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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 1
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 1;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 3
> # Begin Function number 4
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> 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_a1,
> 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_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, 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_a1, 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_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> 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_a1,
> 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_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, 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_a1, 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_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> 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_a1,
> 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_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, 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_a1, 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_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> 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_a1,
> 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_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, 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_a1, 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_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> 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_a1,
> 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_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, 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_a1, 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_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> 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_a1,
> 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_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, 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_a1, 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_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> 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_a1,
> 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, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, 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) or (omniabs(array_y_higher[1,m-1]) < glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_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-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 1
> #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 := false;
> #TOP WHICH RADII EQ = 1
> if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 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 := true;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if ( not found ) 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");
> 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, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found, 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_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, 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_a1, 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 or
omniabs(array_y_higher[1, m - 1]) < glob_small_float or
omniabs(array_y_higher[1, m - 2]) < 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 - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 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 := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
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_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> 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_a1,
> 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_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, 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_a1, 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_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> 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_a1,
> 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 arccos FULL $eq_no = 1
> array_tmp4[1] := arccos(array_tmp3[1]);
> array_tmp4_a1[1] := sin(array_tmp4[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 arccos FULL $eq_no = 1
> temp := att(1,array_tmp4_a1,array_tmp4,2);
> array_tmp4[2] := - (array_tmp3[2] + temp) / array_tmp4_a1[1];
> temp2 := att(1,array_tmp3,array_tmp4,1);
> array_tmp4_a1[2] := temp2;
> #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 arccos FULL $eq_no = 1
> temp := att(2,array_tmp4_a1,array_tmp4,2);
> array_tmp4[3] := - (array_tmp3[3] + temp) / array_tmp4_a1[1];
> temp2 := att(2,array_tmp3,array_tmp4,1);
> array_tmp4_a1[3] := temp2;
> #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 arccos FULL $eq_no = 1
> temp := att(3,array_tmp4_a1,array_tmp4,2);
> array_tmp4[4] := - (array_tmp3[4] + temp) / array_tmp4_a1[1];
> temp2 := att(3,array_tmp3,array_tmp4,1);
> array_tmp4_a1[4] := temp2;
> #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 arccos FULL $eq_no = 1
> temp := att(4,array_tmp4_a1,array_tmp4,2);
> array_tmp4[5] := - (array_tmp3[5] + temp) / array_tmp4_a1[1];
> temp2 := att(4,array_tmp3,array_tmp4,1);
> array_tmp4_a1[5] := temp2;
> #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 arcsin $eq_no = 1
> temp := att(kkk-1,array_tmp4_a1,array_tmp4,2);
> array_tmp4[kkk] := - (array_tmp3[kkk] + temp) / array_tmp4_a1[1];
> temp2 := att(kkk-1,array_tmp3,array_tmp4,1);
> array_tmp4_a1[kkk] := temp2;
> #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;
Warning, `temp` is implicitly declared local to procedure `atomall`
Warning, `temp2` is implicitly declared local to procedure `atomall`
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term, temp, temp2;
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_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, 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_a1, 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] := arccos(array_tmp3[1]);
array_tmp4_a1[1] := sin(array_tmp4[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);
temp := att(1, array_tmp4_a1, array_tmp4, 2);
array_tmp4[2] := -(array_tmp3[2] + temp)/array_tmp4_a1[1];
temp2 := att(1, array_tmp3, array_tmp4, 1);
array_tmp4_a1[2] := temp2;
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)
;
temp := att(2, array_tmp4_a1, array_tmp4, 2);
array_tmp4[3] := -(array_tmp3[3] + temp)/array_tmp4_a1[1];
temp2 := att(2, array_tmp3, array_tmp4, 1);
array_tmp4_a1[3] := temp2;
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)
;
temp := att(3, array_tmp4_a1, array_tmp4, 2);
array_tmp4[4] := -(array_tmp3[4] + temp)/array_tmp4_a1[1];
temp2 := att(3, array_tmp3, array_tmp4, 1);
array_tmp4_a1[4] := temp2;
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)
;
temp := att(4, array_tmp4_a1, array_tmp4, 2);
array_tmp4[5] := -(array_tmp3[5] + temp)/array_tmp4_a1[1];
temp2 := att(4, array_tmp3, array_tmp4, 1);
array_tmp4_a1[5] := temp2;
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);
temp := att(kkk - 1, array_tmp4_a1, array_tmp4, 2);
array_tmp4[kkk] := -(array_tmp3[kkk] + temp)/array_tmp4_a1[1];
temp2 := att(kkk - 1, array_tmp3, array_tmp4, 1);
array_tmp4_a1[kkk] := temp2;
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 := 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 15
> # Begin Function number 16
> 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 16
> # Begin Function number 17
> 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 17
> # Begin Function number 18
> 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 18
> # Begin Function number 19
> 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 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> 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 21
> # Begin Function number 22
> 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 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # End Function number 24
> # Begin Function number 25
> 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 25
> # Begin Function number 26
> 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 26
> # Begin Function number 27
> 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 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> 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 29
> # Begin Function number 30
> 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 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> 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 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x +
> 0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt( 0.1 * x + 0.2)));
> end;
exact_soln_y := proc(x)
return 10.0*(0.1*x + 0.2)*arccos(sqrt(0.1*x + 0.2))
- 5.0*sqrt(0.1*x + 0.2)*sqrt(0.8 - 0.1*x)
+ 5.0*arcsin(sqrt(0.1*x + 0.2))
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp,subiter, 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_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> 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_a1,
> 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_log10normmin := 0.1;
> 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_hmax := 1.0;
> glob_hmin := 0.00000000001;
> glob_hmin_init := 0.001;
> 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_log10_abserr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> 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-50;
> 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_log10abserr := 0.0;
> glob_log10relerr := 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/arccos_sqrtpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = arccos(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 := 0.0;");
> omniout_str(ALWAYS,"x_end := 0.5 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.05;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> 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(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x +");
> omniout_str(ALWAYS,"0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt( 0.1 * x + 0.2)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_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_a1:= 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_a1[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_a1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4_a1[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 := 0.0;
> x_end := 0.5 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.05;
> glob_look_poles := true;
> glob_max_iter := 1000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #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);
> glob_abserr := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_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;
> 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_log10normmin := -glob_large_float ;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((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 ) = arccos(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,"2013-01-12T20:51:11-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"arccos_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = arccos(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," 156 | ")
> ;
> logitem_str(html_log_file,"arccos_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"arccos_sqrt maple results")
> ;
> logitem_str(html_log_file,"Languages compared - single equations")
> ;
> 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, log10norm, 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_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, 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_a1, 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_log10normmin := 0.1;
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_hmax := 1.0;
glob_hmin := 0.1*10^(-10);
glob_hmin_init := 0.001;
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_log10_abserr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
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^(-50);
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_log10abserr := 0.;
glob_log10relerr := 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/arccos_sqrtpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arccos(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 := 0.0;");
omniout_str(ALWAYS, "x_end := 0.5 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.05;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
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(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.\
1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x +");
omniout_str(ALWAYS, "0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt(\
0.1 * x + 0.2)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_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_a1 := 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_a1[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_a1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_a1[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.;
x_end := 0.5;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
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);
glob_abserr := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_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;
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_log10normmin := -glob_large_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
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 ) = arccos(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, "2013-01-12T20:51:11-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"arccos_sqrt");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = arccos(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, " 156 | ");
logitem_str(html_log_file, "arccos_sqrt diffeq.mxt");
logitem_str(html_log_file, "arccos_sqrt maple results");
logitem_str(html_log_file,
"Languages compared - single equations");
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/arccos_sqrtpostode.ode#################
diff ( y , x , 1 ) = arccos(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 := 0.0;
x_end := 0.5 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#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(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x +
0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt( 0.1 * x + 0.2)));
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 = 0.5
estimated_steps = 500
step_error = 2.0000000000000000000000000000000e-13
est_needed_step_err = 2.0000000000000000000000000000000e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 1.1718309454379427110227424203722e-90
max_value3 = 1.1718309454379427110227424203722e-90
value3 = 1.1718309454379427110227424203722e-90
best_h = 0.001
START of Soultion
x[1] = 0
y[1] (analytic) = 2.5325354805922115871054120776631
y[1] (numeric) = 2.5325354805922115871054120776631
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (analytic) = 2.5325354805922115871054120776631
y[1] (numeric) = 2.5325354805922115871054120776631
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.001
y[1] (analytic) = 2.5336425668139110529839867211056
y[1] (numeric) = 2.5336425668139110529839867211056
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
memory used=3.8MB, alloc=2.8MB, time=0.12
TOP MAIN SOLVE Loop
x[1] = 0.002
y[1] (analytic) = 2.5347495280590357775231090564521
y[1] (numeric) = 2.534749528059035777523109056452
absolute error = 1e-31
relative error = 3.9451629793407714705211031505065e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.003
y[1] (analytic) = 2.5358563643509917984772048963088
y[1] (numeric) = 2.5358563643509917984772048963088
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.004
y[1] (analytic) = 2.5369630757131642084953181281344
y[1] (numeric) = 2.5369630757131642084953181281342
absolute error = 2e-31
relative error = 7.8834415019532011442619847215881e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.005
y[1] (analytic) = 2.5380696621689171805513234614831
y[1] (numeric) = 2.538069662168917180551323461483
absolute error = 1e-31
relative error = 3.9400021792366650732682972133140e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.006
y[1] (analytic) = 2.5391761237415939933291082161395
y[1] (numeric) = 2.5391761237415939933291082161395
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
memory used=7.6MB, alloc=3.9MB, time=0.26
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.007
y[1] (analytic) = 2.5402824604545170565628242197235
y[1] (numeric) = 2.5402824604545170565628242197234
absolute error = 1e-31
relative error = 3.9365701081173318582474925334588e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.008
y[1] (analytic) = 2.5413886723309879363323106056772
y[1] (numeric) = 2.541388672330987936332310605677
absolute error = 2e-31
relative error = 7.8697132074865956850880630603678e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.009
y[1] (analytic) = 2.5424947593942873803137880257652
y[1] (numeric) = 2.542494759394287380313788025765
absolute error = 2e-31
relative error = 7.8662895670096527006583623516599e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (analytic) = 2.5436007216676753429859245153375
y[1] (numeric) = 2.5436007216676753429859245153376
absolute error = 1e-31
relative error = 3.9314346449169283849359089256712e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.011
y[1] (analytic) = 2.544706559174391010791372974621
y[1] (numeric) = 2.5447065591743910107913729746211
absolute error = 1e-31
relative error = 3.9297261854995246539848335574659e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=0.41
x[1] = 0.012
y[1] (analytic) = 2.545812271937652827253879955202
y[1] (numeric) = 2.5458122719376528272538799552022
absolute error = 2e-31
relative error = 7.8560388055548668548920216159499e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.013
y[1] (analytic) = 2.5469178599806585180510651676621
y[1] (numeric) = 2.5469178599806585180510651676621
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.014
y[1] (analytic) = 2.5480233233265851160429708539898
y[1] (numeric) = 2.5480233233265851160429708539896
absolute error = 2e-31
relative error = 7.8492217150857535597729348035020e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.015
y[1] (analytic) = 2.549128661998588986256479896954
y[1] (numeric) = 2.5491286619985889862564798969541
absolute error = 1e-31
relative error = 3.9229090901044269371761970674042e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.016
y[1] (analytic) = 2.5502338760198058508257012680502
y[1] (numeric) = 2.55023387601980585082570126805
absolute error = 2e-31
relative error = 7.8424179790185934458172651617407e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.56
x[1] = 0.017
y[1] (analytic) = 2.5513389654133508138884211459273
y[1] (numeric) = 2.5513389654133508138884211459271
absolute error = 2e-31
relative error = 7.8390211066132226948107275930168e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.018
y[1] (analytic) = 2.5524439302023183864387177683937
y[1] (numeric) = 2.5524439302023183864387177683934
absolute error = 3e-31
relative error = 1.1753441337150964453728662897209e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.019
y[1] (analytic) = 2.5535487704097825111358378131185
y[1] (numeric) = 2.5535487704097825111358378131183
absolute error = 2e-31
relative error = 7.8322373285983827595644897793374e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (analytic) = 2.5546534860587965870694318350684
y[1] (numeric) = 2.5546534860587965870694318350681
absolute error = 3e-31
relative error = 1.1743275619850360978677611601425e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.021
y[1] (analytic) = 2.5557580771723934944812460224697
y[1] (numeric) = 2.5557580771723934944812460224694
absolute error = 3e-31
relative error = 1.1738200210714392529240336026311e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.022
y[1] (analytic) = 2.5568625437735856194433672677183
y[1] (numeric) = 2.5568625437735856194433672677183
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.2MB, time=0.71
x[1] = 0.023
y[1] (analytic) = 2.5579668858853648784931182851296
y[1] (numeric) = 2.5579668858853648784931182851295
absolute error = 1e-31
relative error = 3.9093547516893654412121329557898e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.024
y[1] (analytic) = 2.5590711035307027432246992437472
y[1] (numeric) = 2.559071103530702743224699243747
absolute error = 2e-31
relative error = 7.8153357960262895648924294796360e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.025
y[1] (analytic) = 2.5601751967325502648376721206112
y[1] (numeric) = 2.560175196732550264837672120611
absolute error = 2e-31
relative error = 7.8119653785901856276757061300004e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.026
y[1] (analytic) = 2.5612791655138380986423837178978
y[1] (numeric) = 2.5612791655138380986423837178976
absolute error = 2e-31
relative error = 7.8085982462546774842024081060741e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.027
y[1] (analytic) = 2.5623830098974765285224230262083
y[1] (numeric) = 2.5623830098974765285224230262081
absolute error = 2e-31
relative error = 7.8052343942134629302708913747694e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.3MB, time=0.86
x[1] = 0.028
y[1] (analytic) = 2.5634867299063554913542083559833
y[1] (numeric) = 2.5634867299063554913542083559832
absolute error = 1e-31
relative error = 3.9009369088348279922970659497680e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.029
y[1] (analytic) = 2.5645903255633446013837993995546
y[1] (numeric) = 2.5645903255633446013837993995544
absolute error = 2e-31
relative error = 7.7985165118357637975784315224942e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (analytic) = 2.5656937968912931745610291277108
y[1] (numeric) = 2.5656937968912931745610291277107
absolute error = 1e-31
relative error = 3.8975812359668318140508232778741e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.031
y[1] (analytic) = 2.566797143913030252831050166856
y[1] (numeric) = 2.5667971439130302528310501668558
absolute error = 2e-31
relative error = 7.7918116931945798880572540952190e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.032
y[1] (analytic) = 2.5679003666513646283833900458526
y[1] (numeric) = 2.5679003666513646283833900458525
absolute error = 1e-31
relative error = 3.8942320854295306272157444542362e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.033
y[1] (analytic) = 2.5690034651290848678586094454983
y[1] (numeric) = 2.5690034651290848678586094454982
absolute error = 1e-31
relative error = 3.8925599500884789243408487654589e-30 %
Correct digits = 31
h = 0.001
memory used=26.7MB, alloc=4.3MB, time=1.01
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.034
y[1] (analytic) = 2.5701064393689593365126573282399
y[1] (numeric) = 2.5701064393689593365126573282398
absolute error = 1e-31
relative error = 3.8908894382036992415924829762321e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.035
y[1] (analytic) = 2.5712092893937362223390165712191
y[1] (numeric) = 2.5712092893937362223390165712189
absolute error = 2e-31
relative error = 7.7784410948187679745269830088965e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.036
y[1] (analytic) = 2.5723120152261435601487334720356
y[1] (numeric) = 2.5723120152261435601487334720353
absolute error = 3e-31
relative error = 1.1662659826033026785103004993018e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.037
y[1] (analytic) = 2.5734146168888892556084242437244
y[1] (numeric) = 2.5734146168888892556084242437241
absolute error = 3e-31
relative error = 1.1657662858955965741343507169160e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.038
y[1] (analytic) = 2.5745170944046611092363513633575
y[1] (numeric) = 2.5745170944046611092363513633573
absolute error = 2e-31
relative error = 7.7684471559606632609233624952491e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.3MB, time=1.16
x[1] = 0.039
y[1] (analytic) = 2.5756194477961268403566623874014
y[1] (numeric) = 2.5756194477961268403566623874011
absolute error = 3e-31
relative error = 1.1647683443945889177896377147908e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (analytic) = 2.5767216770859341110118835964832
y[1] (numeric) = 2.576721677085934111011883596483
absolute error = 2e-31
relative error = 7.7618006546280925942988753458298e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.041
y[1] (analytic) = 2.5778237822967105498337605825441
y[1] (numeric) = 2.577823782296710549833760582544
absolute error = 1e-31
relative error = 3.8792411136383054116127510701795e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.042
y[1] (analytic) = 2.5789257634510637758725376424703
y[1] (numeric) = 2.5789257634510637758725376424702
absolute error = 1e-31
relative error = 3.8775835046210139950990818472191e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.043
y[1] (analytic) = 2.5800276205715814223847675942074
y[1] (numeric) = 2.5800276205715814223847675942072
absolute error = 2e-31
relative error = 7.7518549958659681694967525947913e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.3MB, time=1.32
x[1] = 0.044
y[1] (analytic) = 2.5811293536808311605797433840643
y[1] (numeric) = 2.5811293536808311605797433840643
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.045
y[1] (analytic) = 2.5822309628013607233246426074027
y[1] (numeric) = 2.5822309628013607233246426074025
absolute error = 2e-31
relative error = 7.7452405645011658019566347941499e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.046
y[1] (analytic) = 2.5833324479556979288084758191746
y[1] (numeric) = 2.5833324479556979288084758191745
absolute error = 1e-31
relative error = 3.8709690686204286577591155942135e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.047
y[1] (analytic) = 2.5844338091663507041649292658398
y[1] (numeric) = 2.5844338091663507041649292658396
absolute error = 2e-31
relative error = 7.7386388960958960935634226574198e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.048
y[1] (analytic) = 2.5855350464558071090541924260106
y[1] (numeric) = 2.5855350464558071090541924260105
absolute error = 1e-31
relative error = 3.8676714182264802579228545599939e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.049
y[1] (analytic) = 2.5866361598465353592038605037978
y[1] (numeric) = 2.5866361598465353592038605037977
absolute error = 1e-31
relative error = 3.8660249768538371219482904097018e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=1.47
x[1] = 0.05
y[1] (analytic) = 2.5877371493609838499090017762012
y[1] (numeric) = 2.587737149360983849909001776201
absolute error = 2e-31
relative error = 7.7287602432645845099172076573468e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.051
y[1] (analytic) = 2.5888380150215811794914794540495
y[1] (numeric) = 2.5888380150215811794914794540494
absolute error = 1e-31
relative error = 3.8627368502685702344748680575091e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.052
y[1] (analytic) = 2.5899387568507361727186174749126
y[1] (numeric) = 2.5899387568507361727186174749125
absolute error = 1e-31
relative error = 3.8610951604738358070564788153358e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.053
y[1] (analytic) = 2.5910393748708379041812994060901
y[1] (numeric) = 2.59103937487083790418129940609
absolute error = 1e-31
relative error = 3.8594550499636831273439745114710e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.054
y[1] (analytic) = 2.5921398691042557216315893962337
y[1] (numeric) = 2.5921398691042557216315893962336
absolute error = 1e-31
relative error = 3.8578165164581250284200593052349e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=1.62
x[1] = 0.055
y[1] (analytic) = 2.5932402395733392692799638753609
y[1] (numeric) = 2.5932402395733392692799638753609
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.056
y[1] (analytic) = 2.594340486300418511052242464984
y[1] (numeric) = 2.5943404863004185110522424649839
absolute error = 1e-31
relative error = 3.8545441713628731380226650490207e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.057
y[1] (analytic) = 2.5954406093078037538063063227887
y[1] (numeric) = 2.5954406093078037538063063227888
absolute error = 1e-31
relative error = 3.8529103552352022745049896696091e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.058
y[1] (analytic) = 2.5965406086177856705086919097713
y[1] (numeric) = 2.5965406086177856705086919097714
absolute error = 1e-31
relative error = 3.8512781070361506059408511158395e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.059
y[1] (analytic) = 2.5976404842526353233711479319465
y[1] (numeric) = 2.5976404842526353233711479319464
absolute error = 1e-31
relative error = 3.8496474245076645017535072348736e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (analytic) = 2.5987402362346041869472429737081
y[1] (numeric) = 2.598740236234604186947242973708
absolute error = 1e-31
relative error = 3.8480183053960452837289479232526e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.3MB, time=1.78
x[1] = 0.061
y[1] (analytic) = 2.5998398645859241711891111056218
y[1] (numeric) = 2.5998398645859241711891111056219
absolute error = 1e-31
relative error = 3.8463907474519387126490176937083e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.062
y[1] (analytic) = 2.600939369328807644464422515871
y[1] (numeric) = 2.600939369328807644464422515871
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.063
y[1] (analytic) = 2.6020387504854474565336659817557
y[1] (numeric) = 2.6020387504854474565336659817555
absolute error = 2e-31
relative error = 7.6862806121810117649526544284739e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.064
y[1] (analytic) = 2.6031380080780169614878297655622
y[1] (numeric) = 2.6031380080780169614878297655622
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.065
y[1] (analytic) = 2.6042371421286700406465672877644
y[1] (numeric) = 2.6042371421286700406465672877644
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.3MB, time=1.93
x[1] = 0.066
y[1] (analytic) = 2.6053361526595411254169336998856
y[1] (numeric) = 2.6053361526595411254169336998856
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.067
y[1] (analytic) = 2.6064350396927452201127792494646
y[1] (numeric) = 2.6064350396927452201127792494646
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.068
y[1] (analytic) = 2.6075338032503779247348851003823
y[1] (numeric) = 2.6075338032503779247348851003823
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.069
y[1] (analytic) = 2.6086324433545154577119270433577
y[1] (numeric) = 2.6086324433545154577119270433577
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (analytic) = 2.6097309600272146786023523036853
y[1] (numeric) = 2.6097309600272146786023523036853
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.071
y[1] (analytic) = 2.6108293532905131107572544262662
y[1] (numeric) = 2.6108293532905131107572544262662
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.4MB, time=2.08
x[1] = 0.072
y[1] (analytic) = 2.6119276231664289639443309916814
y[1] (numeric) = 2.6119276231664289639443309916812
absolute error = 2e-31
relative error = 7.6571800162494868117409401747469e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.073
y[1] (analytic) = 2.6130257696769611569330086914573
y[1] (numeric) = 2.6130257696769611569330086914571
absolute error = 2e-31
relative error = 7.6539620206166305952729610566958e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.074
y[1] (analytic) = 2.6141237928440893400408200657923
y[1] (numeric) = 2.6141237928440893400408200657922
absolute error = 1e-31
relative error = 3.8253735448084101172332915586409e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.075
y[1] (analytic) = 2.6152216926897739176411159828258
y[1] (numeric) = 2.6152216926897739176411159828256
absolute error = 2e-31
relative error = 7.6475352188708175000030042722625e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.076
y[1] (analytic) = 2.6163194692359560706321977150565
y[1] (numeric) = 2.6163194692359560706321977150565
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.4MB, time=2.23
x[1] = 0.077
y[1] (analytic) = 2.617417122504557778867952245744
y[1] (numeric) = 2.6174171225045577788679522457439
absolute error = 1e-31
relative error = 3.8205603203325826531144545502481e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.078
y[1] (analytic) = 2.6185146525174818435500742160356
y[1] (numeric) = 2.6185146525174818435500742160355
absolute error = 1e-31
relative error = 3.8189589622444312661328096455066e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.079
y[1] (analytic) = 2.6196120592966119095819577021938
y[1] (numeric) = 2.6196120592966119095819577021937
absolute error = 1e-31
relative error = 3.8173591255665103884779471852485e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (analytic) = 2.620709342863812487884340791593
y[1] (numeric) = 2.620709342863812487884340791593
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.081
y[1] (analytic) = 2.6218065032409289776727857061663
y[1] (numeric) = 2.6218065032409289776727857061662
absolute error = 1e-31
relative error = 3.8141640077704305568012907967444e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.082
y[1] (analytic) = 2.6229035404497876886970770026613
y[1] (numeric) = 2.6229035404497876886970770026612
absolute error = 1e-31
relative error = 3.8125687223271479996499238947245e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.4MB, time=2.39
x[1] = 0.083
y[1] (analytic) = 2.6240004545121958634426201604468
y[1] (numeric) = 2.6240004545121958634426201604465
absolute error = 3e-31
relative error = 1.1432924848931486955195073064610e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.084
y[1] (analytic) = 2.6250972454499416992939226496591
y[1] (numeric) = 2.6250972454499416992939226496589
absolute error = 2e-31
relative error = 7.6187653751364169979879813835094e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.085
y[1] (analytic) = 2.6261939132847943706602393552228
y[1] (numeric) = 2.6261939132847943706602393552227
absolute error = 1e-31
relative error = 3.8077919339521225569777526001476e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.086
y[1] (analytic) = 2.6272904580385040510634640156885
y[1] (numeric) = 2.6272904580385040510634640156883
absolute error = 2e-31
relative error = 7.6124053733029968454255138763087e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.087
y[1] (analytic) = 2.6283868797328019351883481199248
y[1] (numeric) = 2.6283868797328019351883481199247
absolute error = 1e-31
relative error = 3.8046149435263448546295176873006e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.4MB, time=2.54
x[1] = 0.088
y[1] (analytic) = 2.6294831783894002608951284894697
y[1] (numeric) = 2.6294831783894002608951284894695
absolute error = 2e-31
relative error = 7.6060574048814847607881619577000e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.089
y[1] (analytic) = 2.6305793540299923311946445597706
y[1] (numeric) = 2.6305793540299923311946445597705
absolute error = 1e-31
relative error = 3.8014439612628335992391140504485e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (analytic) = 2.6316754066762525361860261596604
y[1] (numeric) = 2.6316754066762525361860261596602
absolute error = 2e-31
relative error = 7.5997214357296270240633664687846e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.091
y[1] (analytic) = 2.6327713363498363749570323751726
y[1] (numeric) = 2.6327713363498363749570323751724
absolute error = 2e-31
relative error = 7.5965579402458397579702815716909e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.092
y[1] (analytic) = 2.6338671430723804774471218712441
y[1] (numeric) = 2.6338671430723804774471218712439
absolute error = 2e-31
relative error = 7.5933974318348472098457870868041e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.093
y[1] (analytic) = 2.6349628268655026262733348329386
y[1] (numeric) = 2.6349628268655026262733348329385
absolute error = 1e-31
relative error = 3.7951199531326191520021780828390e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.4MB, time=2.70
x[1] = 0.094
y[1] (analytic) = 2.6360583877508017785190664765854
y[1] (numeric) = 2.6360583877508017785190664765851
absolute error = 3e-31
relative error = 1.1380628038970444939418951554701e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.095
y[1] (analytic) = 2.6371538257498580874858118706304
y[1] (numeric) = 2.6371538257498580874858118706302
absolute error = 2e-31
relative error = 7.5839337867646480254285621934620e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.096
y[1] (analytic) = 2.6382491408842329244079615960716
y[1] (numeric) = 2.6382491408842329244079615960714
absolute error = 2e-31
relative error = 7.5807851844109082689134484624809e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.097
y[1] (analytic) = 2.6393443331754689001307275670524
y[1] (numeric) = 2.6393443331754689001307275670521
absolute error = 3e-31
relative error = 1.1366459322079496129304040879179e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.098
y[1] (analytic) = 2.6404394026450898867512781235661
y[1] (numeric) = 2.6404394026450898867512781235658
absolute error = 3e-31
relative error = 1.1361745310249181399132329052602e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.4MB, time=2.85
x[1] = 0.099
y[1] (analytic) = 2.6415343493146010392231613002299
y[1] (numeric) = 2.6415343493146010392231613002295
absolute error = 4e-31
relative error = 1.5142714313133501615666009736553e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 2.6426291732054888169240949677441
y[1] (numeric) = 2.6426291732054888169240949677438
absolute error = 3e-31
relative error = 1.1352330589618910188958243474302e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.101
y[1] (analytic) = 2.6437238743392210051872023369588
y[1] (numeric) = 2.6437238743392210051872023369586
absolute error = 2e-31
relative error = 7.5650865788693043085889766950486e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.102
y[1] (analytic) = 2.6448184527372467367957711094022
y[1] (numeric) = 2.6448184527372467367957711094018
absolute error = 4e-31
relative error = 1.5123911419554004857776722579383e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.103
y[1] (analytic) = 2.6459129084209965134416143527097
y[1] (numeric) = 2.6459129084209965134416143527093
absolute error = 4e-31
relative error = 1.5117655563300770486448358631658e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.104
y[1] (analytic) = 2.6470072414118822271471109746073
y[1] (numeric) = 2.6470072414118822271471109746069
absolute error = 4e-31
relative error = 1.5111405580690619884141777336924e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.4MB, time=3.00
x[1] = 0.105
y[1] (analytic) = 2.648101451731297181651003464944
y[1] (numeric) = 2.6481014517312971816510034649436
absolute error = 4e-31
relative error = 1.5105161463450909907527935794894e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.106
y[1] (analytic) = 2.6491955394006161137580303717548
y[1] (numeric) = 2.6491955394006161137580303717542
absolute error = 6e-31
relative error = 2.2648384804986904402502740205995e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.107
y[1] (analytic) = 2.6502895044411952146524707744374
y[1] (numeric) = 2.6502895044411952146524707744371
absolute error = 3e-31
relative error = 1.1319518094052672513142890327127e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.108
y[1] (analytic) = 2.6513833468743721511756778148674
y[1] (numeric) = 2.6513833468743721511756778148671
absolute error = 3e-31
relative error = 1.1314848166096390600465107498627e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.109
y[1] (analytic) = 2.6524770667214660870676781456237
y[1] (numeric) = 2.6524770667214660870676781456234
absolute error = 3e-31
relative error = 1.1310182612466775162896999811360e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.4MB, time=3.16
x[1] = 0.11
y[1] (analytic) = 2.6535706640037777041729139534923
y[1] (numeric) = 2.653570664003777704172913953492
absolute error = 3e-31
relative error = 1.1305521427017588963113509736881e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.111
y[1] (analytic) = 2.6546641387425892236102040160056
y[1] (numeric) = 2.6546641387425892236102040160052
absolute error = 4e-31
relative error = 1.5067819471485548669121634777635e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.112
y[1] (analytic) = 2.6557574909591644269070000489987
y[1] (numeric) = 2.6557574909591644269070000489984
absolute error = 3e-31
relative error = 1.1296212136133361770251750372438e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.113
y[1] (analytic) = 2.6568507206747486770980144039991
y[1] (numeric) = 2.6568507206747486770980144039989
absolute error = 2e-31
relative error = 7.5277093456423807196248662210541e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.114
y[1] (analytic) = 2.6579438279105689397882949757116
y[1] (numeric) = 2.6579438279105689397882949757114
absolute error = 2e-31
relative error = 7.5246134963364373111427064320796e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.115
y[1] (analytic) = 2.659036812687833804180822981922
y[1] (numeric) = 2.6590368126878338041808229819218
absolute error = 2e-31
relative error = 7.5215205387786274523331809342222e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.4MB, time=3.31
x[1] = 0.116
y[1] (analytic) = 2.6601296750277335040687090808107
y[1] (numeric) = 2.6601296750277335040687090808104
absolute error = 3e-31
relative error = 1.1277645703376182729512972766179e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.117
y[1] (analytic) = 2.6612224149514399387920630939418
y[1] (numeric) = 2.6612224149514399387920630939415
absolute error = 3e-31
relative error = 1.1273014924063541038042290713962e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.118
y[1] (analytic) = 2.6623150324801066941596124070758
y[1] (numeric) = 2.6623150324801066941596124070754
absolute error = 4e-31
relative error = 1.5024517952234072182713480699263e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.119
y[1] (analytic) = 2.6634075276348690633351439254322
y[1] (numeric) = 2.6634075276348690633351439254319
absolute error = 3e-31
relative error = 1.1263766317669110960755900995637e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 2.6644999004368440676888442651182
y[1] (numeric) = 2.6644999004368440676888442651179
absolute error = 3e-31
relative error = 1.1259148478512424706765412309277e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.4MB, time=3.47
x[1] = 0.121
y[1] (analytic) = 2.6655921509071304776136126681135
y[1] (numeric) = 2.6655921509071304776136126681132
absolute error = 3e-31
relative error = 1.1254534940685006272972899601134e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.122
y[1] (analytic) = 2.6666842790668088333064209344859
y[1] (numeric) = 2.6666842790668088333064209344854
absolute error = 5e-31
relative error = 1.8749876163629396282524095689663e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.123
y[1] (analytic) = 2.6677762849369414655147944723789
y[1] (numeric) = 2.6677762849369414655147944723785
absolute error = 4e-31
relative error = 1.4993760993323128140281971193327e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.124
y[1] (analytic) = 2.6688681685385725162484883737823
y[1] (numeric) = 2.6688681685385725162484883737819
absolute error = 4e-31
relative error = 1.4987626766856502197818898486038e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.125
y[1] (analytic) = 2.6699599298927279594564322321427
y[1] (numeric) = 2.6699599298927279594564322321422
absolute error = 5e-31
relative error = 1.8726872804420278269393357044340e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.126
y[1] (analytic) = 2.6710515690204156216690172265206
y[1] (numeric) = 2.6710515690204156216690172265202
absolute error = 4e-31
relative error = 1.4975375415409760814381151559486e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.4MB, time=3.62
x[1] = 0.127
y[1] (analytic) = 2.6721430859426252026057988062245
y[1] (numeric) = 2.672143085942625202605798806224
absolute error = 5e-31
relative error = 1.8711572843174301745009160318009e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.128
y[1] (analytic) = 2.6732344806803282957486881196609
y[1] (numeric) = 2.6732344806803282957486881196606
absolute error = 3e-31
relative error = 1.1222360109751805562621088726823e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.129
y[1] (analytic) = 2.6743257532544784088807051415407
y[1] (numeric) = 2.6743257532544784088807051415404
absolute error = 3e-31
relative error = 1.1217780767167939319918192080808e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 2.6754169036860109845903662635426
y[1] (numeric) = 2.6754169036860109845903662635422
absolute error = 4e-31
relative error = 1.4950940896310652603800775240966e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.131
y[1] (analytic) = 2.676507931995843420741778925096
y[1] (numeric) = 2.6765079319958434207417789250958
absolute error = 2e-31
relative error = 7.4724232126919994942628569997022e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.4MB, time=3.77
x[1] = 0.132
y[1] (analytic) = 2.6775988382048750909105156730654
y[1] (numeric) = 2.6775988382048750909105156730651
absolute error = 3e-31
relative error = 1.1204068201685022358308986983868e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.133
y[1] (analytic) = 2.6786896223339873647853398518146
y[1] (numeric) = 2.6786896223339873647853398518142
absolute error = 4e-31
relative error = 1.4932674419049462917426502120947e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.134
y[1] (analytic) = 2.6797802844040436285358549384082
y[1] (numeric) = 2.679780284404043628535854938408
absolute error = 2e-31
relative error = 7.4632984339788141451559526941395e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.135
y[1] (analytic) = 2.6808708244358893051461493515406
y[1] (numeric) = 2.6808708244358893051461493515404
absolute error = 2e-31
relative error = 7.4602624705755503330036344537268e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.136
y[1] (analytic) = 2.6819612424503518747145083771903
y[1] (numeric) = 2.68196124245035187471450837719
absolute error = 3e-31
relative error = 1.1185843973118249184766634905496e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.137
y[1] (analytic) = 2.6830515384682408947192646689757
y[1] (numeric) = 2.6830515384682408947192646689754
absolute error = 3e-31
relative error = 1.1181298446889714129339708498195e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=3.93
x[1] = 0.138
y[1] (analytic) = 2.6841417125103480202508585967206
y[1] (numeric) = 2.6841417125103480202508585967204
absolute error = 2e-31
relative error = 7.4511714142301997131654527737107e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.139
y[1] (analytic) = 2.6852317645974470242101795328347
y[1] (numeric) = 2.6852317645974470242101795328344
absolute error = 3e-31
relative error = 1.1172219990663416870245492085888e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 2.6863216947502938174732589827746
y[1] (numeric) = 2.6863216947502938174732589827743
absolute error = 3e-31
relative error = 1.1167687049033284340380323310392e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.141
y[1] (analytic) = 2.687411502989626469022386283066
y[1] (numeric) = 2.6874115029896264690223862830657
absolute error = 3e-31
relative error = 1.1163158290654902122868569866380e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.142
y[1] (analytic) = 2.688501189336165226043717408135
y[1] (numeric) = 2.6885011893361652260437174081347
absolute error = 3e-31
relative error = 1.1158633709739027151542961431238e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.4MB, time=4.09
x[1] = 0.143
y[1] (analytic) = 2.6895907538106125339914472455231
y[1] (numeric) = 2.6895907538106125339914472455229
absolute error = 2e-31
relative error = 7.4360755336714321194347134991683e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.144
y[1] (analytic) = 2.6906801964336530566186155179376
y[1] (numeric) = 2.6906801964336530566186155179375
absolute error = 1e-31
relative error = 3.7165323523971536249271152024857e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.145
y[1] (analytic) = 2.691769517225953695974616350011
y[1] (numeric) = 2.6917695172259536959746163500109
absolute error = 1e-31
relative error = 3.7150283246782809968898817039836e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.146
y[1] (analytic) = 2.6928587162081636123694812976206
y[1] (numeric) = 2.6928587162081636123694812976203
absolute error = 3e-31
relative error = 1.1140577045290829598195577393755e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.147
y[1] (analytic) = 2.6939477934009142443050054781357
y[1] (numeric) = 2.6939477934009142443050054781355
absolute error = 2e-31
relative error = 7.4240488434823922618725398632143e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.148
y[1] (analytic) = 2.6950367488248193283727862610285
y[1] (numeric) = 2.6950367488248193283727862610284
absolute error = 1e-31
relative error = 3.7105245427026316892274433118532e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.4MB, time=4.24
x[1] = 0.149
y[1] (analytic) = 2.6961255825004749191192437998819
y[1] (numeric) = 2.6961255825004749191192437998817
absolute error = 2e-31
relative error = 7.4180520854860725039083213111188e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 2.6972142944484594088776925089822
y[1] (numeric) = 2.697214294448459408877692508982
absolute error = 2e-31
relative error = 7.4150578399220983604629511441332e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.151
y[1] (analytic) = 2.6983028846893335475675324103651
y[1] (numeric) = 2.6983028846893335475675324103648
absolute error = 3e-31
relative error = 1.1118099517376464034301499896088e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.152
y[1] (analytic) = 2.6993913532436404624606291004024
y[1] (numeric) = 2.6993913532436404624606291004022
absolute error = 2e-31
relative error = 7.4090775966840140159318426952714e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.153
y[1] (analytic) = 2.7004797001319056779149509087771
y[1] (numeric) = 2.7004797001319056779149509087768
absolute error = 3e-31
relative error = 1.1109137387159267185713867949807e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.4MB, time=4.40
x[1] = 0.154
y[1] (analytic) = 2.701567925374637135075531646976
y[1] (numeric) = 2.7015679253746371350755316469757
absolute error = 3e-31
relative error = 1.1104662488114112866317142018873e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.155
y[1] (analytic) = 2.7026560289923252115428271682568
y[1] (numeric) = 2.7026560289923252115428271682565
absolute error = 3e-31
relative error = 1.1100191692238905931107669239106e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.156
y[1] (analytic) = 2.7037440110054427410085337863847
y[1] (numeric) = 2.7037440110054427410085337863845
absolute error = 2e-31
relative error = 7.3971499959282717865152529279768e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.157
y[1] (analytic) = 2.7048318714344450328589364263175
y[1] (numeric) = 2.7048318714344450328589364263173
absolute error = 2e-31
relative error = 7.3941749249625125523226790792987e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.158
y[1] (analytic) = 2.7059196102997698917458542064128
y[1] (numeric) = 2.7059196102997698917458542064125
absolute error = 3e-31
relative error = 1.1086803867272505558618647669772e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.159
y[1] (analytic) = 2.707007227621837637125250978658
y[1] (numeric) = 2.7070072276218376371252509786578
absolute error = 2e-31
relative error = 7.3882329518456504211960800005590e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.4MB, time=4.55
x[1] = 0.16
y[1] (analytic) = 2.7080947234210511227635781808703
y[1] (numeric) = 2.7080947234210511227635781808701
absolute error = 2e-31
relative error = 7.3852660422212363806651902847533e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.161
y[1] (analytic) = 2.7091820977177957562119171827749
y[1] (numeric) = 2.7091820977177957562119171827748
absolute error = 1e-31
relative error = 3.6911509227910373025334854206550e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.162
y[1] (analytic) = 2.7102693505324395182479881363604
y[1] (numeric) = 2.7102693505324395182479881363602
absolute error = 2e-31
relative error = 7.3793403582086583293603072154756e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.163
y[1] (analytic) = 2.7113564818853329822860921699031
y[1] (numeric) = 2.711356481885332982286092169903
absolute error = 1e-31
relative error = 3.6881907881941559606554646189915e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.164
y[1] (analytic) = 2.7124434917968093337550535945746
y[1] (numeric) = 2.7124434917968093337550535945745
absolute error = 1e-31
relative error = 3.6867127482075875885424849484307e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.4MB, time=4.71
x[1] = 0.165
y[1] (analytic) = 2.7135303802871843894442286225649
y[1] (numeric) = 2.7135303802871843894442286225648
absolute error = 1e-31
relative error = 3.6852360572950938301003477794659e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.166
y[1] (analytic) = 2.7146171473767566168176469262003
y[1] (numeric) = 2.7146171473767566168176469262
absolute error = 3e-31
relative error = 1.1051282140831609625548055398997e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.167
y[1] (analytic) = 2.7157037930858071532963521985763
y[1] (numeric) = 2.7157037930858071532963521985763
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.168
y[1] (analytic) = 2.7167903174345998255090077077872
y[1] (numeric) = 2.7167903174345998255090077077871
absolute error = 1e-31
relative error = 3.6808140605575924730265328684348e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.169
y[1] (analytic) = 2.7178767204433811685108326688821
y[1] (numeric) = 2.7178767204433811685108326688819
absolute error = 2e-31
relative error = 7.3586854950276396004123873619982e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 2.7189630021323804449709350902595
y[1] (numeric) = 2.7189630021323804449709350902594
absolute error = 1e-31
relative error = 3.6778727743471963454048613065741e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.4MB, time=4.86
x[1] = 0.171
y[1] (analytic) = 2.7200491625218096643281065842627
y[1] (numeric) = 2.7200491625218096643281065842625
absolute error = 2e-31
relative error = 7.3528082784568559133820187799822e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.172
y[1] (analytic) = 2.7211352016318636019151444653119
y[1] (numeric) = 2.7211352016318636019151444653117
absolute error = 2e-31
relative error = 7.3498736806631323066386927876824e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.173
y[1] (analytic) = 2.7222211194827198180517662929772
y[1] (numeric) = 2.722221119482719818051766292977
absolute error = 2e-31
relative error = 7.3469417516680009322923401559051e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.174
y[1] (analytic) = 2.7233069160945386771061818519524
y[1] (numeric) = 2.7233069160945386771061818519522
absolute error = 2e-31
relative error = 7.3440124878329015982086236655063e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.175
y[1] (analytic) = 2.7243925914874633665253873959525
y[1] (numeric) = 2.7243925914874633665253873959526
absolute error = 1e-31
relative error = 3.6705429427629598116700961442493e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.4MB, time=5.02
x[1] = 0.176
y[1] (analytic) = 2.7254781456816199158342468181083
y[1] (numeric) = 2.7254781456816199158342468181081
absolute error = 2e-31
relative error = 7.3381619411217706445099765929311e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.177
y[1] (analytic) = 2.7265635786971172156034242464672
y[1] (numeric) = 2.7265635786971172156034242464672
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.178
y[1] (analytic) = 2.7276488905540470363862323997609
y[1] (numeric) = 2.7276488905540470363862323997608
absolute error = 1e-31
relative error = 3.6661610057769474720899702060956e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.179
y[1] (analytic) = 2.7287340812724840476244608755951
y[1] (numeric) = 2.7287340812724840476244608755948
absolute error = 3e-31
relative error = 1.0994109028758922394907830701144e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 2.7298191508724858365232483807511
y[1] (numeric) = 2.729819150872485836523248380751
absolute error = 1e-31
relative error = 3.6632463351295156153123919168602e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.181
y[1] (analytic) = 2.7309040993740929268950627512678
y[1] (numeric) = 2.7309040993740929268950627512676
absolute error = 2e-31
relative error = 7.3235819612207846295268359500818e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.4MB, time=5.17
x[1] = 0.182
y[1] (analytic) = 2.731988926797328797972852448448
y[1] (numeric) = 2.7319889267973287979728524484478
absolute error = 2e-31
relative error = 7.3206738884720559398612027729224e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.183
y[1] (analytic) = 2.733073633162199903192433055904
y[1] (numeric) = 2.7330736331621999031924330559039
absolute error = 1e-31
relative error = 3.6588842242167755503862484052912e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.184
y[1] (analytic) = 2.7341582184886956889441721421835
y[1] (numeric) = 2.7341582184886956889441721421833
absolute error = 2e-31
relative error = 7.3148656375324863141230295179632e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.185
y[1] (analytic) = 2.735242682796788613294035693438
y[1] (numeric) = 2.7352426827967886132940356934379
absolute error = 1e-31
relative error = 3.6559827261012866109709264648213e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.186
y[1] (analytic) = 2.7363270261064341646740591609954
y[1] (numeric) = 2.7363270261064341646740591609954
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.4MB, time=5.32
x[1] = 0.187
y[1] (analytic) = 2.7374112484375708805423060095573
y[1] (numeric) = 2.7374112484375708805423060095572
absolute error = 1e-31
relative error = 3.6530864720117186191033895270683e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.188
y[1] (analytic) = 2.7384953498101203660123764930915
y[1] (numeric) = 2.7384953498101203660123764930915
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.189
y[1] (analytic) = 2.7395793302439873124525292273052
y[1] (numeric) = 2.739579330243987312452529227305
absolute error = 2e-31
relative error = 7.3003908954951843813025180047979e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 2.7406631897590595160544779698599
y[1] (numeric) = 2.74066318975905951605447796986
absolute error = 1e-31
relative error = 3.6487518923765061575283662302936e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.191
y[1] (analytic) = 2.741746928375207896371925862258
y[1] (numeric) = 2.7417469283752078963719258622579
absolute error = 1e-31
relative error = 3.6473096391599205332906488540471e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.192
y[1] (analytic) = 2.7428305461122865148288992305313
y[1] (numeric) = 2.7428305461122865148288992305313
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=5.48
x[1] = 0.193
y[1] (analytic) = 2.7439140429901325931979428855708
y[1] (numeric) = 2.7439140429901325931979428855707
absolute error = 1e-31
relative error = 3.6444290321509758255286063875565e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.194
y[1] (analytic) = 2.7449974190285665320482387080641
y[1] (numeric) = 2.7449974190285665320482387080641
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.195
y[1] (analytic) = 2.7460806742473919291637091476374
y[1] (numeric) = 2.7460806742473919291637091476372
absolute error = 2e-31
relative error = 7.2831072253481137361571123202505e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.196
y[1] (analytic) = 2.7471638086663955979311671108572
y[1] (numeric) = 2.7471638086663955979311671108572
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.197
y[1] (analytic) = 2.7482468223053475856985735582934
y[1] (numeric) = 2.7482468223053475856985735582933
absolute error = 1e-31
relative error = 3.6386833667332579995052723629302e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=5.63
x[1] = 0.198
y[1] (analytic) = 2.7493297151840011921034639768167
y[1] (numeric) = 2.7493297151840011921034639768165
absolute error = 2e-31
relative error = 7.2745003589580317986686604209560e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.199
y[1] (analytic) = 2.7504124873220929873716047397683
y[1] (numeric) = 2.7504124873220929873716047397682
absolute error = 1e-31
relative error = 3.6358182803832392681145763186286e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 2.7514951387393428305859402145249
y[1] (numeric) = 2.7514951387393428305859402145248
absolute error = 1e-31
relative error = 3.6343876677106240026756659088492e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.201
y[1] (analytic) = 2.7525776694554538879258913243396
y[1] (numeric) = 2.7525776694554538879258913243395
absolute error = 1e-31
relative error = 3.6329583397289978521211481910030e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.202
y[1] (analytic) = 2.7536600794901126508770661191469
y[1] (numeric) = 2.7536600794901126508770661191469
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.203
y[1] (analytic) = 2.7547423688629889544114427582683
y[1] (numeric) = 2.7547423688629889544114427582682
absolute error = 1e-31
relative error = 3.6301035309256407201855599636037e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.4MB, time=5.79
x[1] = 0.204
y[1] (analytic) = 2.7558245375937359951380851566583
y[1] (numeric) = 2.7558245375937359951380851566582
absolute error = 1e-31
relative error = 3.6286780466551609156143728156912e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.205
y[1] (analytic) = 2.7569065857019903494244513954846
y[1] (numeric) = 2.7569065857019903494244513954845
absolute error = 1e-31
relative error = 3.6272538401781585244688845055627e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.206
y[1] (analytic) = 2.7579885132073719914883548474212
y[1] (numeric) = 2.7579885132073719914883548474212
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.207
y[1] (analytic) = 2.7590703201294843114606378170801
y[1] (numeric) = 2.7590703201294843114606378170799
absolute error = 2e-31
relative error = 7.2488185074824014368200347179377e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.208
y[1] (analytic) = 2.7601520064879141334186173474786
y[1] (numeric) = 2.7601520064879141334186173474784
absolute error = 2e-31
relative error = 7.2459777407145398534506198877812e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.209
y[1] (analytic) = 2.7612335723022317333903626943693
y[1] (numeric) = 2.7612335723022317333903626943692
absolute error = 1e-31
relative error = 3.6215697579188518914871679645498e-30 %
Correct digits = 31
h = 0.001
memory used=148.7MB, alloc=4.4MB, time=5.94
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 2.7623150175919908573298638216103
y[1] (numeric) = 2.7623150175919908573298638216102
absolute error = 1e-31
relative error = 3.6201519147216449297316278377958e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.211
y[1] (analytic) = 2.7633963423767287390631501225559
y[1] (numeric) = 2.7633963423767287390631501225557
absolute error = 2e-31
relative error = 7.2374706781288186265616791204890e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.212
y[1] (analytic) = 2.7644775466759661182054184246812
y[1] (numeric) = 2.7644775466759661182054184246812
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.213
y[1] (analytic) = 2.7655586305092072580492291873235
y[1] (numeric) = 2.7655586305092072580492291873233
absolute error = 2e-31
relative error = 7.2318119671603233584220521371644e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.214
y[1] (analytic) = 2.7666395938959399634238296555175
y[1] (numeric) = 2.7666395938959399634238296555174
absolute error = 1e-31
relative error = 3.6144932003659180967517073865406e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=6.10
x[1] = 0.215
y[1] (analytic) = 2.7677204368556355985256625864496
y[1] (numeric) = 2.7677204368556355985256625864495
absolute error = 1e-31
relative error = 3.6130816779171690503763140206284e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.216
y[1] (analytic) = 2.7688011594077491047201190190026
y[1] (numeric) = 2.7688011594077491047201190190024
absolute error = 2e-31
relative error = 7.2233428290957633293701286045458e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.217
y[1] (analytic) = 2.7698817615717190183145934112687
y[1] (numeric) = 2.7698817615717190183145934112685
absolute error = 2e-31
relative error = 7.2205248171500879599541839863914e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.218
y[1] (analytic) = 2.7709622433669674883028993257231
y[1] (numeric) = 2.770962243366967488302899325723
absolute error = 1e-31
relative error = 3.6088546583186581768182483541278e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.219
y[1] (analytic) = 2.7720426048129002940811036969951
y[1] (numeric) = 2.7720426048129002940811036969948
absolute error = 3e-31
relative error = 1.0822344486305201456577429505562e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 2.7731228459289068631348375728457
y[1] (numeric) = 2.7731228459289068631348375728455
absolute error = 2e-31
relative error = 7.2120858365005622276921063314776e-30 %
Correct digits = 31
h = 0.001
NO POLE
memory used=156.4MB, alloc=4.4MB, time=6.25
TOP MAIN SOLVE Loop
x[1] = 0.221
y[1] (analytic) = 2.7742029667343602886981410750586
y[1] (numeric) = 2.7742029667343602886981410750584
absolute error = 2e-31
relative error = 7.2092778501866083855350648570858e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.222
y[1] (analytic) = 2.7752829672486173473839001834558
y[1] (numeric) = 2.7752829672486173473839001834556
absolute error = 2e-31
relative error = 7.2064723619255888141595293536057e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.223
y[1] (analytic) = 2.7763628474910185167859328031975
y[1] (numeric) = 2.7763628474910185167859328031974
absolute error = 1e-31
relative error = 3.6018346841937236439539017969827e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.224
y[1] (analytic) = 2.7774426074808879930527814328706
y[1] (numeric) = 2.7774426074808879930527814328705
absolute error = 1e-31
relative error = 3.6004344331240376594888366388249e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.225
y[1] (analytic) = 2.7785222472375337084332696086453
y[1] (numeric) = 2.7785222472375337084332696086452
absolute error = 1e-31
relative error = 3.5990354260946494298330609304663e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.4MB, time=6.41
x[1] = 0.226
y[1] (analytic) = 2.7796017667802473487938791579681
y[1] (numeric) = 2.779601766780247348793879157968
absolute error = 1e-31
relative error = 3.5976376614494325201594611746605e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.227
y[1] (analytic) = 2.7806811661283043711080051548594
y[1] (numeric) = 2.7806811661283043711080051548594
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.228
y[1] (analytic) = 2.7817604453009640209171453279006
y[1] (numeric) = 2.7817604453009640209171453279004
absolute error = 2e-31
relative error = 7.1896917054035404098885670219353e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.229
y[1] (analytic) = 2.7828396043174693497640805314207
y[1] (numeric) = 2.7828396043174693497640805314206
absolute error = 1e-31
relative error = 3.5934518053018154444672303640599e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 2.7839186431970472325981027502363
y[1] (numeric) = 2.7839186431970472325981027502363
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.231
y[1] (analytic) = 2.7849975619589083851523469685351
y[1] (numeric) = 2.784997561958908385152346968535
absolute error = 1e-31
relative error = 3.5906674162279020057948813405819e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.4MB, time=6.56
x[1] = 0.232
y[1] (analytic) = 2.7860763606222473812932830941565
y[1] (numeric) = 2.7860763606222473812932830941564
absolute error = 1e-31
relative error = 3.5892770712740198339946851060846e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.233
y[1] (analytic) = 2.7871550392062426703424239905805
y[1] (numeric) = 2.7871550392062426703424239905803
absolute error = 2e-31
relative error = 7.1757759143875342966300862776764e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.234
y[1] (analytic) = 2.7882335977300565943703055303978
y[1] (numeric) = 2.7882335977300565943703055303976
absolute error = 2e-31
relative error = 7.1730001447089312663985121957997e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.235
y[1] (analytic) = 2.7893120362128354054627944459098
y[1] (numeric) = 2.7893120362128354054627944459096
absolute error = 2e-31
relative error = 7.1702268302526773542101347065022e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.236
y[1] (analytic) = 2.7903903546737092829597796147723
y[1] (numeric) = 2.7903903546737092829597796147719
absolute error = 4e-31
relative error = 1.4334911935530019667858443258095e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.4MB, time=6.71
x[1] = 0.237
y[1] (analytic) = 2.791468553131792350666302281271
y[1] (numeric) = 2.7914685531317923506663022812706
absolute error = 4e-31
relative error = 1.4329375107995887199571122272997e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.238
y[1] (analytic) = 2.7925466316061826940361805768912
y[1] (numeric) = 2.7925466316061826940361805768909
absolute error = 3e-31
relative error = 1.0742882378563887486270710424720e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.239
y[1] (analytic) = 2.7936245901159623773281835673074
y[1] (numeric) = 2.7936245901159623773281835673071
absolute error = 3e-31
relative error = 1.0738737089493728474662362731092e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 2.7947024286801974607348099167907
y[1] (numeric) = 2.7947024286801974607348099167905
absolute error = 2e-31
relative error = 7.1563969726268964157528202019885e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.241
y[1] (analytic) = 2.795780147317938017483726125292
y[1] (numeric) = 2.7957801473179380174837261252918
absolute error = 2e-31
relative error = 7.1536383213774879181533980024791e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.242
y[1] (analytic) = 2.7968577460482181509119191581127
y[1] (numeric) = 2.7968577460482181509119191581124
absolute error = 3e-31
relative error = 1.0726323154042456806249154200304e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.4MB, time=6.87
x[1] = 0.243
y[1] (analytic) = 2.7979352248900560115126181531282
y[1] (numeric) = 2.7979352248900560115126181531278
absolute error = 4e-31
relative error = 1.4296256626731516800565683689276e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.244
y[1] (analytic) = 2.7990125838624538139550397559652
y[1] (numeric) = 2.799012583862453813955039755965
absolute error = 2e-31
relative error = 7.1453769501819500742019876285593e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.245
y[1] (analytic) = 2.8000898229843978540770114993696
y[1] (numeric) = 2.8000898229843978540770114993693
absolute error = 3e-31
relative error = 1.0713942014911983945568982631862e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.246
y[1] (analytic) = 2.8011669422748585258505275092128
y[1] (numeric) = 2.8011669422748585258505275092125
absolute error = 3e-31
relative error = 1.0709822234170973608682035905293e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.247
y[1] (analytic) = 2.8022439417527903383202906862051
y[1] (numeric) = 2.8022439417527903383202906862046
absolute error = 5e-31
relative error = 1.7842843463772549497792160675984e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.4MB, time=7.02
x[1] = 0.248
y[1] (analytic) = 2.8033208214371319325152953793621
y[1] (numeric) = 2.8033208214371319325152953793617
absolute error = 4e-31
relative error = 1.4268791389882326866605586750236e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.249
y[1] (analytic) = 2.8043975813468060983335044346645
y[1] (numeric) = 2.804397581346806098333504434664
absolute error = 5e-31
relative error = 1.7829141036410252544902900052033e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 2.8054742215007197913996743700984
y[1] (numeric) = 2.8054742215007197913996743700981
absolute error = 3e-31
relative error = 1.0693379311805700367415729049663e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.251
y[1] (analytic) = 2.8065507419177641498963822964238
y[1] (numeric) = 2.8065507419177641498963822964236
absolute error = 2e-31
relative error = 7.1261850716918297169224270120872e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.252
y[1] (analytic) = 2.8076271426168145113683080715296
y[1] (numeric) = 2.8076271426168145113683080715294
absolute error = 2e-31
relative error = 7.1234530028653465755612446686600e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.253
y[1] (analytic) = 2.808703423616730429499825045152
y[1] (numeric) = 2.8087034236167304294998250451517
absolute error = 3e-31
relative error = 1.0681084997350626243766218610184e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.4MB, time=7.17
x[1] = 0.254
y[1] (analytic) = 2.8097795849363556908659526200088
y[1] (numeric) = 2.8097795849363556908659526200084
absolute error = 4e-31
relative error = 1.4235992109290679426241740316456e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.255
y[1] (analytic) = 2.8108556265945183316567237250694
y[1] (numeric) = 2.8108556265945183316567237250689
absolute error = 5e-31
relative error = 1.7788177922384905206928176875847e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.256
y[1] (analytic) = 2.8119315486100306543750201667143
y[1] (numeric) = 2.8119315486100306543750201667139
absolute error = 4e-31
relative error = 1.4225097342704679011439969859751e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.257
y[1] (analytic) = 2.813007351001689244507928693955
y[1] (numeric) = 2.8130073510016892445079286939545
absolute error = 5e-31
relative error = 1.7774571396763468465919138956529e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.258
y[1] (analytic) = 2.8140830337882749871716704846656
y[1] (numeric) = 2.8140830337882749871716704846651
absolute error = 5e-31
relative error = 1.7767777069708840307096284216910e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.4MB, time=7.33
x[1] = 0.259
y[1] (analytic) = 2.8151585969885530837301566309443
y[1] (numeric) = 2.8151585969885530837301566309439
absolute error = 4e-31
relative error = 1.4208790951525437925555644913587e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 2.8162340406212730683872220732457
y[1] (numeric) = 2.8162340406212730683872220732453
absolute error = 4e-31
relative error = 1.4203364998448719782532737292767e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.261
y[1] (analytic) = 2.8173093647051688247525903048278
y[1] (numeric) = 2.8173093647051688247525903048272
absolute error = 6e-31
relative error = 2.1296915685466084652258613273919e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.262
y[1] (analytic) = 2.8183845692589586023816210403267
y[1] (numeric) = 2.8183845692589586023816210403262
absolute error = 5e-31
relative error = 1.7740659151120232982263815726869e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.263
y[1] (analytic) = 2.8194596543013450332888929149087
y[1] (numeric) = 2.8194596543013450332888929149084
absolute error = 3e-31
relative error = 1.0640336688000567993426388733348e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.264
y[1] (analytic) = 2.8205346198510151484356731534474
y[1] (numeric) = 2.8205346198510151484356731534469
absolute error = 5e-31
relative error = 1.7727135716788711029338985000175e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.4MB, time=7.48
x[1] = 0.265
y[1] (analytic) = 2.821609465926640394191326022544
y[1] (numeric) = 2.8216094659266403941913260225437
absolute error = 3e-31
relative error = 1.0632229712253161324118609639429e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.266
y[1] (analytic) = 2.8226841925468766487687117519457
y[1] (numeric) = 2.8226841925468766487687117519452
absolute error = 5e-31
relative error = 1.7713635883185909793302902380911e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.267
y[1] (analytic) = 2.8237587997303642386336274859944
y[1] (numeric) = 2.8237587997303642386336274859941
absolute error = 3e-31
relative error = 1.0624136878427664301949373113878e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.268
y[1] (analytic) = 2.8248332874957279548883417002154
y[1] (numeric) = 2.8248332874957279548883417002151
absolute error = 3e-31
relative error = 1.0620095753188893108492071916726e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.269
y[1] (analytic) = 2.8259076558615770696292733929492
y[1] (numeric) = 2.8259076558615770696292733929488
absolute error = 4e-31
relative error = 1.4154744199454244718156671870229e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.4MB, time=7.63
x[1] = 0.27
y[1] (analytic) = 2.8269819048465053522788672371205
y[1] (numeric) = 2.8269819048465053522788672371201
absolute error = 4e-31
relative error = 1.4149365417382058503207376458432e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.271
y[1] (analytic) = 2.8280560344690910858917157527628
y[1] (numeric) = 2.8280560344690910858917157527625
absolute error = 3e-31
relative error = 1.0607993488938021804111754369455e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.272
y[1] (analytic) = 2.8291300447478970834349794368055
y[1] (numeric) = 2.8291300447478970834349794368051
absolute error = 4e-31
relative error = 1.4138621896952915720928584488225e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.273
y[1] (analytic) = 2.830203935701470704043155662878
y[1] (numeric) = 2.8302039357014707040431556628775
absolute error = 5e-31
relative error = 1.7666571432990187577727211270303e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.274
y[1] (analytic) = 2.8312777073483438692472470404825
y[1] (numeric) = 2.831277707348343869247247040482
absolute error = 5e-31
relative error = 1.7659871326019765849795448367421e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.275
y[1] (analytic) = 2.8323513597070330791783797998391
y[1] (numeric) = 2.8323513597070330791783797998387
absolute error = 4e-31
relative error = 1.4122541634148609845048197174525e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.4MB, time=7.79
x[1] = 0.276
y[1] (analytic) = 2.8334248927960394287459226460088
y[1] (numeric) = 2.8334248927960394287459226460085
absolute error = 3e-31
relative error = 1.0587893145244387719961058141446e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.277
y[1] (analytic) = 2.8344983066338486237901564035574
y[1] (numeric) = 2.834498306633848623790156403557
absolute error = 4e-31
relative error = 1.4111844733293422062345588746598e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.278
y[1] (analytic) = 2.8355716012389309972095446510249
y[1] (numeric) = 2.8355716012389309972095446510245
absolute error = 4e-31
relative error = 1.4106503247007769391203165069552e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.279
y[1] (analytic) = 2.8366447766297415250626554228209
y[1] (numeric) = 2.8366447766297415250626554228203
absolute error = 6e-31
relative error = 2.1151749593153804519041379528892e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 2.83771783282471984264478393486
y[1] (numeric) = 2.8377178328247198426447839348596
absolute error = 4e-31
relative error = 1.4095834172555210506660162761298e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.4MB, time=7.95
x[1] = 0.281
y[1] (analytic) = 2.8387907698422902605393261693082
y[1] (numeric) = 2.8387907698422902605393261693077
absolute error = 5e-31
relative error = 1.7613133215442208391601023489260e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.282
y[1] (analytic) = 2.839863587700861780643953033187
y[1] (numeric) = 2.8398635877008617806439530331867
absolute error = 3e-31
relative error = 1.0563887691622483154831453475310e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.283
y[1] (analytic) = 2.8409362864188281121716346853363
y[1] (numeric) = 2.840936286418828112171634685336
absolute error = 3e-31
relative error = 1.0559898911994542870211354866134e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.284
y[1] (analytic) = 2.8420088660145676876265645062951
y[1] (numeric) = 2.8420088660145676876265645062947
absolute error = 4e-31
relative error = 1.4074551447861305275401468542105e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.285
y[1] (analytic) = 2.8430813265064436787550320660951
y[1] (numeric) = 2.8430813265064436787550320660946
absolute error = 5e-31
relative error = 1.7586552848081772205695139058787e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.286
y[1] (analytic) = 2.8441536679128040124712943257123
y[1] (numeric) = 2.844153667912804012471294325712
absolute error = 3e-31
relative error = 1.0547953276383848048234549952162e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.4MB, time=8.10
x[1] = 0.287
y[1] (analytic) = 2.8452258902519813867584941890265
y[1] (numeric) = 2.8452258902519813867584941890261
absolute error = 4e-31
relative error = 1.4058637712050864605826484737880e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.288
y[1] (analytic) = 2.8462979935422932865446754035703
y[1] (numeric) = 2.8462979935422932865446754035701
absolute error = 2e-31
relative error = 7.0266711515716841556110152481359e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.289
y[1] (analytic) = 2.8473699778020419995539426901359
y[1] (numeric) = 2.8473699778020419995539426901354
absolute error = 5e-31
relative error = 1.7560064336492121019250313368200e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 2.8484418430495146321328158634018
y[1] (numeric) = 2.8484418430495146321328158634013
absolute error = 5e-31
relative error = 1.7553456505353985933030690237388e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.291
y[1] (analytic) = 2.8495135893029831250518265882078
y[1] (numeric) = 2.8495135893029831250518265882074
absolute error = 4e-31
relative error = 1.4037483502503444064308354599384e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=206.0MB, alloc=4.4MB, time=8.26
x[1] = 0.292
y[1] (analytic) = 2.8505852165807042692824062988684
y[1] (numeric) = 2.850585216580704269282406298868
absolute error = 4e-31
relative error = 1.4032206357956301791359269426519e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.293
y[1] (analytic) = 2.8516567249009197217491136920384
y[1] (numeric) = 2.8516567249009197217491136920379
absolute error = 5e-31
relative error = 1.7533667205942272250711803545316e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.294
y[1] (analytic) = 2.8527281142818560210572500870868
y[1] (numeric) = 2.8527281142818560210572500870863
absolute error = 5e-31
relative error = 1.7527082146272803327344352976215e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.295
y[1] (analytic) = 2.8537993847417246031959108317084
y[1] (numeric) = 2.8537993847417246031959108317081
absolute error = 3e-31
relative error = 1.0512301656661499659584001472643e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.296
y[1] (analytic) = 2.8548705362987218172165208146087
y[1] (numeric) = 2.8548705362987218172165208146082
absolute error = 5e-31
relative error = 1.7513929043109577733104288630359e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.297
y[1] (analytic) = 2.8559415689710289408869020315276
y[1] (numeric) = 2.8559415689710289408869020315273
absolute error = 3e-31
relative error = 1.0504416590990949673034506627146e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.4MB, time=8.41
x[1] = 0.298
y[1] (analytic) = 2.8570124827768121963209210356377
y[1] (numeric) = 2.8570124827768121963209210356374
absolute error = 3e-31
relative error = 1.0500479147659215487769371220601e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.299
y[1] (analytic) = 2.8580832777342227655837639884228
y[1] (numeric) = 2.8580832777342227655837639884226
absolute error = 2e-31
relative error = 6.9976967276668096035663623186390e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 2.8591539538613968062728869125735
y[1] (numeric) = 2.8591539538613968062728869125733
absolute error = 2e-31
relative error = 6.9950762787674426546818741773224e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.301
y[1] (analytic) = 2.8602245111764554670746886341569
y[1] (numeric) = 2.8602245111764554670746886341565
absolute error = 4e-31
relative error = 1.3984916164342416925123887866177e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.302
y[1] (analytic) = 2.8612949496975049032969537873872
y[1] (numeric) = 2.8612949496975049032969537873868
absolute error = 4e-31
relative error = 1.3979684269959231551825641653571e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.4MB, time=8.57
x[1] = 0.303
y[1] (analytic) = 2.8623652694426362923771131417021
y[1] (numeric) = 2.8623652694426362923771131417018
absolute error = 3e-31
relative error = 1.0480842651448758431597225210694e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.304
y[1] (analytic) = 2.8634354704299258493663683975491
y[1] (numeric) = 2.8634354704299258493663683975488
absolute error = 3e-31
relative error = 1.0476925465862060764491793703585e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.305
y[1] (analytic) = 2.8645055526774348423897284843142
y[1] (numeric) = 2.8645055526774348423897284843138
absolute error = 4e-31
relative error = 1.3964015521845387348661332903139e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.306
y[1] (analytic) = 2.8655755162032096080820042811621
y[1] (numeric) = 2.8655755162032096080820042811618
absolute error = 3e-31
relative error = 1.0469101173696857498388191337673e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.307
y[1] (analytic) = 2.8666453610252815669998085692204
y[1] (numeric) = 2.8666453610252815669998085692201
absolute error = 3e-31
relative error = 1.0465194058490105464860912678522e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.308
y[1] (analytic) = 2.867715087161667239009607911511
y[1] (numeric) = 2.8677150871616672390096079115107
absolute error = 3e-31
relative error = 1.0461290291460796043195457330153e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.4MB, time=8.72
x[1] = 0.309
y[1] (analytic) = 2.8687846946303682586518730453296
y[1] (numeric) = 2.8687846946303682586518730453293
absolute error = 3e-31
relative error = 1.0457389868313342778406352629182e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 2.8698541834493713904813742603777
y[1] (numeric) = 2.8698541834493713904813742603773
absolute error = 4e-31
relative error = 1.3937990379679393586307326799675e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.311
y[1] (analytic) = 2.8709235536366485443836681248718
y[1] (numeric) = 2.8709235536366485443836681248716
absolute error = 2e-31
relative error = 6.9663993576790485822240607471003e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.312
y[1] (analytic) = 2.8719928052101567908678218110916
y[1] (numeric) = 2.8719928052101567908678218110913
absolute error = 3e-31
relative error = 1.0445708619316949646126987458671e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.313
y[1] (analytic) = 2.8730619381878383763354211613662
y[1] (numeric) = 2.8730619381878383763354211613659
absolute error = 3e-31
relative error = 1.0441821528888537730518405581163e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.4MB, time=8.87
x[1] = 0.314
y[1] (analytic) = 2.8741309525876207383259085253647
y[1] (numeric) = 2.8741309525876207383259085253644
absolute error = 3e-31
relative error = 1.0437937760974521980060521226853e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.315
y[1] (analytic) = 2.8751998484274165207382962897108
y[1] (numeric) = 2.8751998484274165207382962897105
absolute error = 3e-31
relative error = 1.0434057311323394145786756622018e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.316
y[1] (analytic) = 2.8762686257251235890293019114243
y[1] (numeric) = 2.8762686257251235890293019114239
absolute error = 4e-31
relative error = 1.3906906900921249577552102646798e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.317
y[1] (analytic) = 2.87733728449862504538795015747
y[1] (numeric) = 2.8773372844986250453879501574696
absolute error = 4e-31
relative error = 1.3901741799786946132697340766060e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.318
y[1] (analytic) = 2.8784058247657892438866881437847
y[1] (numeric) = 2.8784058247657892438866881437843
absolute error = 4e-31
relative error = 1.3896581106055373122460656678614e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.319
y[1] (analytic) = 2.8794742465444698056090586585462
y[1] (numeric) = 2.8794742465444698056090586585456
absolute error = 6e-31
relative error = 2.0837137221144921449578383865064e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.4MB, time=9.03
x[1] = 0.32
y[1] (analytic) = 2.880542549852505633753977146148
y[1] (numeric) = 2.8805425498525056337539771461474
absolute error = 6e-31
relative error = 2.0829409377435587797654239638689e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.321
y[1] (analytic) = 2.8816107347077209287166576203482
y[1] (numeric) = 2.8816107347077209287166576203479
absolute error = 3e-31
relative error = 1.0410844059769534358382080814413e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.322
y[1] (analytic) = 2.8826788011279252031462326673634
y[1] (numeric) = 2.8826788011279252031462326673631
absolute error = 3e-31
relative error = 1.0406986719526884989835667004132e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.323
y[1] (analytic) = 2.8837467491309132969801125922855
y[1] (numeric) = 2.8837467491309132969801125922849
absolute error = 6e-31
relative error = 2.0806265327592462318584088802422e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.324
y[1] (analytic) = 2.8848145787344653924551286551129
y[1] (numeric) = 2.8848145787344653924551286551125
absolute error = 4e-31
relative error = 1.3865709184521500453302872301209e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.4MB, time=9.19
x[1] = 0.325
y[1] (analytic) = 2.8858822899563470290955052358926
y[1] (numeric) = 2.8858822899563470290955052358924
absolute error = 2e-31
relative error = 6.9302895927548478527695771822579e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.326
y[1] (analytic) = 2.8869498828143091186777056619708
y[1] (numeric) = 2.8869498828143091186777056619704
absolute error = 4e-31
relative error = 1.3855453549130014939250701044236e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.327
y[1] (analytic) = 2.8880173573260879601721963241646
y[1] (numeric) = 2.8880173573260879601721963241642
absolute error = 4e-31
relative error = 1.3850332269829074092515674370014e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.328
y[1] (analytic) = 2.8890847135094052546621736027654
y[1] (numeric) = 2.889084713509405254662173602765
absolute error = 4e-31
relative error = 1.3845215342062963784345005090658e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.329
y[1] (analytic) = 2.8901519513819681202392980186773
y[1] (numeric) = 2.8901519513819681202392980186769
absolute error = 4e-31
relative error = 1.3840102760297229079749014067797e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 2.8912190709614691068764799196937
y[1] (numeric) = 2.8912190709614691068764799196935
absolute error = 2e-31
relative error = 6.9174972595034246533538341845921e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.4MB, time=9.34
x[1] = 0.331
y[1] (analytic) = 2.8922860722655862112777609068999
y[1] (numeric) = 2.8922860722655862112777609068996
absolute error = 3e-31
relative error = 1.0372417959507163443666816099947e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.332
y[1] (analytic) = 2.8933529553119828917053351014659
y[1] (numeric) = 2.8933529553119828917053351014655
absolute error = 4e-31
relative error = 1.3824791035799122445961451977803e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.333
y[1] (analytic) = 2.8944197201183080827837542476727
y[1] (numeric) = 2.8944197201183080827837542476724
absolute error = 3e-31
relative error = 1.0364771837159043304007983784818e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.334
y[1] (analytic) = 2.8954863667021962102813605438736
y[1] (numeric) = 2.8954863667021962102813605438733
absolute error = 3e-31
relative error = 1.0360953636320654538932391052356e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.335
y[1] (analytic) = 2.8965528950812672058689909892458
y[1] (numeric) = 2.8965528950812672058689909892452
absolute error = 6e-31
relative error = 2.0714277340451125633231767108155e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.4MB, time=9.50
x[1] = 0.336
y[1] (analytic) = 2.8976193052731265218559969306341
y[1] (numeric) = 2.8976193052731265218559969306337
absolute error = 4e-31
relative error = 1.3804435913029521465343161585952e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.337
y[1] (analytic) = 2.8986855972953651459036223905205
y[1] (numeric) = 2.8986855972953651459036223905201
absolute error = 4e-31
relative error = 1.3799357901154310886152049460591e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.338
y[1] (analytic) = 2.8997517711655596157157846541642
y[1] (numeric) = 2.8997517711655596157157846541638
absolute error = 4e-31
relative error = 1.3794284185891518371318368565017e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.339
y[1] (analytic) = 2.900817826901272033707300491275
y[1] (numeric) = 2.9008178269012720337073004912746
absolute error = 4e-31
relative error = 1.3789214761800131866814329910771e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 2.9018837645200500816496012851651
y[1] (numeric) = 2.9018837645200500816496012851645
absolute error = 6e-31
relative error = 2.0676224435172561858092062432888e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.341
y[1] (analytic) = 2.9029495840394270352939802402023
y[1] (numeric) = 2.9029495840394270352939802402018
absolute error = 5e-31
relative error = 1.7223860956767106647126302630991e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.4MB, time=9.65
x[1] = 0.342
y[1] (analytic) = 2.9040152854769217789724147365534
y[1] (numeric) = 2.9040152854769217789724147365528
absolute error = 6e-31
relative error = 2.0661048273424048490159260588188e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.343
y[1] (analytic) = 2.9050808688500388201760067996379
y[1] (numeric) = 2.9050808688500388201760067996376
absolute error = 3e-31
relative error = 1.0326734901488420269362495223264e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.344
y[1] (analytic) = 2.9061463341762683041110845504524
y[1] (numeric) = 2.9061463341762683041110845504521
absolute error = 3e-31
relative error = 1.0322948864343178429313319544066e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.345
y[1] (analytic) = 2.9072116814730860282330074019152
y[1] (numeric) = 2.907211681473086028233007401915
absolute error = 2e-31
relative error = 6.8794440141579188828564331207375e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.346
y[1] (analytic) = 2.9082769107579534567577176656842
y[1] (numeric) = 2.9082769107579534567577176656839
absolute error = 3e-31
relative error = 1.0315386368136938254782337383765e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.347
y[1] (analytic) = 2.9093420220483177351510811334512
y[1] (numeric) = 2.9093420220483177351510811334508
memory used=244.1MB, alloc=4.4MB, time=9.81
absolute error = 4e-31
relative error = 1.3748813201356800972606703773823e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.348
y[1] (analytic) = 2.910407015361611704596059096572
y[1] (numeric) = 2.9104070153616117045960590965717
absolute error = 3e-31
relative error = 1.0307836615859918008973470620436e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.349
y[1] (analytic) = 2.9114718907152539164377541680067
y[1] (numeric) = 2.9114718907152539164377541680063
absolute error = 4e-31
relative error = 1.3738755344868983582253418758033e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 2.9125366481266486466063721709416
y[1] (numeric) = 2.9125366481266486466063721709414
absolute error = 2e-31
relative error = 6.8668663835917922039796102246567e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.351
y[1] (analytic) = 2.9136012876131859100181422591483
y[1] (numeric) = 2.9136012876131859100181422591478
absolute error = 5e-31
relative error = 1.7160893020115275023468449412257e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.352
y[1] (analytic) = 2.914665809192241474954237335067
y[1] (numeric) = 2.9146658091922414749542373350667
absolute error = 3e-31
relative error = 1.0292775214704315252545931096956e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.4MB, time=9.96
x[1] = 0.353
y[1] (analytic) = 2.9157302128811768774177367328472
y[1] (numeric) = 2.9157302128811768774177367328467
absolute error = 5e-31
relative error = 1.7148362965513374139713775807644e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.354
y[1] (analytic) = 2.9167944986973394354686730350483
y[1] (numeric) = 2.9167944986973394354686730350481
absolute error = 2e-31
relative error = 6.8568423346012679695103613487592e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.355
y[1] (analytic) = 2.9178586666580622635372047934991
y[1] (numeric) = 2.9178586666580622635372047934986
absolute error = 5e-31
relative error = 1.7135853964190444155214559821994e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.356
y[1] (analytic) = 2.9189227167806642867149568268265
y[1] (numeric) = 2.918922716780664286714956826826
absolute error = 5e-31
relative error = 1.7129607341966887246176795460700e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.357
y[1] (analytic) = 2.9199866490824502550245696695023
y[1] (numeric) = 2.9199866490824502550245696695018
absolute error = 5e-31
relative error = 1.7123365963235325090505991343934e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.358
y[1] (analytic) = 2.9210504635807107576674996498126
y[1] (numeric) = 2.9210504635807107576674996498122
absolute error = 4e-31
relative error = 1.3693703857127756460074883057947e-29 %
Correct digits = 30
h = 0.001
NO POLE
memory used=251.7MB, alloc=4.4MB, time=10.12
TOP MAIN SOLVE Loop
x[1] = 0.359
y[1] (analytic) = 2.9221141602927222372501109770189
y[1] (numeric) = 2.9221141602927222372501109770186
absolute error = 3e-31
relative error = 1.0266539345949015090443117125979e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 2.9231777392357470039881011210899
y[1] (numeric) = 2.9231777392357470039881011210895
absolute error = 4e-31
relative error = 1.3683738577749924369870502567121e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.361
y[1] (analytic) = 2.924241200427033249889300671768
y[1] (numeric) = 2.9242412004270332498893006717678
absolute error = 2e-31
relative error = 6.8393811006695880152942252325269e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.362
y[1] (analytic) = 2.9253045438838150629148887673878
y[1] (numeric) = 2.9253045438838150629148887673875
absolute error = 3e-31
relative error = 1.0255342495099722623129193389823e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.363
y[1] (analytic) = 2.9263677696233124411190650877713
y[1] (numeric) = 2.9263677696233124411190650877709
absolute error = 4e-31
relative error = 1.3668821948906604849844888844846e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.4MB, time=10.27
x[1] = 0.364
y[1] (analytic) = 2.9274308776627313067672193097162
y[1] (numeric) = 2.9274308776627313067672193097159
absolute error = 3e-31
relative error = 1.0247893546833147007930501686205e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.365
y[1] (analytic) = 2.9284938680192635204326388280275
y[1] (numeric) = 2.9284938680192635204326388280271
absolute error = 4e-31
relative error = 1.3658898328871925619123215223426e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.366
y[1] (analytic) = 2.9295567407100868950717954497526
y[1] (numeric) = 2.9295567407100868950717954497523
absolute error = 3e-31
relative error = 1.0240457057243542463050528747743e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.367
y[1] (analytic) = 2.9306194957523652100782516742534
y[1] (numeric) = 2.9306194957523652100782516742531
absolute error = 3e-31
relative error = 1.0236743474709680911725757463446e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.368
y[1] (analytic) = 2.9316821331632482253152270769698
y[1] (numeric) = 2.9316821331632482253152270769696
absolute error = 2e-31
relative error = 6.8220219967777512856181773271609e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.369
y[1] (analytic) = 2.9327446529598716951268652202287
y[1] (numeric) = 2.9327446529598716951268652202284
absolute error = 3e-31
relative error = 1.0229325614735162385415713668517e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.4MB, time=10.43
x[1] = 0.37
y[1] (analytic) = 2.9338070551593573823282414201945
y[1] (numeric) = 2.933807055159357382328241420194
absolute error = 5e-31
relative error = 1.7042702215904283312548573126744e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.371
y[1] (analytic) = 2.9348693397788130721741516050729
y[1] (numeric) = 2.9348693397788130721741516050727
absolute error = 2e-31
relative error = 6.8146134238150797566798812466882e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.372
y[1] (analytic) = 2.935931506835332586306722405943
y[1] (numeric) = 2.9359315068353325863067224059425
absolute error = 5e-31
relative error = 1.7030370049025924701251062313688e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.373
y[1] (analytic) = 2.9369935563459957966818825281096
y[1] (numeric) = 2.9369935563459957966818825281093
absolute error = 3e-31
relative error = 1.0214527006768079061650032983203e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.374
y[1] (analytic) = 2.9380554883278686394747353576674
y[1] (numeric) = 2.938055488327868639474735357667
absolute error = 4e-31
relative error = 1.3614446751911123152433011556124e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.4MB, time=10.58
x[1] = 0.375
y[1] (analytic) = 2.9391173027980031289638726649772
y[1] (numeric) = 2.9391173027980031289638726649769
absolute error = 3e-31
relative error = 1.0207146197070927724730091780128e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.376
y[1] (analytic) = 2.9401789997734373713946691740699
y[1] (numeric) = 2.9401789997734373713946691740695
absolute error = 4e-31
relative error = 1.3604613869795783549063330734101e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.377
y[1] (analytic) = 2.9412405792711955788215976745182
y[1] (numeric) = 2.941240579271195578821597674518
absolute error = 2e-31
relative error = 6.7998517839556538566133637289320e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.378
y[1] (analytic) = 2.9423020413082880829296042601295
y[1] (numeric) = 2.9423020413082880829296042601292
absolute error = 3e-31
relative error = 1.0196098014009658395196218107558e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.379
y[1] (analytic) = 2.9433633859017113488345831868461
y[1] (numeric) = 2.9433633859017113488345831868458
absolute error = 3e-31
relative error = 1.0192421412760551120333106781418e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 2.9444246130684479888629907505572
y[1] (numeric) = 2.9444246130684479888629907505568
absolute error = 4e-31
relative error = 1.3584997157836940777480389876821e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.4MB, time=10.74
x[1] = 0.381
y[1] (analytic) = 2.9454857228254667763106374940632
y[1] (numeric) = 2.9454857228254667763106374940627
absolute error = 5e-31
relative error = 1.6975128961765035172176766581120e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.382
y[1] (analytic) = 2.9465467151897226591806979612449
y[1] (numeric) = 2.9465467151897226591806979612443
absolute error = 6e-31
relative error = 2.0362819870017472865975834574779e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.383
y[1] (analytic) = 2.947607590178156773900977125535
y[1] (numeric) = 2.9476075901781567739009771255345
absolute error = 5e-31
relative error = 1.6962909230729027541782863578633e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.384
y[1] (analytic) = 2.9486683478076964590204725290909
y[1] (numeric) = 2.9486683478076964590204725290906
absolute error = 3e-31
relative error = 1.0174084183561939335038016181986e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.385
y[1] (analytic) = 2.9497289880952552688852710786126
y[1] (numeric) = 2.9497289880952552688852710786122
absolute error = 4e-31
relative error = 1.3560567822140643541000804024815e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.4MB, time=10.89
x[1] = 0.386
y[1] (analytic) = 2.9507895110577329872938193535416
y[1] (numeric) = 2.9507895110577329872938193535413
absolute error = 3e-31
relative error = 1.0166770583797510985210507591208e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.387
y[1] (analytic) = 2.9518499167120156411316061924223
y[1] (numeric) = 2.9518499167120156411316061924218
absolute error = 5e-31
relative error = 1.6938530552289604045365095739098e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.388
y[1] (analytic) = 2.9529102050749755139852962334796
y[1] (numeric) = 2.9529102050749755139852962334791
absolute error = 5e-31
relative error = 1.6932448509293726041353207989802e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.389
y[1] (analytic) = 2.9539703761634711597363529960094
y[1] (numeric) = 2.9539703761634711597363529960088
absolute error = 6e-31
relative error = 2.0311645805306353452764802137066e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 2.9550304299943474161341899999376
y[1] (numeric) = 2.9550304299943474161341899999372
absolute error = 4e-31
relative error = 1.3536239625145421845861951078029e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.391
y[1] (analytic) = 2.9560903665844354183488883319307
y[1] (numeric) = 2.9560903665844354183488883319302
absolute error = 5e-31
relative error = 1.6914232584091011311007523936519e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.4MB, time=11.05
x[1] = 0.392
y[1] (analytic) = 2.9571501859505526125035189776857
y[1] (numeric) = 2.9571501859505526125035189776853
absolute error = 4e-31
relative error = 1.3526536524942278292873328101464e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.393
y[1] (analytic) = 2.9582098881095027691861081515411
y[1] (numeric) = 2.9582098881095027691861081515406
absolute error = 5e-31
relative error = 1.6902113741480797775025651370462e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.394
y[1] (analytic) = 2.9592694730780759969412837662728
y[1] (numeric) = 2.9592694730780759969412837662724
absolute error = 4e-31
relative error = 1.3516849467038941236141922151246e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.395
y[1] (analytic) = 2.960328940873048755741641097935
y[1] (numeric) = 2.9603289408730487557416410979348
absolute error = 2e-31
relative error = 6.7560059707762331957038232173885e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.396
y[1] (analytic) = 2.9613882915111838704388656128107
y[1] (numeric) = 2.9613882915111838704388656128104
absolute error = 3e-31
relative error = 1.0130383808835526727477102108826e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.4MB, time=11.20
x[1] = 0.397
y[1] (analytic) = 2.9624475250092305441946508360007
y[1] (numeric) = 2.9624475250092305441946508360003
absolute error = 4e-31
relative error = 1.3502348872787330122243479283436e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.398
y[1] (analytic) = 2.9635066413839243718914490538741
y[1] (numeric) = 2.9635066413839243718914490538738
absolute error = 3e-31
relative error = 1.0123142489733154904734211712755e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.399
y[1] (analytic) = 2.9645656406519873535230925555315
y[1] (numeric) = 2.9645656406519873535230925555313
absolute error = 2e-31
relative error = 6.7463508737156734191616397786302e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 2.9656245228301279075653230316005
y[1] (numeric) = 2.9656245228301279075653230316001
absolute error = 4e-31
relative error = 1.3487884151236907985093273569488e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.401
y[1] (analytic) = 2.9666832879350408843262666620853
y[1] (numeric) = 2.9666832879350408843262666620851
absolute error = 2e-31
relative error = 6.7415352630785858827317040422339e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.402
y[1] (analytic) = 2.9677419359834075792768923386359
y[1] (numeric) = 2.9677419359834075792768923386356
absolute error = 3e-31
relative error = 1.0108695650472395970211638530958e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.4MB, time=11.35
x[1] = 0.403
y[1] (analytic) = 2.9688004669918957463614903804589
y[1] (numeric) = 2.9688004669918957463614903804587
absolute error = 2e-31
relative error = 6.7367275848837287821140194130836e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.404
y[1] (analytic) = 2.9698588809771596112882090172157
y[1] (numeric) = 2.9698588809771596112882090172155
absolute error = 2e-31
relative error = 6.7343267143452580230083477456652e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.405
y[1] (analytic) = 2.9709171779558398847996858265725
y[1] (numeric) = 2.9709171779558398847996858265722
absolute error = 3e-31
relative error = 1.0097891729395737487654196559733e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.406
y[1] (analytic) = 2.9719753579445637759238112286489
y[1] (numeric) = 2.9719753579445637759238112286486
absolute error = 3e-31
relative error = 1.0094296347311635305356061989579e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.407
y[1] (analytic) = 2.9730334209599450052046610544038
y[1] (numeric) = 2.9730334209599450052046610544037
absolute error = 1e-31
relative error = 3.3635679738746965460659447234270e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.4MB, time=11.50
x[1] = 0.408
y[1] (analytic) = 2.9740913670185838179136351200306
y[1] (numeric) = 2.9740913670185838179136351200306
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.409
y[1] (analytic) = 2.9751491961370669972408386546906
y[1] (numeric) = 2.9751491961370669972408386546904
absolute error = 2e-31
relative error = 6.7223519499351478586576041876872e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 2.9762069083319678774667433444046
y[1] (numeric) = 2.9762069083319678774667433444044
absolute error = 2e-31
relative error = 6.7199628977439320492903986065195e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.411
y[1] (analytic) = 2.9772645036198463571141646706398
y[1] (numeric) = 2.9772645036198463571141646706396
absolute error = 2e-31
relative error = 6.7175758068130687371140412692539e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.412
y[1] (analytic) = 2.9783219820172489120805921380678
y[1] (numeric) = 2.9783219820172489120805921380676
absolute error = 2e-31
relative error = 6.7151906747348347195750196220986e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.413
y[1] (analytic) = 2.9793793435407086087509089021463
y[1] (numeric) = 2.979379343540708608750908902146
absolute error = 3e-31
relative error = 1.0069211248658204446213420645945e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.4MB, time=11.66
x[1] = 0.414
y[1] (analytic) = 2.9804365882067451170905372235699
y[1] (numeric) = 2.9804365882067451170905372235698
absolute error = 1e-31
relative error = 3.3552131387625838885194965525893e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.415
y[1] (analytic) = 2.981493716031864723719046093261
y[1] (numeric) = 2.9814937160318647237190460932608
absolute error = 2e-31
relative error = 6.7080470075980699921785492068232e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.416
y[1] (analytic) = 2.9825507270325603449642572884106
y[1] (numeric) = 2.9825507270325603449642572884107
absolute error = 1e-31
relative error = 3.3528348434661277567898885540872e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.417
y[1] (analytic) = 2.983607621225311539896886037164
y[1] (numeric) = 2.9836076212253115398968860371638
absolute error = 2e-31
relative error = 6.7032943131397338778698767660343e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.418
y[1] (analytic) = 2.9846643986265845233457523868186
y[1] (numeric) = 2.9846643986265845233457523868185
absolute error = 1e-31
relative error = 3.3504604419182184184085524152646e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.4MB, time=11.81
x[1] = 0.419
y[1] (analytic) = 2.9857210592528321788935992879435
y[1] (numeric) = 2.9857210592528321788935992879434
absolute error = 1e-31
relative error = 3.3492746983211051465843824350623e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 2.9867776031204940718535533245423
y[1] (numeric) = 2.9867776031204940718535533245421
absolute error = 2e-31
relative error = 6.6961798491808062564035813372551e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.421
y[1] (analytic) = 2.9878340302459964622262639383601
y[1] (numeric) = 2.9878340302459964622262639383599
absolute error = 2e-31
relative error = 6.6938122390798748183410590378168e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.422
y[1] (analytic) = 2.9888903406457523176377569136049
y[1] (numeric) = 2.9888903406457523176377569136047
absolute error = 2e-31
relative error = 6.6914465639709561485506189692385e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.423
y[1] (analytic) = 2.9899465343361613262580378067553
y[1] (numeric) = 2.989946534336161326258037806755
absolute error = 3e-31
relative error = 1.0033624232234208764255234688606e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.424
y[1] (analytic) = 2.9910026113336099097004809247452
y[1] (numeric) = 2.9910026113336099097004809247451
absolute error = 1e-31
relative error = 3.3433605046373601457052609526278e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.4MB, time=11.97
x[1] = 0.425
y[1] (analytic) = 2.9920585716544712359020393736564
y[1] (numeric) = 2.9920585716544712359020393736563
absolute error = 1e-31
relative error = 3.3421805624849310333446390466688e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.426
y[1] (analytic) = 2.9931144153151052319843116190954
y[1] (numeric) = 2.9931144153151052319843116190952
absolute error = 2e-31
relative error = 6.6820031662219186640039410477302e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.427
y[1] (analytic) = 2.9941701423318585970954999187152
y[1] (numeric) = 2.994170142331858597095499918715
absolute error = 2e-31
relative error = 6.6796471306817612618217636665407e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.428
y[1] (analytic) = 2.995225752721064815233295906821
y[1] (numeric) = 2.9952257527210648152332959068208
absolute error = 2e-31
relative error = 6.6772930160041035014299729953118e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.429
y[1] (analytic) = 2.9962812464990441680487285307063
y[1] (numeric) = 2.9962812464990441680487285307063
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.5MB, time=12.12
x[1] = 0.43
y[1] (analytic) = 2.9973366236821037476310094582867
y[1] (numeric) = 2.9973366236821037476310094582863
absolute error = 4e-31
relative error = 1.3345181079748613198287748554802e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.431
y[1] (analytic) = 2.9983918842865374692734109967245
y[1] (numeric) = 2.9983918842865374692734109967244
absolute error = 1e-31
relative error = 3.3351210868753681712027820127400e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.432
y[1] (analytic) = 2.9994470283286260842202114821012
y[1] (numeric) = 2.9994470283286260842202114821008
absolute error = 4e-31
relative error = 1.3335791438293575718269414348773e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.433
y[1] (analytic) = 3.0005020558246371923947430207271
y[1] (numeric) = 3.0005020558246371923947430207268
absolute error = 3e-31
relative error = 9.9983267606044042157771353957533e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.434
y[1] (analytic) = 3.0015569667908252551085763834839
y[1] (numeric) = 3.0015569667908252551085763834836
absolute error = 3e-31
relative error = 9.9948128027951776063233438325431e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.435
y[1] (analytic) = 3.0026117612434316077518777755488
y[1] (numeric) = 3.0026117612434316077518777755484
absolute error = 4e-31
relative error = 1.3321735602419452617423356129352e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.5MB, time=12.27
x[1] = 0.436
y[1] (analytic) = 3.0036664391986844724649721250661
y[1] (numeric) = 3.0036664391986844724649721250658
absolute error = 3e-31
relative error = 9.9877934541903973800284816385907e-30 %
Correct digits = 31
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.437
y[1] (analytic) = 3.0047210006727989707911474557286
y[1] (numeric) = 3.0047210006727989707911474557282
absolute error = 4e-31
relative error = 1.3312384075274689961357053562076e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.438
y[1] (analytic) = 3.0057754456819771363107348298454
y[1] (numeric) = 3.0057754456819771363107348298449
absolute error = 5e-31
relative error = 1.6634642508584188044174716189853e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.439
y[1] (analytic) = 3.0068297742424079272564982703046
y[1] (numeric) = 3.0068297742424079272564982703042
absolute error = 4e-31
relative error = 1.3303047729091442665020210438372e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 3.0078839863702672391103689918661
y[1] (numeric) = 3.0078839863702672391103689918657
absolute error = 4e-31
relative error = 1.3298385237347396686974911263344e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.441
y[1] (analytic) = 3.008938082081717917181558194463
y[1] (numeric) = 3.0089380820817179171815581944624
absolute error = 6e-31
relative error = 1.9940589790564688839929146104425e-29 %
Correct digits = 30
h = 0.001
memory used=309.0MB, alloc=4.5MB, time=12.43
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.442
y[1] (analytic) = 3.0099920613929097691660825936395
y[1] (numeric) = 3.0099920613929097691660825936391
absolute error = 4e-31
relative error = 1.3289071593594011790893368562321e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.443
y[1] (analytic) = 3.0110459243199795776877367859102
y[1] (numeric) = 3.0110459243199795776877367859096
absolute error = 6e-31
relative error = 1.9926630648634333197340657205973e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.444
y[1] (analytic) = 3.0120996708790511128205464696766
y[1] (numeric) = 3.012099670879051112820546469676
absolute error = 6e-31
relative error = 1.9919659558440043618525692525961e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.445
y[1] (analytic) = 3.0131533010862351445927364654197
y[1] (numeric) = 3.0131533010862351445927364654192
absolute error = 5e-31
relative error = 1.6593911760803909266463161850277e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.446
y[1] (analytic) = 3.0142068149576294554722474021423
y[1] (numeric) = 3.0142068149576294554722474021417
absolute error = 6e-31
relative error = 1.9905734305375929156919361299636e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.5MB, time=12.58
x[1] = 0.447
y[1] (analytic) = 3.015260212509318852833834860518
y[1] (numeric) = 3.0152602125093188528338348605174
absolute error = 6e-31
relative error = 1.9898780128852499888981434324712e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.448
y[1] (analytic) = 3.0163134937573751814077846868835
y[1] (numeric) = 3.0163134937573751814077846868829
absolute error = 6e-31
relative error = 1.9891831576584211650161998936733e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.449
y[1] (analytic) = 3.0173666587178573357102781160859
y[1] (numeric) = 3.0173666587178573357102781160855
absolute error = 4e-31
relative error = 1.3256592427847944318057758365818e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 3.018419707406811272455440265287
y[1] (numeric) = 3.0184197074068112724554402652866
absolute error = 4e-31
relative error = 1.3251967545084991793835308909853e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.451
y[1] (analytic) = 3.0194726398402700229491054851046
y[1] (numeric) = 3.0194726398402700229491054851042
absolute error = 4e-31
relative error = 1.3247346398249198355437853731363e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.452
y[1] (analytic) = 3.0205254560342537054643329789651
y[1] (numeric) = 3.0205254560342537054643329789646
absolute error = 5e-31
relative error = 1.6553411228537245715352018823036e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.5MB, time=12.74
x[1] = 0.453
y[1] (analytic) = 3.0215781560047695375987060262198
y[1] (numeric) = 3.0215781560047695375987060262193
absolute error = 5e-31
relative error = 1.6547644117904152398568521266988e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.454
y[1] (analytic) = 3.0226307397678118486134480694696
y[1] (numeric) = 3.0226307397678118486134480694692
absolute error = 4e-31
relative error = 1.3233505328233597974500399688944e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.455
y[1] (analytic) = 3.0236832073393620917543888516246
y[1] (numeric) = 3.0236832073393620917543888516242
absolute error = 4e-31
relative error = 1.3228899080071721659225774217319e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.456
y[1] (analytic) = 3.0247355587353888565548137135093
y[1] (numeric) = 3.0247355587353888565548137135087
absolute error = 6e-31
relative error = 1.9836444818034072758155892797900e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.457
y[1] (analytic) = 3.0257877939718478811202290883064
y[1] (numeric) = 3.0257877939718478811202290883058
absolute error = 6e-31
relative error = 1.9829546579418266948245788876736e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.5MB, time=12.89
x[1] = 0.458
y[1] (analytic) = 3.0268399130646820643950771548133
y[1] (numeric) = 3.0268399130646820643950771548125
absolute error = 8e-31
relative error = 2.6430205196745877510003939309393e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.459
y[1] (analytic) = 3.0278919160298214784114325373528
y[1] (numeric) = 3.0278919160298214784114325373523
absolute error = 5e-31
relative error = 1.6513138971472967789599671297110e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 3.0289438028831833805197138662651
y[1] (numeric) = 3.0289438028831833805197138662645
absolute error = 6e-31
relative error = 1.9808885177363591714709922267001e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.461
y[1] (analytic) = 3.0299955736406722256014429391568
y[1] (numeric) = 3.0299955736406722256014429391562
absolute error = 6e-31
relative error = 1.9802009125679142615061193851770e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.462
y[1] (analytic) = 3.0310472283181796782640841495659
y[1] (numeric) = 3.0310472283181796782640841495653
absolute error = 6e-31
relative error = 1.9795138604056613916861184172341e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.463
y[1] (analytic) = 3.0320987669315846250179967763391
y[1] (numeric) = 3.0320987669315846250179967763385
absolute error = 6e-31
relative error = 1.9788273605849140256251634823424e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.5MB, time=13.04
x[1] = 0.464
y[1] (analytic) = 3.0331501894967531864355326538795
y[1] (numeric) = 3.0331501894967531864355326538788
absolute error = 7e-31
relative error = 2.3078316478490664265534693452627e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.465
y[1] (analytic) = 3.0342014960295387292923116704615
y[1] (numeric) = 3.0342014960295387292923116704609
absolute error = 6e-31
relative error = 1.9774560153145440483548460957243e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.466
y[1] (analytic) = 3.0352526865457818786907074690477
y[1] (numeric) = 3.0352526865457818786907074690472
absolute error = 5e-31
relative error = 1.6473093071174135620472589600223e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.467
y[1] (analytic) = 3.0363037610613105301655756524657
y[1] (numeric) = 3.036303761061310530165575652465
absolute error = 7e-31
relative error = 2.3054346833708159337554597313733e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.468
y[1] (analytic) = 3.037354719591939861772256722427
y[1] (numeric) = 3.0373547195919398617722567224263
absolute error = 7e-31
relative error = 2.3046369773170354246700424651000e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.5MB, time=13.20
x[1] = 0.469
y[1] (analytic) = 3.0384055621534723461568859096791
y[1] (numeric) = 3.0384055621534723461568859096785
absolute error = 6e-31
relative error = 1.9747199237443125442449455067445e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 3.0394562887616977626090419805772
y[1] (numeric) = 3.0394562887616977626090419805767
absolute error = 5e-31
relative error = 1.6450310598271658783951778512419e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.471
y[1] (analytic) = 3.0405068994323932090967670335568
y[1] (numeric) = 3.0405068994323932090967670335561
absolute error = 7e-31
relative error = 2.3022476947204992121098848747137e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.472
y[1] (analytic) = 3.0415573941813231142839892273641
y[1] (numeric) = 3.0415573941813231142839892273634
absolute error = 7e-31
relative error = 2.3014525431581231103665841242667e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.473
y[1] (analytic) = 3.042607773024239249530380311472
y[1] (numeric) = 3.0426077730242392495303803114714
absolute error = 6e-31
relative error = 1.9719925956924190042161405735752e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.474
y[1] (analytic) = 3.0436580359768807408736797578573
y[1] (numeric) = 3.0436580359768807408736797578568
absolute error = 5e-31
relative error = 1.6427601067198139720942148818048e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.5MB, time=13.35
x[1] = 0.475
y[1] (analytic) = 3.044708183054974080994517222265
y[1] (numeric) = 3.0447081830549740809945172222642
absolute error = 8e-31
relative error = 2.6275096065111324575429056571910e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.476
y[1] (analytic) = 3.0457582142742331411637649922075
y[1] (numeric) = 3.0457582142742331411637649922067
absolute error = 8e-31
relative error = 2.6266037673336135007765669705627e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.477
y[1] (analytic) = 3.0468081296503591831724520082709
y[1] (numeric) = 3.04680812965035918317245200827
absolute error = 9e-31
relative error = 2.9539109838967141817510881818136e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.478
y[1] (analytic) = 3.0478579291990408712442709747888
y[1] (numeric) = 3.047857929199040871244270974788
absolute error = 8e-31
relative error = 2.6247942607030744783487242166561e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.479
y[1] (analytic) = 3.0489076129359542839307100056423
y[1] (numeric) = 3.0489076129359542839307100056417
absolute error = 6e-31
relative error = 1.9679179436408972992603715006778e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=335.7MB, alloc=4.5MB, time=13.51
x[1] = 0.48
y[1] (analytic) = 3.0499571808767629259888401808076
y[1] (numeric) = 3.0499571808767629259888401808069
absolute error = 7e-31
relative error = 2.2951141884515667097512175635342e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.481
y[1] (analytic) = 3.0510066330371177402417903193282
y[1] (numeric) = 3.0510066330371177402417903193276
absolute error = 6e-31
relative error = 1.9665640628343417914643632587544e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.482
y[1] (analytic) = 3.0520559694326571194219402046315
y[1] (numeric) = 3.0520559694326571194219402046309
absolute error = 6e-31
relative error = 1.9658879326237691907689412213486e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.483
y[1] (analytic) = 3.0531051900790069179968634285209
y[1] (numeric) = 3.0531051900790069179968634285204
absolute error = 5e-31
relative error = 1.6376769514025857037029184759721e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.484
y[1] (analytic) = 3.0541542949917804639780509507877
y[1] (numeric) = 3.054154294991780463978050950787
absolute error = 7e-31
relative error = 2.2919601709313244926238549849621e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.485
y[1] (analytic) = 3.0552032841865785707124464021609
y[1] (numeric) = 3.0552032841865785707124464021602
absolute error = 7e-31
relative error = 2.2911732375489670271261417305031e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.5MB, time=13.66
x[1] = 0.486
y[1] (analytic) = 3.0562521576789895486568240892913
y[1] (numeric) = 3.0562521576789895486568240892907
absolute error = 6e-31
relative error = 1.9631887980593138356278544222111e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.487
y[1] (analytic) = 3.0573009154845892171350405915994
y[1] (numeric) = 3.0573009154845892171350405915987
absolute error = 7e-31
relative error = 2.2896012507458671016521939214468e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.488
y[1] (analytic) = 3.0583495576189409160781907711516
y[1] (numeric) = 3.058349557618940916078190771151
absolute error = 6e-31
relative error = 1.9618424535720052861782985527750e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.489
y[1] (analytic) = 3.0593980840975955177476989482358
y[1] (numeric) = 3.0593980840975955177476989482351
absolute error = 7e-31
relative error = 2.2880317655898415458424787520145e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 3.0604464949360914384413759269838
y[1] (numeric) = 3.0604464949360914384413759269833
absolute error = 5e-31
relative error = 1.6337485423362745373822358390190e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.5MB, time=13.82
x[1] = 0.491
y[1] (analytic) = 3.0614947901499546501824724872636
y[1] (numeric) = 3.0614947901499546501824724872629
absolute error = 7e-31
relative error = 2.2864647761354295737148931718195e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.492
y[1] (analytic) = 3.0625429697546986923917598910927
y[1] (numeric) = 3.0625429697546986923917598910919
absolute error = 8e-31
relative error = 2.6122082462212042362112845843357e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.493
y[1] (analytic) = 3.0635910337658246835426678840556
y[1] (numeric) = 3.063591033765824683542667884055
absolute error = 6e-31
relative error = 1.9584859512480963434660456966729e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.494
y[1] (analytic) = 3.0646389821988213327995106045944
y[1] (numeric) = 3.0646389821988213327995106045937
absolute error = 7e-31
relative error = 2.2841189584352381067543557058539e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.495
y[1] (analytic) = 3.0656868150691649516388307466147
y[1] (numeric) = 3.0656868150691649516388307466141
absolute error = 6e-31
relative error = 1.9571470805522037699808315359843e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.496
y[1] (analytic) = 3.0667345323923194654538922536043
y[1] (numeric) = 3.0667345323923194654538922536036
absolute error = 7e-31
relative error = 2.2825581823475902980551775561574e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.5MB, time=13.97
x[1] = 0.497
y[1] (analytic) = 3.0677821341837364251423517553725
y[1] (numeric) = 3.0677821341837364251423517553719
absolute error = 6e-31
relative error = 1.9558103338379525229362800115709e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.498
y[1] (analytic) = 3.0688296204588550186771388916292
y[1] (numeric) = 3.0688296204588550186771388916286
absolute error = 6e-31
relative error = 1.9551427554009573638219840022390e-29 %
Correct digits = 30
h = 0.001
NO POLE
TOP MAIN SOLVE Loop
x[1] = 0.499
y[1] (analytic) = 3.0698769912331020826605755998817
y[1] (numeric) = 3.069876991233102082660575599881
absolute error = 7e-31
relative error = 2.2802216570860886271926469834152e-29 %
Correct digits = 30
h = 0.001
NO POLE
Finished!
diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2));
Iterations = 500
Total Elapsed Time = 14 Seconds
Elapsed Time(since restart) = 13 Seconds
Time to Timeout = 2 Minutes 45 Seconds
Percent Done = 100.2 %
> quit
memory used=349.0MB, alloc=4.5MB, time=14.04