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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 <> 0.0) 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 relerr <> 0. 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
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := 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))) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := 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
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2;
> #BOTTOM RADII COMPLEX EQ = 1
> 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
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := 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]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := 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
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
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 arcsin FULL $eq_no = 1
> array_tmp4[1] := arcsin(array_tmp3[1]);
> array_tmp4_a1[1] := cos(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;
> 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 arcsin 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;
> 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 arcsin 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 * (2.0);
> 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 arcsin 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 * (3.0);
> 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 arcsin 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 * (4.0);
> 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 - 2;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 1) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary / glob_h;
> 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] := arcsin(array_tmp3[1]);
array_tmp4_a1[1] := cos(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/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/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*2.0/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*3.0/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*4.0/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 - 2;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 1 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary/glob_h
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 <> 0.0) 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 rel_error <> 0. 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) * arcsin(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)*arcsin(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;
> 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/arcsin_sqrtpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = arcsin(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,"#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) * arcsin(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;
> #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();
> 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 := 1;
> #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
> display_alot(current_iter)
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 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 ) = arcsin(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,"2012-12-14T20:02:02-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"arcsin_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = arcsin(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," 151 | ")
> ;
> logitem_str(html_log_file,"arcsin_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"arcsin_sqrt maple results")
> ;
> logitem_str(html_log_file,"Languages compared")
> ;
> 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;
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/arcsin_sqrtpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin(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, "#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) * arcsin(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_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();
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_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;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,
"diff ( y , x , 1 ) = arcsin(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, "2012-12-14T20:02:02-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"arcsin_sqrt");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = arcsin(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, " 151 | ");
logitem_str(html_log_file, "arcsin_sqrt diffeq.mxt");
logitem_str(html_log_file, "arcsin_sqrt maple results");
logitem_str(html_log_file, "Languages compared");
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/arcsin_sqrtpostode.ode#################
diff ( y , x , 1 ) = arcsin(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;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(10.0 * (0.1 * x + 0.2) * arcsin(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 = 7.9214363215919274570325169638303e-88
max_value3 = 7.9214363215919274570325169638303e-88
value3 = 7.9214363215919274570325169638303e-88
best_h = 0.001
START of Soultion
x[1] = 0
y[1] (analytic) = 0.6090571729975816513572313056163
y[1] (numeric) = 0.6090571729975816513572313056163
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.001
y[1] (analytic) = 0.6095208831026770820978879838655
y[1] (numeric) = 0.60952088310267708210009083456144
absolute error = 2.20285069594e-21
relative error = 3.6140692747502105065184750223716e-19 %
Correct digits = 20
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
memory used=3.8MB, alloc=2.8MB, time=0.35
y[1] (analytic) = 0.6099847181843472541779969702107
y[1] (numeric) = 0.6099847181843472541823977204722
absolute error = 4.40075026150e-21
relative error = 7.2145254304059828048140138760673e-19 %
Correct digits = 20
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 0.6104486782191861298431324520456
y[1] (numeric) = 0.61044867821918612984972616436374
absolute error = 6.59371231814e-21
relative error = 1.0801419600703072766602240734755e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.004
y[1] (analytic) = 0.6109127631838086164442505419117
y[1] (numeric) = 0.61091276318380861645303229235543
absolute error = 8.78175044373e-21
relative error = 1.4374802709904732178976178621076e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 0.6113769730548505410074765302546
y[1] (numeric) = 0.61137697305485054101844140842592
absolute error = 1.096487817132e-20
relative error = 1.7934725471474815596414418406736e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 0.6118413078089686248489230972898
y[1] (numeric) = 0.61184130780896862486206620628044
absolute error = 1.314310899064e-20
relative error = 2.1481238391219558699398536176907e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.007
memory used=7.6MB, alloc=3.8MB, time=0.71
y[1] (analytic) = 0.6123057674228404582344384153974
y[1] (numeric) = 0.61230576742284045824975487174513
absolute error = 1.531645634773e-20
relative error = 2.5014391767361719333002798220412e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 0.6127703518731644750841833511355
y[1] (numeric) = 0.61277035187316447510166828477998
absolute error = 1.748493364448e-20
relative error = 2.8534235690468188255087384793413e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 0.6132350611366599277219372527391
y[1] (numeric) = 0.61323506113665992774158580697925
absolute error = 1.964855424015e-20
relative error = 3.2040820046607387062428637436358e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.01
y[1] (analytic) = 0.6136998951900668616690320848583
y[1] (numeric) = 0.61369989519006686169083941630838
absolute error = 2.180733145008e-20
relative error = 3.5534194515914211076120935485459e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.011
y[1] (analytic) = 0.6141648540101460904828149472665
y[1] (numeric) = 0.61416485401014609050677622581366
absolute error = 2.396127854716e-20
relative error = 3.9014408575656066897728866323439e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.012
y[1] (analytic) = 0.614629937573679170639539288377
y[1] (numeric) = 0.6146299375736791706656496971381
absolute error = 2.611040876110e-20
relative error = 4.2481511499706272386361900852051e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=1.10
NO POLE
x[1] = 0.013
y[1] (analytic) = 0.6150951458574683764615853976086
y[1] (numeric) = 0.61509514585746837648984013288737
absolute error = 2.825473527877e-20
relative error = 4.5935552359760076623934950985979e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.014
y[1] (analytic) = 0.6155604788383366750889110329727
y[1] (numeric) = 0.6155604788383366751193053042171
absolute error = 3.039427124440e-20
relative error = 4.9376580026318392184812592646078e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.015
y[1] (analytic) = 0.6160259364931277014946333117
y[1] (numeric) = 0.61602593649312770152716234145989
absolute error = 3.252902975989e-20
relative error = 5.2804643169846289857200770577785e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.016
y[1] (analytic) = 0.6164915187987057335446432622956
y[1] (numeric) = 0.61649151879870573357930228618089
absolute error = 3.465902388529e-20
relative error = 5.6219790262202652363015055100683e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 0.61695722573195566710115470611
y[1] (numeric) = 0.6169572257319556671379389727479
absolute error = 3.678426663790e-20
relative error = 5.9622069575827219285216941426889e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=1.49
NO POLE
x[1] = 0.018
y[1] (analytic) = 0.6174230572697829911700894053354
y[1] (numeric) = 0.61742305726978299120899417632857
absolute error = 3.890477099317e-20
relative error = 6.3011529185847300124460248290749e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 0.6178890133891137630922006823022
y[1] (numeric) = 0.61788901338911376313322123218722
absolute error = 4.102054988502e-20
relative error = 6.6388216971236921911962366692422e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 0.6183550940668945837778379820439
y[1] (numeric) = 0.61835509406689458382096959824965
absolute error = 4.313161620575e-20
relative error = 6.9752180615308324621228673495914e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 0.6188212992800925729852551163342
y[1] (numeric) = 0.61882129928009257303049309913996
absolute error = 4.523798280576e-20
relative error = 7.3103467605894834696245107600821e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 0.6192876290056953446423651927772
y[1] (numeric) = 0.61928762900569534468970485527141
absolute error = 4.733966249421e-20
relative error = 7.6442125237051418237809090989044e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 0.6197540832207109822118454970576
y[1] (numeric) = 0.6197540832207109822612821650973
absolute error = 4.943666803970e-20
relative error = 7.9768200610780457083205874454845e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.2MB, time=1.89
NO POLE
x[1] = 0.024
y[1] (analytic) = 0.6202206619021680140994958601316
y[1] (numeric) = 0.62022066190216801415102487230084
absolute error = 5.152901216924e-20
relative error = 8.3081740635993277628809206274504e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.025
y[1] (analytic) = 0.6206873650271153891057543049593
y[1] (numeric) = 0.62068736502711538915937101252806
absolute error = 5.361670756876e-20
relative error = 8.6382792029958104563746410738487e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.026
y[1] (analytic) = 0.6211541925726224519202740293642
y[1] (numeric) = 0.62115419257262245197597379624823
absolute error = 5.569976688403e-20
relative error = 8.9671401320402168852761138499980e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 0.6216211445157789186594660427454
y[1] (numeric) = 0.62162114451577891871724424546506
absolute error = 5.777820271966e-20
relative error = 9.2947614844516260089632455284414e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.028
y[1] (analytic) = 0.6220882208336948524469120346621
y[1] (numeric) = 0.62208822083369485250676406230233
absolute error = 5.985202764023e-20
relative error = 9.6211478751388324663440979719166e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.3MB, time=2.29
NO POLE
x[1] = 0.029
y[1] (analytic) = 0.6225554215035006390365523127825
y[1] (numeric) = 0.62255542150350063909847356695271
absolute error = 6.192125417021e-20
relative error = 9.9463039002483115959779305199598e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 0.6230227465023469624785539063179
y[1] (numeric) = 0.62302274650234696254253980111121
absolute error = 6.398589479331e-20
relative error = 1.0270234137120539540098821478842e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.031
y[1] (analytic) = 0.6234901958074047808277641888643
y[1] (numeric) = 0.62349019580740478089381015081833
absolute error = 6.604596195403e-20
relative error = 1.0592943144599422388693275582874e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 0.6239577693958653018946556315594
y[1] (numeric) = 0.62395776939586530196275709961552
absolute error = 6.810146805612e-20
relative error = 1.0914435462845168469231868664185e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 0.6244254672449399590386675536054
y[1] (numeric) = 0.62442546724493995910881997906987
absolute error = 7.015242546447e-20
relative error = 1.1234715613697365770268765193698e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 0.6248932893318603870038509925553
y[1] (numeric) = 0.62489328933186038707604983905955
absolute error = 7.219884650425e-20
relative error = 1.1553788100596413045452926737965e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.3MB, time=2.69
NO POLE
x[1] = 0.035
y[1] (analytic) = 0.6253612356338783977967230712678
y[1] (numeric) = 0.62536123563387839787096381472864
absolute error = 7.424074346084e-20
relative error = 1.1871657408631689206998811703481e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 0.6258293061282659566062374921429
y[1] (numeric) = 0.62582930612826595668251562072376
absolute error = 7.627812858086e-20
relative error = 1.2188328004765332048924824121393e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.037
y[1] (analytic) = 0.6262975007923151577657780421459
y[1] (numeric) = 0.62629750079231515784408905621706
absolute error = 7.831101407116e-20
relative error = 1.2503804337729347943237122702429e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.038
y[1] (analytic) = 0.6267658196033382007570822442044
y[1] (numeric) = 0.62676581960333820083742165630486
absolute error = 8.033941210046e-20
relative error = 1.2818090838346046015715251762078e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 0.6272342625386673662560025418522
y[1] (numeric) = 0.62723426253866736633836587665047
absolute error = 8.236333479827e-20
relative error = 1.3131191919413444658046210160861e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.3MB, time=3.09
NO POLE
x[1] = 0.04
y[1] (analytic) = 0.6277028295756549922200126544619
y[1] (numeric) = 0.62770282957565499230439544871731
absolute error = 8.438279425541e-20
relative error = 1.3443111975846145947721271001631e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.041
y[1] (analytic) = 0.6281715206916734500173669900926
y[1] (numeric) = 0.62817152069167345010376479261658
absolute error = 8.639780252398e-20
relative error = 1.3753855384728080946753504312768e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.042
y[1] (analytic) = 0.6286403358641151205978212518581
y[1] (numeric) = 0.62864033586411512068622962347618
absolute error = 8.840837161808e-20
relative error = 1.4063426505484380841065135205609e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 0.6291092750703923707048226218127
y[1] (numeric) = 0.6291092750703923707952371353261
absolute error = 9.041451351340e-20
relative error = 1.4371829679872916891056507481966e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 0.6295783382879375291290781536472
y[1] (numeric) = 0.6295783382879375292214943937946
absolute error = 9.241624014740e-20
relative error = 1.4679069232069647662183686730523e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 0.6300475254942028630034102520006
y[1] (numeric) = 0.63004752549420286309782381542031
absolute error = 9.441356341971e-20
relative error = 1.4985149468788558815449139262639e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.3MB, time=3.49
NO POLE
x[1] = 0.046
y[1] (analytic) = 0.6305168366666605541388083619203
y[1] (numeric) = 0.63051683666666055423521485711234
absolute error = 9.640649519204e-20
relative error = 1.5290074679323408806578629916175e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 0.6309862717828026754015862369468
y[1] (numeric) = 0.63098627178280267549998128423538
absolute error = 9.839504728858e-20
relative error = 1.5593849135666999602264182398059e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 0.6314558308201411671315543984676
y[1] (numeric) = 0.63145583082014116723193362996327
absolute error = 1.0037923149567e-19
relative error = 1.5896477092514364344478774993013e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 0.631925513756207813601117642372
y[1] (numeric) = 0.63192551375620781370347670193459
absolute error = 1.0235905956259e-19
relative error = 1.6197962787443231423566987556513e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.05
y[1] (analytic) = 0.6323953205685542195152076916603
y[1] (numeric) = 0.63239532056855421961954223486146
absolute error = 1.0433454320116e-19
relative error = 1.6498310440905565183422505871536e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=3.90
NO POLE
x[1] = 0.051
y[1] (analytic) = 0.6328652512347517865519613355036
y[1] (numeric) = 0.63286525123475178665826702958949
absolute error = 1.0630569408589e-19
relative error = 1.6797524256306104522054468557131e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 0.6333353057323916899440546363321
y[1] (numeric) = 0.63333530573239169005232716018675
absolute error = 1.0827252385465e-19
relative error = 1.7095608420162710585880290297754e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.053
y[1] (analytic) = 0.6338054840390848551006040268464
y[1] (numeric) = 0.63380548403908485521083907095434
absolute error = 1.1023504410794e-19
relative error = 1.7392567102045166328963212604389e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 0.6342757861324619342695453583944
y[1] (numeric) = 0.63427578613246193438173862480468
absolute error = 1.1219326641028e-19
relative error = 1.7688404454848540807718488703784e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 0.6347462119901732832404022009587
y[1] (numeric) = 0.63474621199017328335454940324756
absolute error = 1.1414720228886e-19
relative error = 1.7983124614633722417614926879441e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 0.6352167615898889380873549330273
y[1] (numeric) = 0.63521676158988893820345179626202
absolute error = 1.1609686323472e-19
relative error = 1.8276731700867002382621430248414e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=4.30
NO POLE
x[1] = 0.057
y[1] (analytic) = 0.6356874349092985919525223969142
y[1] (numeric) = 0.63568743490929859207056465761654
absolute error = 1.1804226070234e-19
relative error = 1.8569229816408523617751634682167e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 0.6361582319261115718693681316233
y[1] (numeric) = 0.63615823192611157198935153773374
absolute error = 1.1998340611044e-19
relative error = 1.8860623047691037016335046313282e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.059
y[1] (analytic) = 0.6366291526180568156261434311398
y[1] (numeric) = 0.63662915261805681574806374198133
absolute error = 1.2192031084153e-19
relative error = 1.9150915464701569574936906226495e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 0.6371001969628828486692797110698
y[1] (numeric) = 0.63710019696288284879313269731158
absolute error = 1.2385298624178e-19
relative error = 1.9440111121013452686728136050445e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.061
y[1] (analytic) = 0.6375713649383577610466429008477
y[1] (numeric) = 0.63757136493835776117242434446939
absolute error = 1.2578144362169e-19
relative error = 1.9728214053943735827653077745141e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.3MB, time=4.70
NO POLE
x[1] = 0.062
y[1] (analytic) = 0.6380426565222691843905628122902
y[1] (numeric) = 0.63804265652226918451826850654685
absolute error = 1.2770569425665e-19
relative error = 2.0015228284692713473317704006368e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 0.6385140716924242689405506680971
y[1] (numeric) = 0.63851407169242426907017641748325
absolute error = 1.2962574938615e-19
relative error = 2.0301157818271456133715559750285e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.064
y[1] (analytic) = 0.6389856104266496606056182059822
y[1] (numeric) = 0.63898561042664966073715982619563
absolute error = 1.3154162021343e-19
relative error = 2.0586006643498571512942729401596e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 0.6394572727027914780661120054716
y[1] (numeric) = 0.63945727270279147819956532337952
absolute error = 1.3345331790792e-19
relative error = 2.0869778733433337758676194421777e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.066
y[1] (analytic) = 0.6399290584987152899149769150421
y[1] (numeric) = 0.63992905849871529005033776864494
absolute error = 1.3536085360284e-19
relative error = 2.1152478045050637127564829816083e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 0.6404009677923060918383626871547
y[1] (numeric) = 0.64040096779230609197562692555159
absolute error = 1.3726423839689e-19
relative error = 2.1434108519556038157623833720204e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.3MB, time=5.11
NO POLE
x[1] = 0.068
y[1] (analytic) = 0.6408730005614682838354881579287
y[1] (numeric) = 0.64087300056146828397465164128214
absolute error = 1.3916348335344e-19
relative error = 2.1714674082309442290373855215441e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.069
y[1] (analytic) = 0.6413451567841256474776775366449
y[1] (numeric) = 0.64134515678412564761873613614639
absolute error = 1.4105859950149e-19
relative error = 2.1994178643025099001134791659311e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.07
y[1] (analytic) = 0.6418174364382213232064835980089
y[1] (numeric) = 0.6418174364382213233494331958441
absolute error = 1.4294959783520e-19
relative error = 2.2272626095747982018110930024790e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 0.6422898395017177876708127971197
y[1] (numeric) = 0.64228983950171778781564928643372
absolute error = 1.4483648931402e-19
relative error = 2.2550020318923733890265867658472e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 0.6427623659525968311029675533963
y[1] (numeric) = 0.6427623659525968312496868382597
absolute error = 1.4671928486340e-19
relative error = 2.2826365175558585898481715623172e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=53.4MB, alloc=4.3MB, time=5.51
x[1] = 0.073
y[1] (analytic) = 0.643235015768859534733521175312
y[1] (numeric) = 0.6432350157688595348821191706862
absolute error = 1.4859799537420e-19
relative error = 2.3101664513176517560738209724387e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 0.6437077889285262482449411226685
y[1] (numeric) = 0.64370778892852624839541375437171
absolute error = 1.5047263170321e-19
relative error = 2.3375922163949090971449587431464e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.075
y[1] (analytic) = 0.6441806854096365672638765273268
y[1] (numeric) = 0.64418068540963656741621973199998
absolute error = 1.5234320467318e-19
relative error = 2.3649141944748695274862187678349e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.076
y[1] (analytic) = 0.6446537051902493108920261167875
y[1] (numeric) = 0.64465370519024931104623584186054
absolute error = 1.5420972507304e-19
relative error = 2.3921327657231077106102139057009e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 0.6451268482484424992755029077918
y[1] (numeric) = 0.64512684824844249943157511144953
absolute error = 1.5607220365773e-19
relative error = 2.4192483087857101612941158640131e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 0.6456001145623133312126122591918
y[1] (numeric) = 0.64560011456231333137054291034058
absolute error = 1.5793065114878e-19
relative error = 2.4462612008030635433875780626598e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.3MB, time=5.92
NO POLE
x[1] = 0.079
y[1] (analytic) = 0.6460735041099781617999600947252
y[1] (numeric) = 0.64607350410997816195974517295927
absolute error = 1.5978507823407e-19
relative error = 2.4731718174108949524506165639592e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.08
y[1] (analytic) = 0.6465470168695724801168083270176
y[1] (numeric) = 0.64654701686957248027844382258541
absolute error = 1.6163549556781e-19
relative error = 2.4999805327447149302092494502185e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.081
y[1] (analytic) = 0.647020652819250886947594734136
y[1] (numeric) = 0.64702065281925088711107664790744
absolute error = 1.6348191377144e-19
relative error = 2.5266877194584645882277919440040e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 0.6474944119371870725425347593326
y[1] (numeric) = 0.64749441193718707270785910276542
absolute error = 1.6532434343282e-19
relative error = 2.5532937487166759595382269491777e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 0.6479682942015737944162229232389
y[1] (numeric) = 0.64796829420157379458338571834562
absolute error = 1.6716279510672e-19
relative error = 2.5797989902067339867602971155057e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.084
y[1] (analytic) = 0.6484422995906228551841517557181
y[1] (numeric) = 0.64844229959062285535314903503334
absolute error = 1.6899727931524e-19
relative error = 2.6062038121500097625126403699033e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.4MB, time=6.33
NO POLE
x[1] = 0.085
y[1] (analytic) = 0.6489164280825650804370663718461
y[1] (numeric) = 0.64891642808256508060789417839327
absolute error = 1.7082780654717e-19
relative error = 2.6325085812966145422257325593719e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 0.649390679655650296653073033072
y[1] (numeric) = 0.64939067965565029682572742033157
absolute error = 1.7265438725957e-19
relative error = 2.6587136629543671016694570994330e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 0.6498650542881473091474202505273
y[1] (numeric) = 0.64986505428814730932189728240291
absolute error = 1.7447703187561e-19
relative error = 2.6848194209600882898122655649517e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.088
y[1] (analytic) = 0.6503395519583438800598712026741
y[1] (numeric) = 0.65033955195834388023616695346116
absolute error = 1.7629575078706e-19
relative error = 2.7108262177225267425566256729771e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.089
y[1] (analytic) = 0.6508141726445467063795864540647
y[1] (numeric) = 0.65081417264454670655769700841754
absolute error = 1.7811055435284e-19
relative error = 2.7367344142045616779973605864690e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.4MB, time=6.73
NO POLE
x[1] = 0.09
y[1] (analytic) = 0.6512889163250813980074361758667
y[1] (numeric) = 0.65128891632508139818735762876629
absolute error = 1.7992145289959e-19
relative error = 2.7625443699365032862980115182618e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 0.6517637829782924558556612820461
y[1] (numeric) = 0.65176378297829245603738973876821
absolute error = 1.8172845672211e-19
relative error = 2.7882564430273447701262543766013e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.092
y[1] (analytic) = 0.6522387725825432499848031076663
y[1] (numeric) = 0.65223877258254325016833468374921
absolute error = 1.8353157608291e-19
relative error = 2.8138709901623242482630022174479e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 0.6527138851162159977778214676633
y[1] (numeric) = 0.65271388511621599796315228887618
absolute error = 1.8533082121288e-19
relative error = 2.8393883666176607349095841791325e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 0.6531891205577117421513211457083
y[1] (numeric) = 0.65318912055771174233844734801925
absolute error = 1.8712620231095e-19
relative error = 2.8648089262597674970535476092227e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 0.6536644788854503298038070733548
y[1] (numeric) = 0.6536644788854503299927248028991
absolute error = 1.8891772954430e-19
relative error = 2.8901330215528872029192973365377e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.4MB, time=7.13
NO POLE
x[1] = 0.096
y[1] (analytic) = 0.6541399600778703895008886696053
y[1] (numeric) = 0.65413996007787038969159408265397
absolute error = 1.9070541304867e-19
relative error = 2.9153610035682267493892904822515e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 0.6546155641134293103973540203162
y[1] (numeric) = 0.65461556411342931058984328324474
absolute error = 1.9248926292854e-19
relative error = 2.9404932219910705966677248642197e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.098
y[1] (analytic) = 0.6550912909706032203960347854942
y[1] (numeric) = 0.65509129097060322059030407475091
absolute error = 1.9426928925671e-19
relative error = 2.9655300251187082756643701033256e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.099
y[1] (analytic) = 0.655567140627886964543382930522
y[1] (numeric) = 0.6555671406278869647394284325973
absolute error = 1.9604550207530e-19
relative error = 2.9904717598800357262205302955315e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1
y[1] (analytic) = 0.6560431130637940834616805846994
y[1] (numeric) = 0.65604311306379408365949849609388
absolute error = 1.9781791139448e-19
relative error = 3.0153187718204740952854305488866e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.4MB, time=7.53
NO POLE
x[1] = 0.101
y[1] (analytic) = 0.6565192082568567918178045371763
y[1] (numeric) = 0.65651920825685679201739106437048
absolute error = 1.9958652719418e-19
relative error = 3.0400714051323491695625448837705e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 0.6569954261856259568284670864246
y[1] (numeric) = 0.65699542618562595702981844584794
absolute error = 2.0135135942334e-19
relative error = 3.0647300026476996520788719842783e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 0.6574717668286710768018551648088
y[1] (numeric) = 0.65747176682867107700496758280842
absolute error = 2.0311241799962e-19
relative error = 3.0892949058381172581343084077376e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 0.6579482301645802597155898646028
y[1] (numeric) = 0.6579482301645802599204595774135
absolute error = 2.0486971281070e-19
relative error = 3.1137664548387576149706273283342e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 0.6584248161719602018309286959577
y[1] (numeric) = 0.658424816171960202037551949671
absolute error = 2.0662325371330e-19
relative error = 3.1381449884376228529234976089972e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 0.6589015248294361663431331108386
y[1] (numeric) = 0.65890152482943616655150616137246
absolute error = 2.0837305053386e-19
relative error = 3.1624308440900881636944563836807e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.4MB, time=7.93
NO POLE
x[1] = 0.107
y[1] (analytic) = 0.6593783561156519620679240298475
y[1] (numeric) = 0.6593783561156519622780431429156
absolute error = 2.1011911306810e-19
relative error = 3.1866243579163836561137163413745e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 0.6598553100092699221639483111091
y[1] (numeric) = 0.65985531000926992237580976219132
absolute error = 2.1186145108222e-19
relative error = 3.2107258647239450435645253729307e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 0.6603323864889708828911793020446
y[1] (numeric) = 0.66033238648897088310477937635618
absolute error = 2.1360007431158e-19
relative error = 3.2347356979915088245171679341656e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 0.6608095855334541624051748158676
y[1] (numeric) = 0.66080958553345416262050980832979
absolute error = 2.1533499246219e-19
relative error = 3.2586541898958038851101417661564e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 0.661286907121437539587116075046
y[1] (numeric) = 0.66128690712143753980418229025561
absolute error = 2.1706621520961e-19
relative error = 3.2824816712989654006527138956875e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.4MB, time=8.33
NO POLE
x[1] = 0.112
y[1] (analytic) = 0.6617643512316572329095513637445
y[1] (numeric) = 0.66176435123165723312834511594435
absolute error = 2.1879375219985e-19
relative error = 3.3062184717662293317401584270284e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 0.6622419178428678793377683304356
y[1] (numeric) = 0.66224191784286787955828594348489
absolute error = 2.2051761304929e-19
relative error = 3.3298649195687560453257356751537e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 0.6627196069338425132667190804147
y[1] (numeric) = 0.66271960693384251348895688775919
absolute error = 2.2223780734449e-19
relative error = 3.3534213416847857466870032029051e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 0.6631974184833725454934223958961
y[1] (numeric) = 0.66319741848337254571737674053864
absolute error = 2.2395434464254e-19
relative error = 3.3768880638089351257853064129265e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 0.663675352470267742224767618699
y[1] (numeric) = 0.66367535247026774245043485317074
absolute error = 2.2566723447174e-19
relative error = 3.4002654103664299747898518068241e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 0.6641534088733562041206449272595
y[1] (numeric) = 0.66415340887335620434802141358974
absolute error = 2.2737648633024e-19
relative error = 3.4235537044965643420107368440572e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.4MB, time=8.73
NO POLE
x[1] = 0.118
y[1] (analytic) = 0.6646315876714843453723269358173
y[1] (numeric) = 0.66463158767148434560140904550477
absolute error = 2.2908210968747e-19
relative error = 3.4467532680782129876781987197015e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 0.6651098888435168728160267391523
y[1] (numeric) = 0.66510988884351687304681085313637
absolute error = 2.3078411398407e-19
relative error = 3.4698644217326848911385522373982e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 0.665588312368336765081557721158
y[1] (numeric) = 0.66558831236833676531404022978891
absolute error = 2.3248250863091e-19
relative error = 3.4928874848128960579616657874943e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 0.6660668582248452517760206398544
y[1] (numeric) = 0.66606685822484525201019794286517
absolute error = 2.3417730301077e-19
relative error = 3.5158227754325286409281235013197e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 0.6665455263919617927024436951737
y[1] (numeric) = 0.66654552639196179293831220165127
absolute error = 2.3586850647757e-19
relative error = 3.5386706104583114758485520657734e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
memory used=87.7MB, alloc=4.4MB, time=9.13
y[1] (analytic) = 0.6670243168486240571133014789723
y[1] (numeric) = 0.66702431684862405735085760732835
absolute error = 2.3755612835605e-19
relative error = 3.5614313055090838943097230972388e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 0.6675032295737879029988388992606
y[1] (numeric) = 0.66750322957378790323807907720343
absolute error = 2.3924017794283e-19
relative error = 3.5841051749755412906377080517821e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 0.6679822645464273564101263625918
y[1] (numeric) = 0.66798226454642735665104702709799
absolute error = 2.4092066450619e-19
relative error = 3.6066925320207372067947054680716e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.126
y[1] (analytic) = 0.6684614217455345908167726899054
y[1] (numeric) = 0.66846142174553459105937028719104
absolute error = 2.4259759728564e-19
relative error = 3.6291936885774453218469287362544e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 0.6689407011501199064992224318933
y[1] (numeric) = 0.66894070115011990674349341738591
absolute error = 2.4427098549261e-19
relative error = 3.6516089553622792718203752065451e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 0.6694201027392117099755644401484
y[1] (numeric) = 0.6694201027392117102215052784589
absolute error = 2.4594083831050e-19
relative error = 3.6739386418801948887254035116304e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.4MB, time=9.54
NO POLE
x[1] = 0.129
y[1] (analytic) = 0.6698996264918564934627787399603
y[1] (numeric) = 0.66989962649185649371038590485482
absolute error = 2.4760716489452e-19
relative error = 3.6961830564258418658526753197109e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 0.6703792723871188143723489396501
y[1] (numeric) = 0.67037927238711881462161891402218
absolute error = 2.4926997437208e-19
relative error = 3.7183425060931174757606820812043e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 0.6708590404040812748401675997883
y[1] (numeric) = 0.67085904040408127509109687563065
absolute error = 2.5092927584235e-19
relative error = 3.7404172967723106336705714046677e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 0.6713389305218445012906621735106
y[1] (numeric) = 0.67133893052184450154324725188791
absolute error = 2.5258507837731e-19
relative error = 3.7624077331694561684841580510755e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 0.6718189427195271240350693164531
y[1] (numeric) = 0.67181894271952712428930670747394
absolute error = 2.5423739102084e-19
relative error = 3.7843141187964351050659917207414e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 0.672299076976265756903785551551
y[1] (numeric) = 0.67229907697626575715967177434031
absolute error = 2.5588622278931e-19
relative error = 3.8061367559834323185065860730312e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.4MB, time=9.95
NO POLE
x[1] = 0.135
y[1] (analytic) = 0.6727793332712149769127224601103
y[1] (numeric) = 0.67277933327121497717025404278206
absolute error = 2.5753158267176e-19
relative error = 3.8278759458852501845682679763781e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 0.6732597115835473039635947561522
y[1] (numeric) = 0.67325971158354730422276823578223
absolute error = 2.5917347963003e-19
relative error = 3.8495319884868559832728195171412e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 0.6737402118924531805780697860585
y[1] (numeric) = 0.67374021189245318083888170865643
absolute error = 2.6081192259793e-19
relative error = 3.8711051825946601655948155059475e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 0.6742208341771409516657071800052
y[1] (numeric) = 0.67422083417714095192815410048817
absolute error = 2.6244692048297e-19
relative error = 3.8925958258658050767920528249047e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 0.6747015784168368443256175655827
y[1] (numeric) = 0.67470157841683684458969604774802
absolute error = 2.6407848216532e-19
relative error = 3.9140042147962766946828652526662e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=10.35
NO POLE
x[1] = 0.14
y[1] (analytic) = 0.6751824445907849476817694373346
y[1] (numeric) = 0.6751824445907849479474760538322
absolute error = 2.6570661649760e-19
relative error = 3.9353306447213634763107455582816e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 0.6756634326782471927518734587348
y[1] (numeric) = 0.67566343267824719301920479104119
absolute error = 2.6733133230639e-19
relative error = 3.9565754098415730679411104546257e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.142
y[1] (analytic) = 0.6761445426585033323497736553574
y[1] (numeric) = 0.6761445426585033326187262937484
absolute error = 2.6895263839100e-19
relative error = 3.9777388032079178461675515059639e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.143
y[1] (analytic) = 0.6766257745108509210212751396609
y[1] (numeric) = 0.67662577451085092129184568318479
absolute error = 2.7057054352389e-19
relative error = 3.9988211167316522434427859436642e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 0.677107128214605295013338188938
y[1] (numeric) = 0.67710712821460529528552324538927
absolute error = 2.7218505645127e-19
relative error = 4.0198226411966302268563636554629e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 0.6775886037490995522765686785562
y[1] (numeric) = 0.67758860374909955255036486444893
absolute error = 2.7379618589273e-19
relative error = 4.0407436662572979090415390051142e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.4MB, time=10.74
NO POLE
x[1] = 0.146
y[1] (analytic) = 0.6780702010936845325009350526384
y[1] (numeric) = 0.67807020109368453277633899317974
absolute error = 2.7540394054134e-19
relative error = 4.0615844804436294004558170986938e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 0.6785519202277287971846421938149
y[1] (numeric) = 0.67855192022772879746165052287861
absolute error = 2.7700832906371e-19
relative error = 4.0823453711654553993925758086383e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 0.6790337611306186097360927326137
y[1] (numeric) = 0.6790337611306186100147020927142
absolute error = 2.7860936010050e-19
relative error = 4.1030266247234036520438280903755e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 0.679515723781757915608866515452
y[1] (numeric) = 0.67951572378175791588907355771811
absolute error = 2.8020704226611e-19
relative error = 4.1236285263077286565279491925097e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 0.6799978081605683224696491280433
y[1] (numeric) = 0.67999780816056832275145051219215
absolute error = 2.8180138414885e-19
relative error = 4.1441513600042083783655509593085e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.4MB, time=11.13
NO POLE
x[1] = 0.151
y[1] (analytic) = 0.6804800142464890803990405483521
y[1] (numeric) = 0.6804800142464890806824329426631
absolute error = 2.8339239431100e-19
relative error = 4.1645954087984025750552247787449e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 0.6809623420189770621251751800064
y[1] (numeric) = 0.68096234201897706241015526129541
absolute error = 2.8498008128901e-19
relative error = 4.1849609545819521044431938205819e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 0.6814447914575067432900846933234
y[1] (numeric) = 0.68144479145750674357664914691712
absolute error = 2.8656445359372e-19
relative error = 4.2052482781591481202373325511811e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.154
y[1] (analytic) = 0.6819273625415701827487352768161
y[1] (numeric) = 0.68192736254157018303688079652601
absolute error = 2.8814551970991e-19
relative error = 4.2254576592436514129585146515517e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 0.682410055250677002900671077227
y[1] (numeric) = 0.68241005525067700319039436532395
absolute error = 2.8972328809695e-19
relative error = 4.2455893764713481244927341466032e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.156
y[1] (analytic) = 0.6828928695643543700541957807906
y[1] (numeric) = 0.68289286956435437034549354797949
absolute error = 2.9129776718889e-19
relative error = 4.2656437074049536350215324405897e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.4MB, time=11.52
NO POLE
x[1] = 0.157
y[1] (analytic) = 0.6833758054621469748230244625494
y[1] (numeric) = 0.68337580546214697511589342794337
absolute error = 2.9286896539397e-19
relative error = 4.2856209285301127285909211743440e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.158
y[1] (analytic) = 0.6838588629236170125553380041459
y[1] (numeric) = 0.68385886292361701284977489524113
absolute error = 2.9443689109523e-19
relative error = 4.3055213152676045386967662072103e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.159
y[1] (analytic) = 0.6843420419283441637951725535923
y[1] (numeric) = 0.68434204192834416409117410624286
absolute error = 2.9600155265056e-19
relative error = 4.3253451419773158157406799479902e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 0.6848253424559255747760766730715
y[1] (numeric) = 0.68482534245592557507363963146427
absolute error = 2.9756295839277e-19
relative error = 4.3450926819624924474844070703289e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.161
y[1] (analytic) = 0.6853087644859758379469689928586
y[1] (numeric) = 0.6853087644859758382460901094876
absolute error = 2.9912111662900e-19
relative error = 4.3647642074643453076233777390638e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 0.6857923079981269725301293609648
y[1] (numeric) = 0.68579230799812697283080539660712
absolute error = 3.0067603564232e-19
relative error = 4.3843599896886157940087139750919e-17 %
Correct digits = 18
h = 0.001
memory used=114.4MB, alloc=4.4MB, time=11.92
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 0.6862759729720284051112566491137
y[1] (numeric) = 0.68627597297202840541348437280376
absolute error = 3.0222772369006e-19
relative error = 4.4038802987843835757544651859246e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.164
y[1] (analytic) = 0.6867597593873469502615265461338
y[1] (numeric) = 0.68675975938734695056530273513906
absolute error = 3.0377618900526e-19
relative error = 4.4233254038683975873391862173119e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.165
y[1] (analytic) = 0.6872436672237667911915828398352
y[1] (numeric) = 0.68724366722376679149690427963111
absolute error = 3.0532143979591e-19
relative error = 4.4426955730171497780930471226705e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 0.6877276964609894604373958578915
y[1] (numeric) = 0.68772769646098946074425934213714
absolute error = 3.0686348424564e-19
relative error = 4.4619910732800691840279529249768e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 0.6882118470787338205779219072069
y[1] (numeric) = 0.68821184707873382088632423771994
absolute error = 3.0840233051304e-19
relative error = 4.4812121706727565894149032565422e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.4MB, time=12.32
NO POLE
x[1] = 0.168
y[1] (analytic) = 0.6886961190567360449844977196877
y[1] (numeric) = 0.68869611905673604529443570642059
absolute error = 3.0993798673289e-19
relative error = 4.5003591301979842025836828305334e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.169
y[1] (analytic) = 0.6891805123747495986019040802846
y[1] (numeric) = 0.68918051237474959891337454129954
absolute error = 3.1147046101494e-19
relative error = 4.5194322158310602247685092023842e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.17
y[1] (analytic) = 0.6896650270125452187610329805987
y[1] (numeric) = 0.6896650270125452190740327420439
absolute error = 3.1299976144520e-19
relative error = 4.5384316905416524500816107574453e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 0.6901496629499108960230928082872
y[1] (numeric) = 0.69014966294991089633761870437221
absolute error = 3.1452589608501e-19
relative error = 4.5573578162833558748253532299929e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 0.6906344201666518550552862489296
y[1] (numeric) = 0.69063442016665185537133512190136
absolute error = 3.1604887297176e-19
relative error = 4.5762108540071981527586834030966e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 0.6911192986425905355378957429561
y[1] (numeric) = 0.69111929864259053585546444307464
absolute error = 3.1756870011854e-19
relative error = 4.5949910636596089255940972300095e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.4MB, time=12.71
NO POLE
x[1] = 0.174
y[1] (analytic) = 0.6916042983575665731027115056725
y[1] (numeric) = 0.69160429835756657342179689118754
absolute error = 3.1908538551504e-19
relative error = 4.6136987041984744360442520608050e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.175
y[1] (analytic) = 0.6920894192914367803027372833639
y[1] (numeric) = 0.69208941929143678062333622049023
absolute error = 3.2059893712633e-19
relative error = 4.6323340335784955613764283765021e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.176
y[1] (analytic) = 0.6925746614240751276131091828998
y[1] (numeric) = 0.69257466142407512793521854579447
absolute error = 3.2210936289467e-19
relative error = 4.6508973087803599708414726156470e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.177
y[1] (analytic) = 0.6930600247353727244631630762324
y[1] (numeric) = 0.69306002473537272478677974696956
absolute error = 3.2361667073716e-19
relative error = 4.6693887857797708543400116359927e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 0.6935455092052378002995862446305
y[1] (numeric) = 0.69354550920523780062470711317895
absolute error = 3.2512086854845e-19
relative error = 4.6878087195895669049256540937854e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.4MB, time=13.09
NO POLE
x[1] = 0.179
y[1] (analytic) = 0.694031114813595685680589090488
y[1] (numeric) = 0.69403111481359568600721105468741
absolute error = 3.2662196419941e-19
relative error = 4.7061573642434576388712022719348e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.18
y[1] (analytic) = 0.6945168415403887934010329070236
y[1] (numeric) = 0.6945168415403887937291528725603
absolute error = 3.2811996553670e-19
relative error = 4.7244349727927883113072896588912e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 0.6950026893655765996484498581985
y[1] (numeric) = 0.6950026893655765999780647385833
absolute error = 3.2961488038480e-19
relative error = 4.7426417973387166828332937616802e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 0.69548865826913562518989148271
y[1] (numeric) = 0.69548865826913562552099819925371
absolute error = 3.3110671654371e-19
relative error = 4.7607780890019992427052780167568e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 0.6959747482310594165895421969455
y[1] (numeric) = 0.69597474823105941692213767873634
absolute error = 3.3259548179084e-19
relative error = 4.7788440979531100325993111349444e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 0.6964609592313585274570344323578
y[1] (numeric) = 0.69646095923135852779111561623801
absolute error = 3.3408118388021e-19
relative error = 4.7968400734036121961151412160755e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.4MB, time=13.49
NO POLE
x[1] = 0.185
y[1] (analytic) = 0.6969472912500604997264022027948
y[1] (numeric) = 0.69694729125006050006196603333775
absolute error = 3.3556383054295e-19
relative error = 4.8147662636162210752524546272971e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.186
y[1] (analytic) = 0.6974337442672098449656100569291
y[1] (numeric) = 0.69743374426720984530265348641585
absolute error = 3.3704342948675e-19
relative error = 4.8326229158997726669576907323944e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 0.6979203182628680257165945300589
y[1] (numeric) = 0.69792031826286802605511451845604
absolute error = 3.3851998839714e-19
relative error = 4.8504102766304365230798109871266e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.188
y[1] (analytic) = 0.6984070132171134368657553682163
y[1] (numeric) = 0.69840701321711343720574888315226
absolute error = 3.3999351493596e-19
relative error = 4.8681285912326081846675850901832e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 0.6988938291100413870448339556942
y[1] (numeric) = 0.69889382911004138738629797243729
absolute error = 3.4146401674309e-19
relative error = 4.8857781042065292017621094678837e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.4MB, time=13.88
NO POLE
x[1] = 0.19
y[1] (analytic) = 0.6993807659217640800621165348311
y[1] (numeric) = 0.6993807659217640804050480362657
absolute error = 3.4293150143460e-19
relative error = 4.9033590591046062693334113994419e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.191
y[1] (analytic) = 0.6998678236324105963638999641248
y[1] (numeric) = 0.69986782363241059670829594073015
absolute error = 3.4439597660535e-19
relative error = 4.9208716985714152406121032721748e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 0.7003550022221268745261579175431
y[1] (numeric) = 0.70035500222212687487201536736971
absolute error = 3.4585744982661e-19
relative error = 4.9383162643124340001309608329459e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.193
y[1] (analytic) = 0.7008423016710756927763455841952
y[1] (numeric) = 0.70084230167107569312366151284296
absolute error = 3.4731592864776e-19
relative error = 4.9556929971211239556301516091216e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 0.7013297219594366505452810833935
y[1] (numeric) = 0.70132972195943665089405250398881
absolute error = 3.4877142059531e-19
relative error = 4.9730021368676880680052341227938e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.195
y[1] (analytic) = 0.7018172630674061500490419655119
y[1] (numeric) = 0.701817263067406150399265898686
absolute error = 3.5022393317410e-19
relative error = 4.9902439225189404743630088651722e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=14.29
NO POLE
x[1] = 0.196
y[1] (analytic) = 0.7023049249751973779008153239836
y[1] (numeric) = 0.70230492497519737825248879784956
absolute error = 3.5167347386596e-19
relative error = 5.0074185921219292475171401934495e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 0.7027927076630402867526401982392
y[1] (numeric) = 0.70279270766304028710576024837049
absolute error = 3.5312005013129e-19
relative error = 5.0245263828291783715574833797285e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 0.7032806111111815769669811014075
y[1] (numeric) = 0.70328061111118157732154477081572
absolute error = 3.5456366940822e-19
relative error = 5.0415675308894170146974027849959e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 0.7037686352998846783180716601475
y[1] (numeric) = 0.70376863529988467867407599925992
absolute error = 3.5600433911242e-19
relative error = 5.0585422716475858264251805661897e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.2
y[1] (analytic) = 0.7042567802094297317229675070826
y[1] (numeric) = 0.70425678020942973208040957372085
absolute error = 3.5744206663825e-19
relative error = 5.0754508395638728423701194790122e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 0.7047450458201135710022477189595
y[1] (numeric) = 0.70474504582011357136112457831747
absolute error = 3.5887685935797e-19
relative error = 5.0922934682051450524194284841144e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=14.70
NO POLE
x[1] = 0.202
y[1] (analytic) = 0.7052334321122497046703042458437
y[1] (numeric) = 0.70523343211224970503061297046571
absolute error = 3.6030872462201e-19
relative error = 5.1090703902514484843005554608565e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.203
y[1] (analytic) = 0.7057219390661682977551589284141
y[1] (numeric) = 0.70572193906616829811689659817322
absolute error = 3.6173766975912e-19
relative error = 5.1257818375007833519375150242351e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.204
y[1] (analytic) = 0.7062105666622161536477478517158
y[1] (numeric) = 0.70621056666221615401091155379222
absolute error = 3.6316370207642e-19
relative error = 5.1424280408724458001993777340521e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.205
y[1] (analytic) = 0.706699314880756695980612934581
y[1] (numeric) = 0.7066993148807566963451997634408
absolute error = 3.6458682885980e-19
relative error = 5.1590092304153107974941747341688e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 0.707188183702169950535940804336
y[1] (numeric) = 0.70718818370216995090194786170891
absolute error = 3.6600705737291e-19
relative error = 5.1755256352961449592924155053347e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.4MB, time=15.10
NO POLE
x[1] = 0.207
y[1] (analytic) = 0.7076771731068525271828891563688
y[1] (numeric) = 0.70767717310685252755031355122769
absolute error = 3.6742439485889e-19
relative error = 5.1919774838266884224856300827904e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.208
y[1] (analytic) = 0.708166283075217601844140947662
y[1] (numeric) = 0.70816628307521760221297979620078
absolute error = 3.6883884853878e-19
relative error = 5.2083650034437452522884523914719e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.209
y[1] (analytic) = 0.7086555135876948984916269224629
y[1] (numeric) = 0.70865551358769489886187734807569
absolute error = 3.7025042561279e-19
relative error = 5.2246884207297167656817065229166e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.21
y[1] (analytic) = 0.7091448646247306711713571169135
y[1] (numeric) = 0.70914486462473067154301625017351
absolute error = 3.7165913326001e-19
relative error = 5.2409479614110538950381744015205e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 0.7096343361667876860573021376597
y[1] (numeric) = 0.70963433616678768643036711629778
absolute error = 3.7306497863808e-19
relative error = 5.2571438503561546124632857614701e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.212
y[1] (analytic) = 0.710123928194345203534265157226
y[1] (numeric) = 0.7101239281943452039087331261097
absolute error = 3.7446796888370e-19
relative error = 5.2732763115851013007022267784142e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.4MB, time=15.49
NO POLE
x[1] = 0.213
y[1] (analytic) = 0.7106136406878989603096857162753
y[1] (numeric) = 0.71061364068789896068555382738841
absolute error = 3.7586811111311e-19
relative error = 5.2893455682789380215981708064288e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 0.7111034736279611515543165697729
y[1] (numeric) = 0.7111034736279611519315819821934
absolute error = 3.7726541242050e-19
relative error = 5.3053518427598020568516324050218e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 0.7115934269950604130717149605324
y[1] (numeric) = 0.71159342699506041345037484041273
absolute error = 3.7865987988033e-19
relative error = 5.3212953565260869125265825953160e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 0.7120835007697418034964898496711
y[1] (numeric) = 0.71208350076974180387654137021699
absolute error = 3.8005152054589e-19
relative error = 5.3371763302346596515526561040330e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 0.7125736949325667865212467790967
y[1] (numeric) = 0.71257369493256678690268712054625
absolute error = 3.8144034144955e-19
relative error = 5.3529949837068707026674630917793e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=15.89
NO POLE
x[1] = 0.218
y[1] (analytic) = 0.7130640094641132131521721863338
y[1] (numeric) = 0.71306400946411321353499853593732
absolute error = 3.8282634960352e-19
relative error = 5.3687515359416933831510223427610e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 0.7135544443449753039931991367536
y[1] (numeric) = 0.71355444434497530437740868875264
absolute error = 3.8420955199904e-19
relative error = 5.3844462051068089676956046064480e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 0.7140449995557636315586965825946
y[1] (numeric) = 0.71404499955576363194428653820158
absolute error = 3.8558995560698e-19
relative error = 5.4000792085494773815395497332325e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.221
y[1] (analytic) = 0.7145356750771051026146244020733
y[1] (numeric) = 0.71453567507710510300159196945145
absolute error = 3.8696756737815e-19
relative error = 5.4156507628033067659065198024601e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 0.7150264708896429405480966153678
y[1] (numeric) = 0.71502647088964294093643900961022
absolute error = 3.8834239424242e-19
relative error = 5.4311610835783546349199713610610e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.223
y[1] (analytic) = 0.7155173869740366677652953173176
y[1] (numeric) = 0.71551738697403666815500976042753
absolute error = 3.8971444310993e-19
relative error = 5.4466103857804816069396391696211e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.4MB, time=16.29
NO POLE
x[1] = 0.224
y[1] (analytic) = 0.7160084233109620881176780093363
y[1] (numeric) = 0.71600842331096208850876173020634
absolute error = 3.9108372087004e-19
relative error = 5.4619988834990638397709257209845e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.225
y[1] (analytic) = 0.7164995798811112693564211552532
y[1] (numeric) = 0.71649957988111126974887138964591
absolute error = 3.9245023439271e-19
relative error = 5.4773267900286730515411847841004e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.226
y[1] (analytic) = 0.716990856665192525615042927622
y[1] (numeric) = 0.71699085666519252600885691814913
absolute error = 3.9381399052713e-19
relative error = 5.4925943178523148606639759032688e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.227
y[1] (analytic) = 0.7174822536439303999201482524222
y[1] (numeric) = 0.71748225364393040031532324852508
absolute error = 3.9517499610288e-19
relative error = 5.5078016786600003364537604928050e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.228
y[1] (analytic) = 0.7179737707980656467302394010729
y[1] (numeric) = 0.71797377079806564712677265900226
absolute error = 3.9653325792936e-19
relative error = 5.5229490833431478533589992263351e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
memory used=160.2MB, alloc=4.4MB, time=16.68
y[1] (analytic) = 0.7184654081083552145025355192442
y[1] (numeric) = 0.71846540810835521490042430204076
absolute error = 3.9788878279656e-19
relative error = 5.5380367420076609184458285593676e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 0.7189571655555722282877446221203
y[1] (numeric) = 0.71895716555557222868698619959413
absolute error = 3.9924157747383e-19
relative error = 5.5530648639591363968169663350877e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 0.7194490431205059723527317255132
y[1] (numeric) = 0.71944904312050597275332337422495
absolute error = 4.0059164871175e-19
relative error = 5.5680336577312240444280657858479e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.232
y[1] (analytic) = 0.7199410407839618728310269215833
y[1] (numeric) = 0.719941040783961873232965924824
absolute error = 4.0193900324070e-19
relative error = 5.5829433310680348077759415728590e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 0.720433158526761480401117346851
y[1] (numeric) = 0.72043315852676148080440099462239
absolute error = 4.0328364777139e-19
relative error = 5.5977940909338291418272967180813e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 0.7209253963297424529924671287255
y[1] (numeric) = 0.72092539632974245339709271772052
absolute error = 4.0462558899502e-19
relative error = 5.6125861435175354502354036936453e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.4MB, time=17.08
NO POLE
x[1] = 0.235
y[1] (analytic) = 0.7214177541737585385192095349051
y[1] (numeric) = 0.72141775417375853892517436848884
absolute error = 4.0596483358374e-19
relative error = 5.6273196942414105796296322330548e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 0.7219102320396795576414556877343
y[1] (numeric) = 0.72191023203967955804875707592423
absolute error = 4.0730138818993e-19
relative error = 5.6419949477533214077755588756585e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 0.7224028299083913865541643429273
y[1] (numeric) = 0.72240282990839138696279960237371
absolute error = 4.0863525944641e-19
relative error = 5.6566121079319337550332826432196e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 0.7228955477607959398035173689986
y[1] (numeric) = 0.72289554776079594021348382296594
absolute error = 4.0996645396734e-19
relative error = 5.6711713779014270809482178616857e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 0.723388385577811153130745700274
y[1] (numeric) = 0.7233883855778111535420406786211
absolute error = 4.1129497834710e-19
relative error = 5.6856729600182269316469162038355e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 0.7238813433403709663433506724822
y[1] (numeric) = 0.72388134334037096675597151164341
absolute error = 4.1262083916121e-19
relative error = 5.7001170558859750159604205652251e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.4MB, time=17.48
NO POLE
x[1] = 0.241
y[1] (analytic) = 0.7243744210294253062136657856727
y[1] (numeric) = 0.72437442102942530662760982863859
absolute error = 4.1394404296589e-19
relative error = 5.7145038663516653549441459156486e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 0.7248676186259400694047040745436
y[1] (numeric) = 0.72486761862594006981996867084249
absolute error = 4.1526459629889e-19
relative error = 5.7288335915193186407678616680800e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.243
y[1] (analytic) = 0.7253609361108971054232364012199
y[1] (numeric) = 0.72536093611089710583981890689813
absolute error = 4.1658250567823e-19
relative error = 5.7431064307347895568144258568096e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.244
y[1] (analytic) = 0.7258543734652941996000461200743
y[1] (numeric) = 0.72585437346529420001794389767792
absolute error = 4.1789777760362e-19
relative error = 5.7573225826075600388872286130757e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 0.7263479306701450560973056983617
y[1] (numeric) = 0.72634793067014505651651611691732
absolute error = 4.1921041855562e-19
relative error = 5.7714822450013311212423763983859e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.4MB, time=17.87
NO POLE
x[1] = 0.246
y[1] (analytic) = 0.7268416077064792809430210102102
y[1] (numeric) = 0.72684160770647928136354144520632
absolute error = 4.2052043499612e-19
relative error = 5.7855856150428158343586204591263e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.247
y[1] (analytic) = 0.7273354045553423650924891549096
y[1] (numeric) = 0.72733540455534236551431698827819
absolute error = 4.2182783336859e-19
relative error = 5.7996328891273360243080361332305e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 0.7278293211977956675167157834441
y[1] (numeric) = 0.72782932119779566793984840354136
absolute error = 4.2313262009726e-19
relative error = 5.8136242629096970774916083521326e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 0.7283233576149163983177380498334
y[1] (numeric) = 0.72832335761491639874217285142163
absolute error = 4.2443480158823e-19
relative error = 5.8275599313216009301359756454741e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 0.7288175137877976018707994360911
y[1] (numeric) = 0.72881751378779760229653382031989
absolute error = 4.2573438422879e-19
relative error = 5.8414400885644298544140388839394e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.251
y[1] (analytic) = 0.7293117896975481399933228314572
y[1] (numeric) = 0.72931178969754814042035420584557
absolute error = 4.2703137438837e-19
relative error = 5.8552649281244113280317202994293e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.4MB, time=18.27
NO POLE
x[1] = 0.252
y[1] (analytic) = 0.729806185325292675140628378043
y[1] (numeric) = 0.72980618532529267556895415646027
absolute error = 4.2832577841727e-19
relative error = 5.8690346427573041472160918116559e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 0.7303007006521716536283427261124
y[1] (numeric) = 0.73030070065217165405796032876016
absolute error = 4.2961760264776e-19
relative error = 5.8827494245056010215230529884537e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 0.7307953356593412888814464729472
y[1] (numeric) = 0.7307953356593412893123533263413
absolute error = 4.3090685339410e-19
relative error = 5.8964094647008848021332248297792e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 0.7312900903279735447099066895784
y[1] (numeric) = 0.73129009032797354514210022653013
absolute error = 4.3219353695173e-19
relative error = 5.9100149539548272099009017785818e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.256
y[1] (analytic) = 0.7317849646392561186108415696249
y[1] (numeric) = 0.73178496463925611904431922922358
absolute error = 4.3347765959868e-19
relative error = 5.9235660821805627287668950950692e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.4MB, time=18.67
NO POLE
x[1] = 0.257
y[1] (analytic) = 0.732279958574392425097164364076
y[1] (numeric) = 0.7322799585743924255319235916701
absolute error = 4.3475922759410e-19
relative error = 5.9370630385746484725154367337295e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.258
y[1] (analytic) = 0.732775072114601579052653895057
y[1] (numeric) = 0.73277507211460157948869214223688
absolute error = 4.3603824717988e-19
relative error = 5.9505060116412674787381427821036e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 0.7332703052411183791133990704699
y[1] (numeric) = 0.73327030524111837955071379504921
absolute error = 4.3731472457931e-19
relative error = 5.9638951891759686883593246194193e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.26
y[1] (analytic) = 0.7337656579351932910755649498601
y[1] (numeric) = 0.73376565793519329151415361585838
absolute error = 4.3858866599828e-19
relative error = 5.9772307582840905507822188826153e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 0.7342611301780924313294280399698
y[1] (numeric) = 0.73426113017809243176928811759424
absolute error = 4.3986007762444e-19
relative error = 5.9905129053713288510479972736486e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 0.7347567219510975503196286261624
y[1] (numeric) = 0.73475672195109755076075759179024
absolute error = 4.4112896562784e-19
relative error = 6.0037418161544872291191318362194e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.4MB, time=19.07
NO POLE
x[1] = 0.263
y[1] (analytic) = 0.735252433235506016031588073272
y[1] (numeric) = 0.73525243323550601647398340943256
absolute error = 4.4239533616056e-19
relative error = 6.0169176756584492518308138717208e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 0.7357482640126307975040391564251
y[1] (numeric) = 0.73574826401263079794769835178268
absolute error = 4.4365919535758e-19
relative error = 6.0300406682300181103498542272036e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 0.73624421426380044836761760902
y[1] (numeric) = 0.73624421426380044881253815835554
absolute error = 4.4492054933554e-19
relative error = 6.0431109775230432094019135645620e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 0.7367402839703590904094632013101
y[1] (numeric) = 0.73674028397035909085564260550415
absolute error = 4.4617940419405e-19
relative error = 6.0561287865182205318771925707154e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.267
y[1] (analytic) = 0.7372364731136663971637787889528
y[1] (numeric) = 0.73723647311366639761121455496784
absolute error = 4.4743576601504e-19
relative error = 6.0690942775162290694581834963502e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 0.7377327816750975775282958964235
y[1] (numeric) = 0.73773278167509757797698553728632
absolute error = 4.4868964086282e-19
relative error = 6.0820076321405207843588116506442e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.4MB, time=19.46
NO POLE
x[1] = 0.269
y[1] (analytic) = 0.7382292096360433594065955253814
y[1] (numeric) = 0.73822920963604335985653656016617
absolute error = 4.4994103478477e-19
relative error = 6.0948690313486350093169930542223e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.27
y[1] (analytic) = 0.7387257569779099733762330029017
y[1] (numeric) = 0.73872575697790997382742295671213
absolute error = 4.5118995381043e-19
relative error = 6.1076786554218100508274022441100e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 0.7392224236821191363826158089509
y[1] (numeric) = 0.73922242368211913683505221290336
absolute error = 4.5243640395246e-19
relative error = 6.1204366839799352445226430809939e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 0.7397192097301080354585834465999
y[1] (numeric) = 0.73971920973010803591226383780593
absolute error = 4.5368039120603e-19
relative error = 6.1331432959752202365608036457425e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.273
y[1] (analytic) = 0.7402161151033293114696385422192
y[1] (numeric) = 0.74021611510332931192456046376852
absolute error = 4.5492192154932e-19
relative error = 6.1457986697008870916418603406396e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.4MB, time=19.86
NO POLE
x[1] = 0.274
y[1] (analytic) = 0.7407131397832510428847784863063
y[1] (numeric) = 0.74071313978325104334093948724972
absolute error = 4.5616100094342e-19
relative error = 6.1584029827917288250285079115308e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.275
y[1] (analytic) = 0.7412102837513567295728770486412
y[1] (numeric) = 0.74121028375135673003027468397355
absolute error = 4.5739763533235e-19
relative error = 6.1709564122262863584326211744975e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.276
y[1] (analytic) = 0.7417075469891452766245655241632
y[1] (numeric) = 0.74170754698914527708319735480612
absolute error = 4.5863183064292e-19
relative error = 6.1834591343268612290477632271619e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.277
y[1] (analytic) = 0.7422049294781309781995630883063
y[1] (numeric) = 0.74220492947813097865942668109186
absolute error = 4.5986359278556e-19
relative error = 6.1959113247725991017350497345483e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 0.7427024311998435013994061625305
y[1] (numeric) = 0.7427024311998435018604990901837
absolute error = 4.6109292765320e-19
relative error = 6.2083131585862669144866629295172e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.279
y[1] (analytic) = 0.7432000521358278701655267124262
y[1] (numeric) = 0.74320005213582787062784655354877
absolute error = 4.6231984112257e-19
relative error = 6.2206648101536466897652875867486e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.4MB, time=20.26
NO POLE
x[1] = 0.28
y[1] (analytic) = 0.7436977922676444492026295220786
y[1] (numeric) = 0.74369779226764444966617386113149
absolute error = 4.6354433905289e-19
relative error = 6.2329664532077582485719444592493e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 0.7441956515768689279273186093222
y[1] (numeric) = 0.74419565157686892839208503660952
absolute error = 4.6476642728732e-19
relative error = 6.2452182608502339087052960281555e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.282
y[1] (analytic) = 0.7446936300450923044419230671348
y[1] (numeric) = 0.74469363004509230490790917878697
absolute error = 4.6598611165217e-19
relative error = 6.2574204055425296091926750494214e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.283
y[1] (analytic) = 0.7451917276539208695334727366772
y[1] (numeric) = 0.74519172765392087000067613463415
absolute error = 4.6720339795695e-19
relative error = 6.2695730591084451660641837400970e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 0.7456899443849761906977742374102
y[1] (numeric) = 0.74568994438497619116619252940507
absolute error = 4.6841829199487e-19
relative error = 6.2816763927426707408109971953362e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.4MB, time=20.66
NO POLE
x[1] = 0.285
y[1] (analytic) = 0.7461882802198950961885379993017
y[1] (numeric) = 0.74618828021989509665816879884457
absolute error = 4.6963079954287e-19
relative error = 6.2937305770130020125523589811242e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 0.7466867351403296590915070613761
y[1] (numeric) = 0.7466867351403296595623479877366
absolute error = 4.7084092636050e-19
relative error = 6.3057357818471467119504569216407e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 0.7471853091279471814235385197536
y[1] (numeric) = 0.74718530912794718189558719794577
absolute error = 4.7204867819217e-19
relative error = 6.3176921765646881755098960210932e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.288
y[1] (analytic) = 0.7476840021644301782565886269014
y[1] (numeric) = 0.74768400216443017872984268766638
absolute error = 4.7325406076498e-19
relative error = 6.3295999298498067305737342915501e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 0.7481828142314763618665526620276
y[1] (numeric) = 0.74818281423147636234100974181822
absolute error = 4.7445707979062e-19
relative error = 6.3414592097785102200908433040792e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 0.7486817453107986259069108104533
y[1] (numeric) = 0.7486817453107986263825685514171
absolute error = 4.7565774096380e-19
relative error = 6.3532701837994091292553112209203e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.4MB, time=21.05
NO POLE
x[1] = 0.291
y[1] (analytic) = 0.7491807953841250296071314073389
y[1] (numeric) = 0.74918079538412503008398745730216
absolute error = 4.7685604996326e-19
relative error = 6.3650330187490077121139609757767e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 0.7496799644331987819957830183699
y[1] (numeric) = 0.7496799644331987824738350308219
absolute error = 4.7805201245200e-19
relative error = 6.3767478808565311809757266026249e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.293
y[1] (analytic) = 0.7501792524397782261483069468916
y[1] (numeric) = 0.75017925243977822662755258096809
absolute error = 4.7924563407649e-19
relative error = 6.3884149357351384221741319289863e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.294
y[1] (analytic) = 0.7506786593856368234594018735347
y[1] (numeric) = 0.75067865938563682393983879400225
absolute error = 4.8043692046755e-19
relative error = 6.4000343483954178639487980127194e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 0.7511781852525631379399724506047
y[1] (numeric) = 0.75117818525256313842159832784425
absolute error = 4.8162587723955e-19
relative error = 6.4116062832364661892705980486868e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
memory used=206.0MB, alloc=4.4MB, time=21.45
y[1] (analytic) = 0.7516778300223608205385937893963
y[1] (numeric) = 0.75167783002236082102140629938793
absolute error = 4.8281250999163e-19
relative error = 6.4231309040638773695884205554237e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 0.7521775936768485934874438941689
y[1] (numeric) = 0.75217759367684859397144071847552
absolute error = 4.8399682430662e-19
relative error = 6.4346083740770836447442508410372e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.298
y[1] (analytic) = 0.7526774761978602346726562117504
y[1] (numeric) = 0.75267747619786023515783503750217
absolute error = 4.8517882575177e-19
relative error = 6.4460388558807959323953057459598e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.299
y[1] (analytic) = 0.7531774775672445620290445806569
y[1] (numeric) = 0.7531774775672445625154031005351
absolute error = 4.8635851987820e-19
relative error = 6.4574225114794055314526771335203e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.3
y[1] (analytic) = 0.753677597766865417959152978198
y[1] (numeric) = 0.75367759776686541844668889041973
absolute error = 4.8753591222173e-19
relative error = 6.4687595022897198317536717288696e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 0.7541778367786016537765825783062
y[1] (numeric) = 0.75417783677860165426529358660902
absolute error = 4.8871100830282e-19
relative error = 6.4800499891418479207326257587370e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.4MB, time=21.85
NO POLE
x[1] = 0.302
y[1] (analytic) = 0.7546781945843471141735487467675
y[1] (numeric) = 0.75467819458434711466343256039282
absolute error = 4.8988381362532e-19
relative error = 6.4912941322643158370621435947764e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.303
y[1] (analytic) = 0.7551786711660106217126207141443
y[1] (numeric) = 0.75517867116601062220367504782256
absolute error = 4.9105433367826e-19
relative error = 6.5024920913094978621824860819914e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 0.7556792665055159613425967799888
y[1] (numeric) = 0.7556792665055159618348193539242
absolute error = 4.9222257393540e-19
relative error = 6.5136440253493060357197675575660e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.305
y[1] (analytic) = 0.7561799805848018649384680149155
y[1] (numeric) = 0.75617998058480186543185655476984
absolute error = 4.9338853985434e-19
relative error = 6.5247500928650795243680732279774e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 0.7566808133858219958654235397591
y[1] (numeric) = 0.75668081338582199635997577663703
absolute error = 4.9455223687793e-19
relative error = 6.5358104517679115076237685556084e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 0.7571817648905449335668505733925
y[1] (numeric) = 0.75718176489054493406256424382563
absolute error = 4.9571367043313e-19
relative error = 6.5468252593852193385721985913516e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.4MB, time=22.25
NO POLE
x[1] = 0.308
y[1] (analytic) = 0.7576828350809541581762825527935
y[1] (numeric) = 0.75768283508095415867315539872569
absolute error = 4.9687284593219e-19
relative error = 6.5577946724779890952612564249260e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 0.7581840239390480351532487406665
y[1] (numeric) = 0.75818402393904803565127850943815
absolute error = 4.9802976877165e-19
relative error = 6.5687188472292002822055067088156e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 0.7586853314468397999429788473102
y[1] (numeric) = 0.75868533144683980044216329164312
absolute error = 4.9918444433292e-19
relative error = 6.5795979392531233388495532631101e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.311
y[1] (analytic) = 0.7591867575863575426599163045076
y[1] (numeric) = 0.75918675758635754316025318249012
absolute error = 5.0033687798252e-19
relative error = 6.5904321036001032703288059285099e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 0.7596883023396441927949939399795
y[1] (numeric) = 0.75968830233964419329648101505125
absolute error = 5.0148707507175e-19
relative error = 6.6012214947538226723324937742067e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.4MB, time=22.66
NO POLE
x[1] = 0.313
y[1] (analytic) = 0.7601899656887575039466259113965
y[1] (numeric) = 0.7601899656887575044492609523332
absolute error = 5.0263504093670e-19
relative error = 6.6119662666330495667810215961404e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 0.7606917476157700385753698690896
y[1] (numeric) = 0.76069174761577003907915064998828
absolute error = 5.0378078089868e-19
relative error = 6.6226665725989010225438427948261e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 0.7611936481027691527822134264352
y[1] (numeric) = 0.76119364810276915328713772669907
absolute error = 5.0492430026387e-19
relative error = 6.6333225654518323828910573313036e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.316
y[1] (analytic) = 0.7616956671318569811104391264134
y[1] (numeric) = 0.76169566713185698161650473073711
absolute error = 5.0606560432371e-19
relative error = 6.6439343974383549534593506771641e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.317
y[1] (analytic) = 0.7621978046851504213710222020593
y[1] (numeric) = 0.76219780468515042187822690041402
absolute error = 5.0720469835472e-19
relative error = 6.6545022202502501565605905530941e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 0.7627000607447811194915155374362
y[1] (numeric) = 0.76270006074478111999985712505482
absolute error = 5.0834158761862e-19
relative error = 6.6650261850277215613104692324090e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.4MB, time=23.07
NO POLE
x[1] = 0.319
y[1] (analytic) = 0.7632024352928954543883763443664
y[1] (numeric) = 0.76320243529289545489785262172887
absolute error = 5.0947627736247e-19
relative error = 6.6755064423627978955434211747442e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 0.7637049283116545228626891784563
y[1] (numeric) = 0.76370492831165452337329795127457
absolute error = 5.1060877281827e-19
relative error = 6.6859431422956531977501910572257e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 0.7642075397832341245192400259476
y[1] (numeric) = 0.76420753978323412503097910515127
absolute error = 5.1173907920367e-19
relative error = 6.6963364343254676991282637318630e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.322
y[1] (analytic) = 0.764710269689824746708896300624
y[1] (numeric) = 0.76471026968982474722176350234595
absolute error = 5.1286720172195e-19
relative error = 6.7066864674117011319508523077397e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.323
y[1] (analytic) = 0.7652131180136315494942476973938
y[1] (numeric) = 0.76521311801363155000824084295503
absolute error = 5.1399314556123e-19
relative error = 6.7169933899652998005088477731376e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=225.0MB, alloc=4.4MB, time=23.47
x[1] = 0.324
y[1] (analytic) = 0.7657160847368743506384629562579
y[1] (numeric) = 0.76571608473687435115357987215328
absolute error = 5.1511691589538e-19
relative error = 6.7272573498621410814488096685957e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.325
y[1] (analytic) = 0.7662191698417876106173176971697
y[1] (numeric) = 0.76621916984178761113355621505369
absolute error = 5.1623851788399e-19
relative error = 6.7374784944441582830933964946164e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.326
y[1] (analytic) = 0.7667223733106204176543485927833
y[1] (numeric) = 0.76672237331062041817170654945533
absolute error = 5.1735795667203e-19
relative error = 6.7476569705164192119249835895987e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.327
y[1] (analytic) = 0.7672256951256364727790892522811
y[1] (numeric) = 0.76722569512563647329756448967119
absolute error = 5.1847523739009e-19
relative error = 6.7577929243517772605529797611257e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.328
y[1] (analytic) = 0.7677291352691140749083432953719
y[1] (numeric) = 0.7677291352691140754279336605263
absolute error = 5.1959036515440e-19
relative error = 6.7678865016926399243820822906297e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 0.7682326937233461059504502011517
y[1] (numeric) = 0.76823269372334610647115354621863
absolute error = 5.2070334506693e-19
relative error = 6.7779378477537730244098488177042e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.4MB, time=23.88
NO POLE
x[1] = 0.33
y[1] (analytic) = 0.7687363704706400159324996218269
y[1] (numeric) = 0.76873637047064001645431380404232
absolute error = 5.2181418221542e-19
relative error = 6.7879471072241846256175508243080e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 0.7692401654933178081504499563123
y[1] (numeric) = 0.76924016549331780867337283798603
absolute error = 5.2292288167373e-19
relative error = 6.7979144242731627985432032229478e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.332
y[1] (analytic) = 0.7697440787737160243421070834381
y[1] (numeric) = 0.76974407877371602486613653193899
absolute error = 5.2402944850089e-19
relative error = 6.8078399425394022262305926813880e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 0.7702481102941857298829192589228
y[1] (numeric) = 0.77024811029418573040805314666527
absolute error = 5.2513388774247e-19
relative error = 6.8177238051502949435886403900059e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 0.7707522600370924990045442844134
y[1] (numeric) = 0.77075226003709249953078048884316
absolute error = 5.2623620442976e-19
relative error = 6.8275661547127328685391823675329e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 0.7712565279848164000361451607332
y[1] (numeric) = 0.77125652798481640056348156431278
absolute error = 5.2733640357958e-19
relative error = 6.8373671333121161567117654436911e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.4MB, time=24.29
NO POLE
x[1] = 0.336
y[1] (analytic) = 0.7717609141197519806683705410363
y[1] (numeric) = 0.77176091411975198119680503123195
absolute error = 5.2843449019565e-19
relative error = 6.8471268825315802322805867772072e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 0.7722654184243082532399764028416
y[1] (numeric) = 0.77226541842430825376950687210858
absolute error = 5.2953046926698e-19
relative error = 6.8568455434325609601876712642251e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 0.7727700408809086800470454608894
y[1] (numeric) = 0.77277004088090868057766980665883
absolute error = 5.3062434576943e-19
relative error = 6.8665232565764584526813331350944e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 0.7732747814719911586747609454703
y[1] (numeric) = 0.77327478147199115920647707013447
absolute error = 5.3171612466417e-19
relative error = 6.8761601620061280621299554326711e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.34
y[1] (analytic) = 0.773779640180008007351691473272
y[1] (numeric) = 0.77377964018000800788449728417143
absolute error = 5.3280581089943e-19
relative error = 6.8857563992699636183994913350758e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.4MB, time=24.70
NO POLE
x[1] = 0.341
y[1] (analytic) = 0.7742846169874259503265438399263
y[1] (numeric) = 0.77428461698742595086043724933547
absolute error = 5.3389340940917e-19
relative error = 6.8953121074061090341311896323751e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 0.774789711876726103267340665267
y[1] (numeric) = 0.77478971187672610380231959038068
absolute error = 5.3497892511368e-19
relative error = 6.9048274249516428567914733671225e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 0.7752949248304039586829799238739
y[1] (numeric) = 0.77529492483040395921904228679375
absolute error = 5.3606236291985e-19
relative error = 6.9143024899474717066715046549970e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.344
y[1] (analytic) = 0.7758002558309693713671334947511
y[1] (numeric) = 0.77580025583096937190427722247186
absolute error = 5.3714372772076e-19
relative error = 6.9237374399344406660791721902814e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.345
y[1] (analytic) = 0.7763057048609465438644419649799
y[1] (numeric) = 0.77630570486094654440266498937586
absolute error = 5.3822302439596e-19
relative error = 6.9331324119583483206892906555967e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.346
y[1] (analytic) = 0.7768112719028740119589630229027
y[1] (numeric) = 0.77681127190287401249826328071422
absolute error = 5.3930025781152e-19
relative error = 6.9424875425719826089687516458923e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.4MB, time=25.11
NO POLE
x[1] = 0.347
y[1] (analytic) = 0.7773169569393046301848308768273
y[1] (numeric) = 0.77731695693930463072520630964746
absolute error = 5.4037543282016e-19
relative error = 6.9518029678381791071812788756138e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.348
y[1] (analytic) = 0.7778227599528055573590842353981
y[1] (numeric) = 0.77782275995280555790053278965863
absolute error = 5.4144855426053e-19
relative error = 6.9610788233219406375382493709097e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 0.7783286809259582421366204856551
y[1] (numeric) = 0.77832868092595824267914011261386
absolute error = 5.4251962695876e-19
relative error = 6.9703152441117538536858126521621e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 0.7788347198413584085872338044118
y[1] (numeric) = 0.77883471984135840913082246013859
absolute error = 5.4358865572679e-19
relative error = 6.9795123647994801115657359070365e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.351
y[1] (analytic) = 0.7793408766816160417946950378968
y[1] (numeric) = 0.77934087668161604233935068326113
absolute error = 5.4465564536433e-19
relative error = 6.9886703195069036766520605539793e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=244.1MB, alloc=4.4MB, time=25.51
x[1] = 0.352
y[1] (analytic) = 0.7798471514293553734778312836697
y[1] (numeric) = 0.7798471514293553740235518843261
absolute error = 5.4572060065640e-19
relative error = 6.9977892418554999459682349885401e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 0.7803535440672148676335632075812
y[1] (numeric) = 0.78035354406721486818034673395736
absolute error = 5.4678352637616e-19
relative error = 7.0068692650041123024964006192769e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 0.7808600545778472062018582270715
y[1] (numeric) = 0.78086005457784720674970265435404
absolute error = 5.4784442728254e-19
relative error = 7.0159105216198902987035427703940e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 0.7813666829439192747525577903125
y[1] (numeric) = 0.78136668294391927530146109843461
absolute error = 5.4890330812211e-19
relative error = 7.0249131439036059129109342647780e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 0.7818734291481121481940370786768
y[1] (numeric) = 0.78187342914811214874399725230451
absolute error = 5.4996017362771e-19
relative error = 7.0338772635734336079592539735671e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 0.7823802931731210765036555576927
y[1] (numeric) = 0.78238029317312107705467058621217
absolute error = 5.5101502851947e-19
relative error = 7.0428030118793423660279497719314e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.4MB, time=25.92
NO POLE
x[1] = 0.358
y[1] (analytic) = 0.7828872750016554704799568990739
y[1] (numeric) = 0.78288727500165547103202477657853
absolute error = 5.5206787750463e-19
relative error = 7.0516905196021050853215193567648e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 0.7833943746164388875165768935592
y[1] (numeric) = 0.78339437461643888806969561883622
absolute error = 5.5311872527702e-19
relative error = 7.0605399170479728620932928809693e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 0.78390159200020901739781807118
y[1] (numeric) = 0.7839015920002090179519856476978
absolute error = 5.5416757651780e-19
relative error = 7.0693513340594445209136572143551e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.361
y[1] (analytic) = 0.7844089271357176681158498421933
y[1] (numeric) = 0.78440892713571766867106427808871
absolute error = 5.5521443589541e-19
relative error = 7.0781249000159242118583206159898e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.362
y[1] (analytic) = 0.7849163800057307517094930682652
y[1] (numeric) = 0.78491638000573075226575237633028
absolute error = 5.5625930806508e-19
relative error = 7.0868607438287718759001614264135e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.363
y[1] (analytic) = 0.7854239505930282701245480695735
y[1] (numeric) = 0.78542395059302827068185026724277
absolute error = 5.5730219766927e-19
relative error = 7.0955589939482147498204142642765e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.4MB, time=26.32
NO POLE
x[1] = 0.364
y[1] (analytic) = 0.7859316388804043010956251693202
y[1] (numeric) = 0.78593163888040430165396827865819
absolute error = 5.5834310933799e-19
relative error = 7.1042197783687063520346307074971e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 0.7864394448506669840494369727006
y[1] (numeric) = 0.78643944485066698460881902038895
absolute error = 5.5938204768835e-19
relative error = 7.1128432246244748452523269095922e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 0.7869473684866385060295116726672
y[1] (numeric) = 0.78694736848663850658993068999163
absolute error = 5.6041901732443e-19
relative error = 7.1214294597891560733876839375946e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 0.7874554097711550876422867698579
y[1] (numeric) = 0.78745540977115508820374079269629
absolute error = 5.6145402283839e-19
relative error = 7.1299786104911760403426819270079e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 0.787963568687066969024542688833
y[1] (numeric) = 0.78796356868706696958702975764204
absolute error = 5.6248706880904e-19
relative error = 7.1384908028968399724847354642088e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.4MB, time=26.73
NO POLE
x[1] = 0.369
y[1] (analytic) = 0.7884718452172383958321358672659
y[1] (numeric) = 0.78847184521723839639565402706888
absolute error = 5.6351815980298e-19
relative error = 7.1469661627260825473645544269661e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.37
y[1] (analytic) = 0.7889802393445476052499909889917
y[1] (numeric) = 0.78898023934454760581453828936618
absolute error = 5.6454730037448e-19
relative error = 7.1554048152521883457598287300814e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.371
y[1] (analytic) = 0.7894887510518868120233121258048
y[1] (numeric) = 0.7894887510518868125888866208693
absolute error = 5.6557449506450e-19
relative error = 7.1638068852906213210523836821586e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.372
y[1] (analytic) = 0.7899973803221621945099726466266
y[1] (numeric) = 0.78999738032216219507657239502928
absolute error = 5.6659974840268e-19
relative error = 7.1721724972254935439023409124357e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 0.7905061271382938807540438461515
y[1] (numeric) = 0.79050612713829388132166691105695
absolute error = 5.6762306490545e-19
relative error = 7.1805017749868503470508437195430e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 0.7910149914832159345804223382854
y[1] (numeric) = 0.79101499148321593514906678736258
absolute error = 5.6864444907718e-19
relative error = 7.1887948420664758070102470297442e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.4MB, time=27.14
NO POLE
x[1] = 0.375
y[1] (analytic) = 0.7915239733398763417105163526672
y[1] (numeric) = 0.79152397333987634228018025807694
absolute error = 5.6966390540974e-19
relative error = 7.1970518215135504882591425540475e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 0.7920330726912369958989511652662
y[1] (numeric) = 0.79203307269123699646963260364923
absolute error = 5.7068143838303e-19
relative error = 7.2052728359425739361685881569678e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 0.7925422895202736850912539865094
y[1] (numeric) = 0.79254228952027368566295103897356
absolute error = 5.7169705246416e-19
relative error = 7.2134580075242238842530174604600e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.378
y[1] (analytic) = 0.7930516238099760776024787225898
y[1] (numeric) = 0.79305162380997607817518947469839
absolute error = 5.7271075210859e-19
relative error = 7.2216074580009663723789770986323e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.379
y[1] (analytic) = 0.7935610755433477083167311175649
y[1] (numeric) = 0.793561075543347708890453659324
absolute error = 5.7372254175910e-19
relative error = 7.2297213086752616932006882178788e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.4MB, time=27.54
NO POLE
x[1] = 0.38
y[1] (analytic) = 0.7940706447034059649075548755455
y[1] (numeric) = 0.79407064470340596548228730139228
absolute error = 5.7473242584678e-19
relative error = 7.2377996804232553042022389465637e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 0.7945803312731820740791394537311
y[1] (numeric) = 0.79458033127318207465487986252153
absolute error = 5.7574040879043e-19
relative error = 7.2458426936884065212117896789220e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 0.7950901352357210878283103082411
y[1] (numeric) = 0.79509013523572108840505680323765
absolute error = 5.7674649499655e-19
relative error = 7.2538504684825632714275744694395e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 0.7956000565740818697272624656426
y[1] (numeric) = 0.79560005657408187030501315450249
absolute error = 5.7775068885989e-19
relative error = 7.2618231243940724447600843405213e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 0.7961100952713370812269983837782
y[1] (numeric) = 0.79611009527133708180575137854138
absolute error = 5.7875299476318e-19
relative error = 7.2697607805855600016947514410588e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 0.7966202513105731679814311559483
y[1] (numeric) = 0.79662025131057316856118457302553
absolute error = 5.7975341707723e-19
relative error = 7.2776635557963652294514866499829e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.4MB, time=27.95
NO POLE
x[1] = 0.386
y[1] (analytic) = 0.7971305246748903461921142027108
y[1] (numeric) = 0.79713052467489034677286616287174
absolute error = 5.8075196016094e-19
relative error = 7.2855315683438375992321813373560e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.387
y[1] (analytic) = 0.7976409153474025889735586855218
y[1] (numeric) = 0.79764091534740258955530731388302
absolute error = 5.8174862836122e-19
relative error = 7.2933649361235013111905401400176e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 0.7981514233112376127390999661562
y[1] (numeric) = 0.79815142331123761332184339216917
absolute error = 5.8274342601297e-19
relative error = 7.3011637766099719350506263262711e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 0.7986620485495368636072745253181
y[1] (numeric) = 0.79866204854953686419101088275791
absolute error = 5.8373635743981e-19
relative error = 7.3089282068672612284531946354673e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 0.7991727910454555038286688430814
y[1] (numeric) = 0.79917279104545550441339627003453
absolute error = 5.8472742695313e-19
relative error = 7.3166583435380216900455581447499e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.391
y[1] (analytic) = 0.79968365078216239823320183278
y[1] (numeric) = 0.79968365078216239881891847163301
absolute error = 5.8571663885301e-19
relative error = 7.3243543028562175467365248583971e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.4MB, time=28.37
NO POLE
x[1] = 0.392
y[1] (analytic) = 0.8001946277428401006978025087165
y[1] (numeric) = 0.80019462774284010128450650614388
absolute error = 5.8670399742738e-19
relative error = 7.3320162006377535289303208556023e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 0.8007057219106848406344446565529
y[1] (numeric) = 0.80070572191068484122213416350564
absolute error = 5.8768950695274e-19
relative error = 7.3396441522906233048604383191267e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.394
y[1] (analytic) = 0.8012169332689065094985003635128
y[1] (numeric) = 0.80121693326890651008717353520679
absolute error = 5.8867317169399e-19
relative error = 7.3472382728139119366362922145990e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.395
y[1] (analytic) = 0.8017282618007286473173743535422
y[1] (numeric) = 0.80172826180072864790702934944659
absolute error = 5.8965499590439e-19
relative error = 7.3547986767984246026666917017826e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.396
y[1] (analytic) = 0.8022397074893884292393811603581
y[1] (numeric) = 0.80223970748938842983001614418414
absolute error = 5.9063498382604e-19
relative error = 7.3623254784337957215575834310561e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.4MB, time=28.77
NO POLE
x[1] = 0.397
y[1] (analytic) = 0.8027512703181366521028272588598
y[1] (numeric) = 0.80275127031813665269444039854866
absolute error = 5.9161313968886e-19
relative error = 7.3698187914968861065379271477423e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
y[1] (analytic) = 0.803262950270237721025260362678
y[1] (numeric) = 0.80326295027023772161784983038959
absolute error = 5.9258946771159e-19
relative error = 7.3772787293653728319078741691117e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.399
y[1] (analytic) = 0.8037747473289696360128481827122
y[1] (numeric) = 0.80377474732896963660641215481382
absolute error = 5.9356397210162e-19
relative error = 7.3847054050167318218191459482953e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 0.8042866614776239785898490283349
y[1] (numeric) = 0.80428666147762397918438568539012
absolute error = 5.9453665705522e-19
relative error = 7.3920989310321986036650572836078e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 0.8047986926995058984481367195416
y[1] (numeric) = 0.80479869269950589904364424629813
absolute error = 5.9550752675653e-19
relative error = 7.3994594195853072915685744736911e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 0.8053108409779341001167423646828
y[1] (numeric) = 0.80531084097793410071321895006176
absolute error = 5.9647658537896e-19
relative error = 7.4067869824604005548356788178004e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.4MB, time=29.18
NO POLE
x[1] = 0.403
y[1] (analytic) = 0.8058231062962408296513756445515
y[1] (numeric) = 0.80582310629624083024881948163585
absolute error = 5.9744383708435e-19
relative error = 7.4140817310432722648841912496143e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.404
y[1] (analytic) = 0.8063354886377718613438883294862
y[1] (numeric) = 0.80633548863777186194229761551009
absolute error = 5.9840928602389e-19
relative error = 7.4213437763336738641655711783553e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 0.8068479879858864844516428418212
y[1] (numeric) = 0.80684798798588648505101577815766
absolute error = 5.9937293633646e-19
relative error = 7.4285732289257977101983601711686e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 0.8073606043239574899467487614365
y[1] (numeric) = 0.80736060432395749054708355358714
absolute error = 6.0033479215064e-19
relative error = 7.4357701990342924269066938200832e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 0.807873337635371157285130257373
y[1] (numeric) = 0.80787333763537115788642511495659
absolute error = 6.0129485758359e-19
relative error = 7.4429347964814364269108491375802e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.4MB, time=29.59
NO POLE
x[1] = 0.408
y[1] (analytic) = 0.8083861879035272411953875134378
y[1] (numeric) = 0.80838618790352724179764065017894
absolute error = 6.0225313674114e-19
relative error = 7.4500671306993292287400236958698e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 0.8088991551118389584874153004696
y[1] (numeric) = 0.80889915511183895909062493418803
absolute error = 6.0320963371843e-19
relative error = 7.4571673107388747052165786938672e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.41
y[1] (analytic) = 0.8094122392437329748807419324471
y[1] (numeric) = 0.80941223924373297548490628504652
absolute error = 6.0416435259942e-19
relative error = 7.4642354452647703165201807172389e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 0.8099254402826493918525519279037
y[1] (numeric) = 0.80992544028264939245766922536022
absolute error = 6.0511729745652e-19
relative error = 7.4712716425519978899137444896565e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.412
y[1] (analytic) = 0.8104387582120417335053557821674
y[1] (numeric) = 0.81043875821204173411142425451945
absolute error = 6.0606847235205e-19
relative error = 7.4782760105049089854868748406498e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.413
y[1] (analytic) = 0.8109521930153769334542703397805
y[1] (numeric) = 0.81095219301537693406128822111752
absolute error = 6.0701788133702e-19
relative error = 7.4852486566431910857637093721666e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.4MB, time=30.00
NO POLE
x[1] = 0.414
y[1] (analytic) = 0.8114657446761353217338733400484
y[1] (numeric) = 0.81146574467613532234183886849952
absolute error = 6.0796552845112e-19
relative error = 7.4921896881027992165537498031866e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 0.8119794131778106117245957920491
y[1] (numeric) = 0.81197941317781061233350720977282
absolute error = 6.0891141772372e-19
relative error = 7.4990992116493236532256756989519e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 0.8124931985039098870986159185909
y[1] (numeric) = 0.81249319850390988770847147176395
absolute error = 6.0985555317305e-19
relative error = 7.5059773336689076001669254911156e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.417
y[1] (analytic) = 0.8130071006379535887852184915294
y[1] (numeric) = 0.81300710063795358939601643033611
absolute error = 6.1079793880671e-19
relative error = 7.5128241601755591865110487385414e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 0.8135211195634755019555834635663
y[1] (numeric) = 0.81352111956347550256732204218769
absolute error = 6.1173857862139e-19
relative error = 7.5196397968087257375404677380752e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.419
y[1] (analytic) = 0.8140352552640227430269678841331
y[1] (numeric) = 0.81403525526402274363964536073609
absolute error = 6.1267747660299e-19
relative error = 7.5264243488357918825461848465237e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.4MB, time=30.41
NO POLE
x[1] = 0.42
y[1] (analytic) = 0.8145495077231557466862451692259
y[1] (numeric) = 0.81454950772315574729985980595293
absolute error = 6.1361463672703e-19
relative error = 7.5331779211581293063192006329583e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 0.8150638769244482529327658770997
y[1] (numeric) = 0.81506387692444825354731594005753
absolute error = 6.1455006295783e-19
relative error = 7.5399006183020336017492742069979e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.422
y[1] (analytic) = 0.8155783628514872941405042235466
y[1] (numeric) = 0.81557836285148729475598798279592
absolute error = 6.1548375924932e-19
relative error = 7.5465925444296820792343030640566e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 0.8160929654878731821394546520879
y[1] (numeric) = 0.81609296548787318275587038163299
absolute error = 6.1641572954509e-19
relative error = 7.5532538033407383084808424858014e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 0.8166076848172194953162428557894
y[1] (numeric) = 0.81660768481721949593358883356712
absolute error = 6.1734597777772e-19
relative error = 7.5598844984651344592481633798507e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.4MB, time=30.81
NO POLE
x[1] = 0.425
y[1] (analytic) = 0.8171225208231530657339157285699
y[1] (numeric) = 0.81712252082315306635219023643935
absolute error = 6.1827450786945e-19
relative error = 7.5664847328722807631189918506457e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 0.8176374734893139662708748048227
y[1] (numeric) = 0.81763747348931396689007612855468
absolute error = 6.1920132373198e-19
relative error = 7.5730546092696006025060958486111e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 0.8181525427993554977789178268946
y[1] (numeric) = 0.81815254279935549839904425616117
absolute error = 6.2012642926657e-19
relative error = 7.5795942300047387511659759370746e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 0.8186677287369441762603531604804
y[1] (numeric) = 0.81866772873694417688140298884444
absolute error = 6.2104982836404e-19
relative error = 7.5861036970665406025870346084934e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.429
y[1] (analytic) = 0.8191830312857597200641518582865
y[1] (numeric) = 0.81918303128575972068612338319122
absolute error = 6.2197152490472e-19
relative error = 7.5925831120854181552579840683194e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.43
y[1] (analytic) = 0.819698450429495037101102252398
y[1] (numeric) = 0.81969845042949503772399377515666
absolute error = 6.2289152275866e-19
relative error = 7.5990325763368873293510606766453e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.4MB, time=31.22
NO POLE
x[1] = 0.431
y[1] (analytic) = 0.8202139861518562120779320356516
y[1] (numeric) = 0.82021398615185621270174186143685
absolute error = 6.2380982578525e-19
relative error = 7.6054521907378995109877737736474e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 0.8207296384365624937503628719667
y[1] (numeric) = 0.82072963843656249437508930980083
absolute error = 6.2472643783413e-19
relative error = 7.6118420558589054512252758611486e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 0.8212454072673462821950626550325
y[1] (numeric) = 0.82124540726734628282070401777633
absolute error = 6.2564136274383e-19
relative error = 7.6182022719082335709128099244223e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.434
y[1] (analytic) = 0.8217612926279531161004606139672
y[1] (numeric) = 0.82176129262795311672701521831093
absolute error = 6.2655460434373e-19
relative error = 7.6245329387569289188386157991293e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 0.822277294502141660076390543594
y[1] (numeric) = 0.82227729450214166070385671004597
absolute error = 6.2746616645197e-19
relative error = 7.6308341559142459662538099265709e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.4MB, time=31.62
NO POLE
x[1] = 0.436
y[1] (analytic) = 0.8227934128736836919825275157683
y[1] (numeric) = 0.82279341287368369261090356864521
absolute error = 6.2837605287691e-19
relative error = 7.6371060225463801041708907167421e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 0.8233096477263640902755835067975
y[1] (numeric) = 0.82330964772636409090486777421442
absolute error = 6.2928426741692e-19
relative error = 7.6433486374748455003606475766811e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 0.8238259990439808213752274543724
y[1] (numeric) = 0.82382599904398082200541826823233
absolute error = 6.3019081385993e-19
relative error = 7.6495620991719465941710449163481e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 0.8243424668103449270486953356048
y[1] (numeric) = 0.82434246681034492767979103158867
absolute error = 6.3109569598387e-19
relative error = 7.6557465057670638749804312517621e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 0.8248590510092805118140559357349
y[1] (numeric) = 0.82485905100928051244605485329167
absolute error = 6.3199891755677e-19
relative error = 7.6619019550487949102810188934595e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.441
y[1] (analytic) = 0.8253757516246247303620980548297
y[1] (numeric) = 0.82537575162462473099499853716619
absolute error = 6.3290048233649e-19
relative error = 7.6680285444626052964889853557807e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.4MB, time=32.02
NO POLE
x[1] = 0.442
y[1] (analytic) = 0.8258925686402277749968049773448
y[1] (numeric) = 0.82589256864022777563060537141529
absolute error = 6.3380039407049e-19
relative error = 7.6741263711089735201256788743625e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.443
y[1] (analytic) = 0.8264095020399528630943821067657
y[1] (numeric) = 0.82640950203995286372908076326305
absolute error = 6.3469865649735e-19
relative error = 7.6801955317627194942168015934549e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 0.826926551807676224580803744691
y[1] (numeric) = 0.82692655180767622521639901803534
absolute error = 6.3559527334434e-19
relative error = 7.6862361228444941140417731393573e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.445
y[1] (analytic) = 0.8274437179272870894278450706394
y[1] (numeric) = 0.82744371792728709006433531896921
absolute error = 6.3649024832981e-19
relative error = 7.6922482404506281578981093108353e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.446
y[1] (analytic) = 0.8279610003826876751675654556086
y[1] (numeric) = 0.82796100038268767580494904077034
absolute error = 6.3738358516174e-19
relative error = 7.6982319803364910914214857431690e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.447
y[1] (analytic) = 0.8284783991577931744252093189246
y[1] (numeric) = 0.82847839915779317506348460646313
absolute error = 6.3827528753853e-19
relative error = 7.7041874379269504741821110669533e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=309.0MB, alloc=4.4MB, time=32.44
NO POLE
x[1] = 0.448
y[1] (analytic) = 0.8289959142365317424704908142506
y[1] (numeric) = 0.82899591423653174310965617339941
absolute error = 6.3916535914881e-19
relative error = 7.7101147083149714214332059758832e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 0.8295135456028444847872287067398
y[1] (numeric) = 0.82951354560284448542728251041051
absolute error = 6.4005380367071e-19
relative error = 7.7160138862537122092807761653244e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 0.8300312932406854446612978792303
y[1] (numeric) = 0.83003129324068544530223850400395
absolute error = 6.4094062477365e-19
relative error = 7.7218850661790105053584639430128e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 0.8305491571340215907868639811044
y[1] (numeric) = 0.83054915713402159142868980722086
absolute error = 6.4182582611646e-19
relative error = 7.7277283421875986015976208725537e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 0.8310671372668328048908678089355
y[1] (numeric) = 0.83106713726683280553357722028443
absolute error = 6.4270941134893e-19
relative error = 7.7335438080566730602774814194401e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.4MB, time=32.84
NO POLE
x[1] = 0.453
y[1] (analytic) = 0.8315852336231118693757260833726
y[1] (numeric) = 0.83158523362311187001931746748301
absolute error = 6.4359138411041e-19
relative error = 7.7393315572279175448719916190692e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 0.8321034461868644549802153618143
y[1] (numeric) = 0.83210344618686445562468710984577
absolute error = 6.4447174803147e-19
relative error = 7.7450916828283603381645885210348e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 0.832621774942109108458505901351
y[1] (numeric) = 0.83262177494210910910385640808335
absolute error = 6.4535050673235e-19
relative error = 7.7508242776526017802197956107254e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.456
y[1] (analytic) = 0.8331402198728772402773123611579
y[1] (numeric) = 0.83314021987287724092354002498237
absolute error = 6.4622766382447e-19
relative error = 7.7565294341818372752949701606323e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.457
y[1] (analytic) = 0.8336587809632131123311283080525
y[1] (numeric) = 0.83365878096321311297823153096104
absolute error = 6.4710322290854e-19
relative error = 7.7622072445620259663146345562588e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.458
y[1] (analytic) = 0.8341774581971738256755115632374
y[1] (numeric) = 0.83417745819717382632348875081427
absolute error = 6.4797718757687e-19
relative error = 7.7678578006324905511243467967788e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.4MB, time=33.25
NO POLE
x[1] = 0.459
y[1] (analytic) = 0.8346962515588293082783875023893
y[1] (numeric) = 0.83469625155882930892723706380096
absolute error = 6.4884956141166e-19
relative error = 7.7734811939062499533070461907186e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 0.8352151610322623027893374951687
y[1] (numeric) = 0.83521516103226230343905784315472
absolute error = 6.4972034798602e-19
relative error = 7.7790775155831121769717616129015e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 0.8357341866015683543268397439686
y[1] (numeric) = 0.83573418660156835497742929483183
absolute error = 6.5058955086323e-19
relative error = 7.7846468565416597682347621655350e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.462
y[1] (analytic) = 0.8362533282508557982834298552511
y[1] (numeric) = 0.83625332825085579893488702884847
absolute error = 6.5145717359737e-19
relative error = 7.7901893073476484179997979809762e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.463
y[1] (analytic) = 0.8367725859642457481487485501695
y[1] (numeric) = 0.8367725859642457488010717699027
absolute error = 6.5232321973320e-19
relative error = 7.7957049582534119950667721351976e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.4MB, time=33.66
NO POLE
x[1] = 0.464
y[1] (analytic) = 0.837291959725872083350443994321
y[1] (numeric) = 0.83729195972587208400363168712674
absolute error = 6.5318769280574e-19
relative error = 7.8011938991936875053299114264503e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.465
y[1] (analytic) = 0.8378114495198814371128962994305
y[1] (numeric) = 0.83781144951988143776694689577184
absolute error = 6.5405059634134e-19
relative error = 7.8066562197992407064903218956363e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 0.8383310553304331843337318225359
y[1] (numeric) = 0.83833105533043318498864375639245
absolute error = 6.5491193385655e-19
relative error = 7.8120920093841991348287550870683e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.467
y[1] (analytic) = 0.8388507771416994294780949608097
y[1] (numeric) = 0.83885077714169943013386666966857
absolute error = 6.5577170885887e-19
relative error = 7.8175013569558445050771213037026e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 0.8393706149378649944906452125399
y[1] (numeric) = 0.83937061493786499514727513738642
absolute error = 6.5662992484652e-19
relative error = 7.8228843512126940043780852324243e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.469
y[1] (analytic) = 0.8398905687031274067252473469794
y[1] (numeric) = 0.83989056870312740738273393228756
absolute error = 6.5748658530816e-19
relative error = 7.8282410805419940729926848734549e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.4MB, time=34.07
NO POLE
x[1] = 0.47
y[1] (analytic) = 0.840410638421696886892322597773
y[1] (numeric) = 0.84041063842169688755066429149676
absolute error = 6.5834169372376e-19
relative error = 7.8335716330309079560971221115530e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 0.8409308240777963370238288664851
y[1] (numeric) = 0.84093082407779633768302412004936
absolute error = 6.5919525356426e-19
relative error = 7.8388760964632735989607477238534e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 0.8414511256556613284558379943694
y[1] (numeric) = 0.84145112565566132911588526266017
absolute error = 6.6004726829077e-19
relative error = 7.8441545583109074834084431001970e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 0.8419715431395400898286782319531
y[1] (numeric) = 0.84197154313954009048957597330887
absolute error = 6.6089774135577e-19
relative error = 7.8494071057486951519951332423889e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 0.8424920765136934951046101072593
y[1] (numeric) = 0.84249207651369349576635678346201
absolute error = 6.6174667620271e-19
relative error = 7.8546338256506351964011000027576e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.475
y[1] (analytic) = 0.8430127257623950516030039645435
y[1] (numeric) = 0.84301272576239505226559804080932
absolute error = 6.6259407626582e-19
relative error = 7.8598348045883896219535097911352e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.4MB, time=34.48
NO POLE
x[1] = 0.476
y[1] (analytic) = 0.8435334908699308880529875162926
y[1] (numeric) = 0.84353349086993088871642746126302
absolute error = 6.6343994497042e-19
relative error = 7.8650101288357676872748216046575e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 0.8440543718205997426635318219209
y[1] (numeric) = 0.84405437182059974332781610765359
absolute error = 6.6428428573269e-19
relative error = 7.8701598843667961103038417315836e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.478
y[1] (analytic) = 0.8445753685987129512109441770946
y[1] (numeric) = 0.84457536859871295187607127905458
absolute error = 6.6512710195998e-19
relative error = 7.8752841568601908134520008021357e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 0.8450964811885944351437364679326
y[1] (numeric) = 0.84509648118859443580970486498326
absolute error = 6.6596839705066e-19
relative error = 7.8803830316983696130436975153782e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.48
y[1] (analytic) = 0.845617709574580689704837614459
y[1] (numeric) = 0.84561770957458069037164578885328
absolute error = 6.6680817439428e-19
relative error = 7.8854565939701351637600107042812e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.4MB, time=34.89
NO POLE
x[1] = 0.481
y[1] (analytic) = 0.8461390537410207720711187976299
y[1] (numeric) = 0.84613905374102077273876523500132
absolute error = 6.6764643737142e-19
relative error = 7.8905049284696849299951010196107e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.482
y[1] (analytic) = 0.8466605136722762895102002340184
y[1] (numeric) = 0.84666051367227629017868342337199
absolute error = 6.6848318935359e-19
relative error = 7.8955281196962160109233531698510e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 0.8471820893527213875545083318205
y[1] (numeric) = 0.84718208935272138822382676552453
absolute error = 6.6931843370403e-19
relative error = 7.9005262518641555204452110375289e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 0.8477037807667427381925521312454
y[1] (numeric) = 0.84770378076674273886270430502226
absolute error = 6.7015217377686e-19
relative error = 7.9054994088938894863074656385954e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 0.8482255878987395280773880015639
y[1] (numeric) = 0.8482255878987395287483724144809
absolute error = 6.7098441291700e-19
relative error = 7.9104476744116043627654010869717e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 0.848747510733123446752241636125
y[1] (numeric) = 0.8487475107331234474240567905864
absolute error = 6.7181515446140e-19
relative error = 7.9153711317645642737232546912148e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=335.7MB, alloc=4.4MB, time=35.30
NO POLE
x[1] = 0.487
y[1] (analytic) = 0.8492695492543186748932564555087
y[1] (numeric) = 0.84926954925431867556590085724644
absolute error = 6.7264440173774e-19
relative error = 7.9202698640065422425605697351480e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 0.8497917034467618725693375976481
y[1] (numeric) = 0.84979170344676187324280975571331
absolute error = 6.7347215806521e-19
relative error = 7.9251439539077823248300119417113e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.489
y[1] (analytic) = 0.8503139732949021675190607422556
y[1] (numeric) = 0.85031397329490216819335916900996
absolute error = 6.7429842675436e-19
relative error = 7.9299934839539885265062447131831e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 0.8508363587832011434446150851991
y[1] (numeric) = 0.85083635878320114411973829630607
absolute error = 6.7512321110697e-19
relative error = 7.9348185363455531237519538756401e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.491
y[1] (analytic) = 0.851358859896132828322749846611
y[1] (numeric) = 0.85135885989613282899869636102745
absolute error = 6.7594651441645e-19
relative error = 7.9396191930030137817225915195069e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.4MB, time=35.69
NO POLE
x[1] = 0.492
y[1] (analytic) = 0.8518814766181836827326937644736
y[1] (numeric) = 0.85188147661818368340946210444087
absolute error = 6.7676833996727e-19
relative error = 7.9443955355611046421458580053846e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 0.8524042089338525882010170932022
y[1] (numeric) = 0.85240420893385258887860578423764
absolute error = 6.7758869103544e-19
relative error = 7.9491476453751480041665834342263e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.494
y[1] (analytic) = 0.8529270568276508355634056943552
y[1] (numeric) = 0.8529270568276508362418132652437
absolute error = 6.7840757088850e-19
relative error = 7.9538756035216781900020947374267e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 0.8534500202841021133433168740263
y[1] (numeric) = 0.85345002028410211402254185681205
absolute error = 6.7922498278575e-19
relative error = 7.9585794908018758350400043091329e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 0.8539730992877424961474866887285
y[1] (numeric) = 0.85397309928774249682752761870586
absolute error = 6.8004092997736e-19
relative error = 7.9632593877318749900154919903750e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.497
y[1] (analytic) = 0.8544962938231204330782585086519
y[1] (numeric) = 0.85449629382312043375911392435746
absolute error = 6.8085541570556e-19
relative error = 7.9679153745574482511691350752825e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.4MB, time=36.09
NO POLE
x[1] = 0.498
y[1] (analytic) = 0.8550196038747967361627026940869
y[1] (numeric) = 0.85501960387479673684437113729091
absolute error = 6.8166844320401e-19
relative error = 7.9725475312473525133467648116754e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 0.8555430294273445687984973075261
y[1] (numeric) = 0.85554302942734456948097732322403
absolute error = 6.8248001569793e-19
relative error = 7.9771559374955829786237175363459e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 0.8560665704653494342165398505159
y[1] (numeric) = 0.85606657046534943489982998692012
absolute error = 6.8329013640422e-19
relative error = 7.9817406727235026755979664750660e-17 %
Correct digits = 18
h = 0.001
Finished!
diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2));
Iterations = 500
Total Elapsed Time = 36 Seconds
Elapsed Time(since restart) = 36 Seconds
Time to Timeout = 2 Minutes 23 Seconds
Percent Done = 100.2 %
> quit
memory used=345.0MB, alloc=4.4MB, time=36.26