute error = 7e-31
relative error = 2.3819250794246034169607775989435e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.438
y[1] (analytic) = -2.9395052084987234341765807945304
y[1] (numeric) = -2.9395052084987234341765807945311
absolute error = 7e-31
relative error = 2.3813531541844314966622463023115e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.439
y[1] (analytic) = -2.9402108095006400616586261288217
y[1] (numeric) = -2.9402108095006400616586261288224
absolute error = 7e-31
relative error = 2.3807816695935714173272218406457e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = -2.9409162055005009250511076416075
y[1] (numeric) = -2.9409162055005009250511076416082
absolute error = 7e-31
relative error = 2.3802106251472412762257979834112e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.441
y[1] (analytic) = -2.9416213965823232650278811637472
y[1] (numeric) = -2.9416213965823232650278811637478
absolute error = 6e-31
memory used=160.2MB, alloc=4.4MB, time=6.45
relative error = 2.0396914460069558922639102469005e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.442
y[1] (analytic) = -2.9423263828300554838787574870708
y[1] (numeric) = -2.9423263828300554838787574870714
absolute error = 6e-31
relative error = 2.0392027325768472782174307843170e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.443
y[1] (analytic) = -2.9430311643275772300775511917398
y[1] (numeric) = -2.9430311643275772300775511917405
absolute error = 7e-31
relative error = 2.3785001276394426642397489114230e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.444
y[1] (analytic) = -2.943735741158699482711663553599
y[1] (numeric) = -2.9437357411586994827116635535996
absolute error = 6e-31
relative error = 2.0382264332050091174950768064728e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.445
y[1] (analytic) = -2.9444401134071646357734828088171
y[1] (numeric) = -2.9444401134071646357734828088177
absolute error = 6e-31
relative error = 2.0377388464040072683259343137139e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.446
y[1] (analytic) = -2.9451442811566465823138843579577
y[1] (numeric) = -2.9451442811566465823138843579582
absolute error = 5e-31
relative error = 1.6977096952399051510099931400954e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.447
y[1] (analytic) = -2.9458482444907507984581127984452
y[1] (numeric) = -2.9458482444907507984581127984457
absolute error = 5e-31
relative error = 1.6973039970239032816363819301933e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.448
y[1] (analytic) = -2.9465520034930144272843269832124
y[1] (numeric) = -2.9465520034930144272843269832129
absolute error = 5e-31
relative error = 1.6968986103325882836853189063498e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.449
y[1] (analytic) = -2.9472555582469063625650886140979
y[1] (numeric) = -2.9472555582469063625650886140984
absolute error = 5e-31
relative error = 1.6964935348104363307488809307829e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.4MB, time=6.61
x[1] = 0.45
y[1] (analytic) = -2.9479589088358273323720741913271
y[1] (numeric) = -2.9479589088358273323720741913277
absolute error = 6e-31
relative error = 2.0353065241229730117333157883451e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.451
y[1] (analytic) = -2.9486620553431099825442894551303
y[1] (numeric) = -2.9486620553431099825442894551308
absolute error = 5e-31
relative error = 1.6956843158542947316445212395333e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.452
y[1] (analytic) = -2.9493649978520189600200647722325
y[1] (numeric) = -2.9493649978520189600200647722329
absolute error = 4e-31
relative error = 1.3562241373696181154360626289336e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.453
y[1] (analytic) = -2.9500677364457509960331092385818
y[1] (numeric) = -2.9500677364457509960331092385823
absolute error = 5e-31
relative error = 1.6948763373223465484812908675322e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.454
y[1] (analytic) = -2.9507702712074349891729005902572
y[1] (numeric) = -2.9507702712074349891729005902577
absolute error = 5e-31
relative error = 1.6944728123325013160673914000308e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.455
y[1] (analytic) = -2.9514726022201320883096873370091
y[1] (numeric) = -2.9514726022201320883096873370096
absolute error = 5e-31
relative error = 1.6940695963902703109031471306073e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.456
y[1] (analytic) = -2.9521747295668357753843788573347
y[1] (numeric) = -2.9521747295668357753843788573353
absolute error = 6e-31
relative error = 2.0324000269727811747079185430268e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.457
y[1] (analytic) = -2.9528766533304719480635985203581
y[1] (numeric) = -2.9528766533304719480635985203586
absolute error = 5e-31
relative error = 1.6932640902425204407992646981670e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.4MB, time=6.76
x[1] = 0.458
y[1] (analytic) = -2.9535783735938990022601742280732
y[1] (numeric) = -2.9535783735938990022601742280737
absolute error = 5e-31
relative error = 1.6928617993353010871367188904803e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.459
y[1] (analytic) = -2.954279890439907914519340101717
y[1] (numeric) = -2.9542798904399079145193401017175
absolute error = 5e-31
relative error = 1.6924598160722928428774741885616e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = -2.954981203951222324270922368141
y[1] (numeric) = -2.9549812039512223242709223681416
absolute error = 6e-31
relative error = 2.0304697681248065210797487231763e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.461
y[1] (analytic) = -2.9556823142104986159477818360669
y[1] (numeric) = -2.9556823142104986159477818360674
absolute error = 5e-31
relative error = 1.6916567710814906581427183123967e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.462
y[1] (analytic) = -2.9563832213003260009707846880103
y[1] (numeric) = -2.9563832213003260009707846880109
absolute error = 6e-31
relative error = 2.0295068503876095850972483208995e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.463
y[1] (analytic) = -2.957083925303226599600572651455
y[1] (numeric) = -2.9570839253032265996005726514555
absolute error = 5e-31
relative error = 1.6908549524806901793771350137442e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.464
y[1] (analytic) = -2.9577844263016555226564029525272
y[1] (numeric) = -2.9577844263016555226564029525277
absolute error = 5e-31
relative error = 1.6904545022072088845361358750391e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.465
y[1] (analytic) = -2.9584847243780009531023277969779
y[1] (numeric) = -2.9584847243780009531023277969785
absolute error = 6e-31
relative error = 2.0280652289869283132689416671911e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.4MB, time=6.92
x[1] = 0.466
y[1] (analytic) = -2.9591848196145842275009824666953
y[1] (numeric) = -2.9591848196145842275009824666958
absolute error = 5e-31
relative error = 1.6896545179801305892424005951116e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.467
y[1] (analytic) = -2.9598847120936599173352504652544
y[1] (numeric) = -2.959884712093659917335250465255
absolute error = 6e-31
relative error = 2.0271059800014742673812864496879e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.468
y[1] (analytic) = -2.9605844018974159101980734931583
y[1] (numeric) = -2.9605844018974159101980734931588
absolute error = 5e-31
relative error = 1.6888557532072175425348705983471e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.469
y[1] (analytic) = -2.9612838891079734908506733824083
y[1] (numeric) = -2.9612838891079734908506733824087
absolute error = 4e-31
relative error = 1.3507654618027583297903236818893e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = -2.9619831738073874221494524708909
y[1] (numeric) = -2.9619831738073874221494524708914
absolute error = 5e-31
relative error = 1.6880582051291359707270542491171e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.471
y[1] (analytic) = -2.9626822560776460258418382497403
y[1] (numeric) = -2.9626822560776460258418382497408
absolute error = 5e-31
relative error = 1.6876598864906962594105837824865e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.472
y[1] (analytic) = -2.9633811360006712632313374713503
y[1] (numeric) = -2.9633811360006712632313374713507
absolute error = 4e-31
relative error = 1.3498094967960590819241452683659e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.473
y[1] (analytic) = -2.9640798136583188157120642620511
y[1] (numeric) = -2.9640798136583188157120642620515
absolute error = 4e-31
relative error = 1.3494913266397946579290670076503e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.474
y[1] (analytic) = -2.9647782891323781651730061416283
y[1] (numeric) = -2.9647782891323781651730061416287
absolute error = 4e-31
relative error = 1.3491733984501661672188998800325e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.4MB, time=7.08
x[1] = 0.475
y[1] (analytic) = -2.9654765625045726742722912118377
y[1] (numeric) = -2.965476562504572674272291211838
absolute error = 3e-31
relative error = 1.0116417839654984936815484208836e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.476
y[1] (analytic) = -2.9661746338565596665817191378612
y[1] (numeric) = -2.9661746338565596665817191378615
absolute error = 3e-31
relative error = 1.0114037001589017310608138080688e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.477
y[1] (analytic) = -2.9668725032699305066018179102406
y[1] (numeric) = -2.966872503269930506601817910241
absolute error = 4e-31
relative error = 1.3482210629514449362458077398145e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.478
y[1] (analytic) = -2.9675701708262106796476877402172
y[1] (numeric) = -2.9675701708262106796476877402176
absolute error = 4e-31
relative error = 1.3479040999008111870598315105702e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.479
y[1] (analytic) = -2.9682676366068598716058928085888
y[1] (numeric) = -2.9682676366068598716058928085892
absolute error = 4e-31
relative error = 1.3475873774551383806348427649318e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = -2.9689649006932720485626609571689
y[1] (numeric) = -2.9689649006932720485626609571693
absolute error = 4e-31
relative error = 1.3472708953433483657608975046326e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.481
y[1] (analytic) = -2.9696619631667755363036507826826
y[1] (numeric) = -2.969661963166775536303650782683
absolute error = 4e-31
relative error = 1.3469546532947800413740441130090e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.482
y[1] (analytic) = -2.9703588241086330996855449654618
y[1] (numeric) = -2.9703588241086330996855449654622
absolute error = 4e-31
relative error = 1.3466386510391885465960297159781e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.4MB, time=7.23
x[1] = 0.483
y[1] (analytic) = -2.9710554836000420218797280396
y[1] (numeric) = -2.9710554836000420218797280396004
absolute error = 4e-31
relative error = 1.3463228883067444526741831281675e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.484
y[1] (analytic) = -2.9717519417221341834883061872882
y[1] (numeric) = -2.9717519417221341834883061872886
absolute error = 4e-31
relative error = 1.3460073648280329568162505528759e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.485
y[1] (analytic) = -2.9724481985559761415327260178722
y[1] (numeric) = -2.9724481985559761415327260178725
absolute error = 3e-31
relative error = 1.0092690602505398084362325014048e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.486
y[1] (analytic) = -2.9731442541825692083152486717427
y[1] (numeric) = -2.9731442541825692083152486717431
absolute error = 4e-31
relative error = 1.3453770345562168541572401398601e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.487
y[1] (analytic) = -2.9738401086828495301535349704926
y[1] (numeric) = -2.9738401086828495301535349704929
absolute error = 3e-31
relative error = 1.0087966704197614068844267042117e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.488
y[1] (analytic) = -2.9745357621376881659885967178292
y[1] (numeric) = -2.9745357621376881659885967178295
absolute error = 3e-31
relative error = 1.0085607435575128650719078632587e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.489
y[1] (analytic) = -2.9752312146278911658663686405339
y[1] (numeric) = -2.9752312146278911658663686405341
absolute error = 2e-31
relative error = 6.7221666341993449369964058520928e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = -2.9759264662341996492931548452798
y[1] (numeric) = -2.97592646623419964929315484528
absolute error = 2e-31
relative error = 6.7205961662448008669393468338422e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.4MB, time=7.39
x[1] = 0.491
y[1] (analytic) = -2.9766215170372898834652030553755
y[1] (numeric) = -2.9766215170372898834652030553758
absolute error = 3e-31
relative error = 1.0078540327780669068407365626985e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.492
y[1] (analytic) = -2.9773163671177733613726592814683
y[1] (numeric) = -2.9773163671177733613726592814685
absolute error = 2e-31
relative error = 6.7174587896956475161362077915492e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.493
y[1] (analytic) = -2.978011016556196879778154971926
y[1] (numeric) = -2.9780110165561968797781549719262
absolute error = 2e-31
relative error = 6.7158918784418095961412701044847e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.494
y[1] (analytic) = -2.9787054654330426170702780820097
y[1] (numeric) = -2.9787054654330426170702780820099
absolute error = 2e-31
relative error = 6.7143261500990366068629442067945e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.495
y[1] (analytic) = -2.9793997138287282109921788960398
y[1] (numeric) = -2.97939971382872821099217889604
absolute error = 2e-31
relative error = 6.7127616033427956115416107578407e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.496
y[1] (analytic) = -2.9800937618236068362455608335527
y[1] (numeric) = -2.9800937618236068362455608335529
absolute error = 2e-31
relative error = 6.7111982368505791629455743347870e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.497
y[1] (analytic) = -2.9807876094979672819703058689276
y[1] (numeric) = -2.9807876094979672819703058689278
absolute error = 2e-31
relative error = 6.7096360493019013933773873850010e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.498
y[1] (analytic) = -2.9814812569320340290999835941314
y[1] (numeric) = -2.9814812569320340290999835941316
absolute error = 2e-31
relative error = 6.7080750393782941137977818062895e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.499
y[1] (analytic) = -2.9821747042059673275934923560807
y[1] (numeric) = -2.9821747042059673275934923560809
absolute error = 2e-31
relative error = 6.7065152057633029220422935999447e-30 %
Correct digits = 31
h = 0.001
memory used=186.9MB, alloc=4.4MB, time=7.54
NO POLE for equation 1
Finished!
diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));
Iterations = 400
Total Elapsed Time = 7 Seconds
Elapsed Time(since restart) = 7 Seconds
Time to Timeout = 2 Minutes 52 Seconds
Percent Done = 100.2 %
> quit
memory used=187.0MB, alloc=4.4MB, time=7.55