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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_large_float, array_pole,
glob_type_given_pole, array_given_rad_poles, array_given_ord_poles,
array_complex_poles, array_poles, array_real_poles, array_x;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_x[1] - array_given_rad_poles[1, 1], 2.0)
+ expt(array_given_rad_poles[1, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_poles[1, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if 0. < array_real_poles[1, 1] and
array_real_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_real_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if 0. < array_complex_poles[1, 1] and
array_complex_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 2
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 2;
> 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 4
> # Begin Function number 5
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 2
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> if (min_size < 1.0) then # if number 2
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0,
array_y_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 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,"");
> est_tmp := 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 (est_tmp >= max_estimated_step_error) then # if number 2
> max_estimated_step_error := est_tmp;
> fi;# end if 2;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0,
array_y_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
max_estimated_step_error := 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, "");
est_tmp := 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_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2
> ret := true;
> else
> ret := false;
> fi;# end if 2;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0,
array_y_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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 2
> if (iter >= 0) then # if number 3
> 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 4
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 5
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 5;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 4;
> if (glob_iter = 1) then # if number 4
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 4;
> 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 3;
> #BOTTOM DISPLAY ALOT
> fi;# end if 2;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0,
array_y_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
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 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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 2
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 3
> glob_normmax := tmp;
> fi;# end if 3
> fi;# end if 2;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 3
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 3
> fi;# end if 2;
> if ( not glob_reached_optimal_h) then # if number 2
> 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 2;
> 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, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0,
array_y_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 9
> # Begin Function number 10
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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 2
> 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 2;
> 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, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0,
array_y_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3
> if (tmp_rad < rad_c) then # if number 4
> rad_c := tmp_rad;
> fi;# end if 4;
> elif
> (cnt = 0) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5
> fi;# end if 4;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 4
> if (rad_c < array_pole[1]) then # if number 5
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 5;
> fi;# end if 4;
> #BOTTOM radius ratio test in Henrici1
> #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]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 4
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 5
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 5
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 4;
> #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 1
> if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 4;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 4
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6
> 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) <> 0.0) then # if number 7
> if (rcs > 0.0) then # if number 8
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 8
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> fi;# end if 5;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 4;
> #BOTTOM RADII COMPLEX EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> 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 1;
> glob_h := h_new;
> fi;# end if 4;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 4
> display_poles();
> fi;# end if 4
> 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_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0,
array_y_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y_higher[1, n]) = 0. or
omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or
omniabs(array_y_higher[1, m - 1]) = 0. or
omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
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) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. 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 omniabs(rcs) <> 0. 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_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
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_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 4
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 5;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 4;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0,
array_y_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre sub FULL - CONST $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] - array_const_1[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_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #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_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1;
> array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1;
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sub FULL CONST $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #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_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2;
> array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2;
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre sub FULL CONST $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #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_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3;
> array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3;
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre sub FULL CONST $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #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_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4;
> array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4;
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre sub FULL CONST $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #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_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit FULL - NOT FULL sub $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0,
array_y_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_tmp2[1] - array_const_1[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2];
array_tmp1_g[2] := -array_tmp1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2];
array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2];
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := array_tmp2[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2];
array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2];
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := array_tmp2[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2];
array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2];
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := array_tmp2[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp3[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp3[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 13
> #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
", 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
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", 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
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", 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, " |
")
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 Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,m,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_int(ALWAYS,"m",4, m ,4," ");
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, m, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_int(ALWAYS, "m", 4, m, 4, " ");
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> 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")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
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, "
")
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 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> 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 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> 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 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> 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 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> 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 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> 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(2.0 - cos(x) - x);
> end;
exact_soln_y := proc(x) return 2.0 - cos(x) - x end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_estimated_step_error := 0.0;
> glob_ratio_of_radius := 0.1;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_min_h := 0.000001;
> glob_type_given_pole := 0;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/sub_sin_cpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin(x) - 1,0;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(2.0 - cos(x) - x);");
> 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 := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(2 + 1),[]);
> array_last_rel_error:= Array(0..(2 + 1),[]);
> array_type_pole:= Array(0..(2 + 1),[]);
> array_type_real_pole:= Array(0..(2 + 1),[]);
> array_type_complex_pole:= Array(0..(2 + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= 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_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..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 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 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_const_0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0[1] := 0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> found_h := false;
> glob_h := glob_min_h;
> if (glob_max_h < glob_h) then # if number 4
> glob_h := glob_max_h;
> fi;# end if 4;
> if (glob_display_interval < glob_h) then # if number 4
> glob_h := glob_display_interval;
> fi;# end if 4;
> best_h := glob_h;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> 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,"");
> estimated_step_error := 0.0;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> 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 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
> ;
> atomall();
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4
> found_h := true;
> glob_h := glob_max_h;
> best_h := glob_h;
> elif
> ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5
> glob_h := glob_h/2.0;
> best_h := glob_h;
> found_h := true;
> else
> glob_h := glob_h*2.0;
> best_h := glob_h;
> fi;# end if 5;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 5
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 5;
> if (opt_iter > 100) then # if number 5
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 5;
> if (glob_display_interval < glob_h) then # if number 5
> glob_h := glob_display_interval;
> fi;# end if 5;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 5
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 5;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 5
> 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 1
> 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 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> 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 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 6
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 6;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 6
> #left paren 0004C
> check_for_pole();
> fi;# end if 6;#was right paren 0004C
> if (reached_interval()) then # if number 6
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 6;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> 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 2;
> #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 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> 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 2
> 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 2;
> #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 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> 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 2
> 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 2;
> #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 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> 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 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 6
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 6;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 6;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sin(x) - 1,0;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 6
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T05:18:56-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sub_sin_c")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin(x) - 1,0;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 7
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 7;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"sub_sin_c diffeq.mxt")
> ;
> logitem_str(html_log_file,"sub_sin_c maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0,
array_y_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_y,
array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_estimated_step_error := 0.;
glob_ratio_of_radius := 0.1;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_min_h := 0.1*10^(-5);
glob_type_given_pole := 0;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sub_sin_cpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) - 1,0;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(2.0 - cos(x) - x);");
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.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1_g := 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_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 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 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 <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_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_g[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_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 <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
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_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[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_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_0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0[term] := 0.; term := term + 1
end do;
array_const_0[1] := 0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
found_h := false;
glob_h := glob_min_h;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
best_h := glob_h;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
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, "");
estimated_step_error := 0.;
while opt_iter <= 100 and not found_h 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();
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if est_needed_step_err < estimated_step_error and opt_iter = 1 or
glob_max_h <= glob_h then
found_h := true; glob_h := glob_max_h; best_h := glob_h
elif est_needed_step_err < estimated_step_error and not found_h
then glob_h := glob_h/2.0; best_h := glob_h; found_h := true
else glob_h := glob_h*2.0; best_h := glob_h
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = sin(x) - 1,0;");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T05:18:56-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sub_sin_c");
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) - 1,0;")
;
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_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, " 189 | ");
logitem_str(html_log_file, "sub_sin_c diffeq.mxt");
logitem_str(html_log_file, "sub_sin_c maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 13
> main();
##############ECHO OF PROBLEM#################
##############temp/sub_sin_cpostode.ode#################
diff ( y , x , 1 ) = sin(x) - 1,0;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(2.0 - cos(x) - x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 4.9
estimated_steps = 4900000
step_error = 2.0408163265306122448979591836735e-17
est_needed_step_err = 2.0408163265306122448979591836735e-17
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.4672086055323049562331277806886e-183
estimated_step_error = 2.4672086055323049562331277806886e-183
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.6557156646065677204134289038210e-175
estimated_step_error = 1.6557156646065677204134289038210e-175
best_h = 4.00e-06
opt_iter = 3
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.1111319694584368636820923174825e-167
estimated_step_error = 1.1111319694584368636820923174825e-167
best_h = 8.000e-06
opt_iter = 4
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.4566803670241957246681619817550e-160
estimated_step_error = 7.4566803670241957246681619817550e-160
best_h = 1.60000e-05
opt_iter = 5
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.0040934120378230048946847695115e-152
estimated_step_error = 5.0040934120378230048946847695115e-152
best_h = 3.200000e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.3581901424816281269073121711214e-144
estimated_step_error = 3.3581901424816281269073121711214e-144
best_h = 6.4000000e-05
opt_iter = 7
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.2536431215809227087580736291234e-136
estimated_step_error = 2.2536431215809227087580736291234e-136
best_h = 0.000128
opt_iter = 8
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.5123941176543087498746423194483e-128
estimated_step_error = 1.5123941176543087498746423194483e-128
best_h = 0.000256
opt_iter = 9
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.0149502701580566739311213784162e-120
estimated_step_error = 1.0149502701580566739311213784162e-120
best_h = 0.000512
opt_iter = 10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.8112127244081165253087202414269e-113
estimated_step_error = 6.8112127244081165253087202414269e-113
best_h = 0.001024
opt_iter = 11
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.5709231343600303584753702483543e-105
estimated_step_error = 4.5709231343600303584753702483543e-105
best_h = 0.002048
opt_iter = 12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.0674887502340254951354356814932e-97
estimated_step_error = 3.0674887502340254951354356814932e-97
best_h = 0.004096
opt_iter = 13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.0585490116180929098885606683401e-89
estimated_step_error = 2.0585490116180929098885606683401e-89
best_h = 0.008192
opt_iter = 14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.3814583197402461309888420940037e-81
estimated_step_error = 1.3814583197402461309888420940037e-81
best_h = 0.016384
opt_iter = 15
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 9.2706681184281159182706538798633e-74
estimated_step_error = 9.2706681184281159182706538798633e-74
best_h = 0.032768
opt_iter = 16
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.2212490020161221570851682852212e-66
estimated_step_error = 6.2212490020161221570851682852212e-66
best_h = 0.065536
opt_iter = 17
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.1747508750792467142506979498165e-58
estimated_step_error = 4.1747508750792467142506979498165e-58
best_h = 0.131072
opt_iter = 18
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.8012747543996062244493916551861e-50
estimated_step_error = 2.8012747543996062244493916551861e-50
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 0.9049958347219742339044380121961
y[1] (numeric) = 0.9049958347219742339044380121961
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 0.8960439020433031496421603885802
y[1] (numeric) = 0.89604390204330314964216038858012
absolute error = 8e-32
relative error = 8.9281339695043018982492888831759e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=4000928, alloc=3145152, time=0.16
x[1] = 0.12
y[1] (analytic) = 0.8871913641461337477519018321424
y[1] (numeric) = 0.88719136414613374775190183214233
absolute error = 7e-32
relative error = 7.8900677834449646703150802112003e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 0.8784381062852119604054878288482
y[1] (numeric) = 0.87843810628521196040548782884815
absolute error = 5e-32
relative error = 5.6919206535156799674834546373504e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 0.8697840037873628281010517729886
y[1] (numeric) = 0.86978400378736282810105177298856
absolute error = 4e-32
relative error = 4.5988429110934591878542288753573e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 0.8612289220639577132650190013457
y[1] (numeric) = 0.86122892206395771326501900134562
absolute error = 8e-32
relative error = 9.2890517202183480475059375536191e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 0.8527727166243730509590474759817
y[1] (numeric) = 0.85277271662437305095904747598162
absolute error = 8e-32
relative error = 9.3811631681502513398392823985365e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 0.8444152330904392908280700097875
y[1] (numeric) = 0.84441523309043929082807000978745
absolute error = 5e-32
relative error = 5.9212574620435414081668567452419e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 0.8361563072118785854072839753885
y[1] (numeric) = 0.83615630721187858540728397538842
absolute error = 8e-32
relative error = 9.5675891349496604925193324540079e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 0.8279957648827296810321224958101
y[1] (numeric) = 0.82799576488272968103212249581004
absolute error = 6e-32
relative error = 7.2464138761021190327268752107331e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 0.8199334221587583688758034832518
y[1] (numeric) = 0.81993342215875836887580348325178
absolute error = 2e-32
relative error = 2.4392224367855479668575624085650e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 0.8119690852758517550838614319006
y[1] (numeric) = 0.8119690852758517550838614319006
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 0.8041025506693945105939770189553
y[1] (numeric) = 0.80410255066939451059397701895525
absolute error = 5e-32
relative error = 6.2181123487764461479103951291073e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 0.7963336049946251630322693519284
y[1] (numeric) = 0.79633360499462516303226935192835
absolute error = 5e-32
relative error = 6.2787755893257165696901522161668e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 0.7886620251479703950738247530366
y[1] (numeric) = 0.78866202514797039507382475303657
absolute error = 3e-32
relative error = 3.8039108063268721670251860427544e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 0.7810875782893552158554045505058
y[1] (numeric) = 0.78108757828935521585540455050576
absolute error = 4e-32
relative error = 5.1210646682671904270177260658908e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 0.7736100218654867744417823535499
y[1] (numeric) = 0.77361002186548677444178235354988
absolute error = 2e-32
relative error = 2.5852819165620305389142045360047e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 0.7662291036341094869837672905078
y[1] (numeric) = 0.76622910363410948698376729050774
absolute error = 6e-32
relative error = 7.8305561241969297442463337700022e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 0.7589445616892290520754099464035
y[1] (numeric) = 0.75894456168922905207540994640347
absolute error = 3e-32
relative error = 3.9528578916524780290869744474147e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 0.7517561244873028319298752220681
y[1] (numeric) = 0.75175612448730283192987522206808
absolute error = 2e-32
relative error = 2.6604372546535602171370904575310e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 0.744663510874393980357689772432
y[1] (numeric) = 0.74466351087439398035768977243189
absolute error = 1.1e-31
relative error = 1.4771772538020093147228601916431e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 0.7376664301142866021571945637978
y[1] (numeric) = 0.73766643011428660215719456379773
absolute error = 7e-32
relative error = 9.4893839738857176258646676136850e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 0.7307645819175591324246927262339
y[1] (numeric) = 0.73076458191755913242469272623385
absolute error = 5e-32
relative error = 6.8421487900792552126362806750896e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 0.7239576564716130284705894216338
y[1] (numeric) = 0.72395765647161302847058942163374
absolute error = 6e-32
relative error = 8.2877775327945093773112493957858e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 0.7172453344716537714973559399734
y[1] (numeric) = 0.71724533447165377149735593997337
absolute error = 3e-32
relative error = 4.1826692427492714462626484260157e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=8002340, alloc=4324584, time=0.32
x[1] = 0.35
y[1] (analytic) = 0.7106272871526210799649676426963
y[1] (numeric) = 0.71062728715262107996496764269628
absolute error = 2e-32
relative error = 2.8144148643851062306985224707337e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 0.7041031763220651416490876318753
y[1] (numeric) = 0.7041031763220651416490876318752
absolute error = 1.0e-31
relative error = 1.4202463980116859217913254843573e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 0.6976726543939655767961870955091
y[1] (numeric) = 0.69767265439396557679618709550906
absolute error = 4e-32
relative error = 5.7333478312613615993668419081333e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 0.6913353644234897505074691922754
y[1] (numeric) = 0.69133536442348975050746919227538
absolute error = 2e-32
relative error = 2.8929519635782214877614243967053e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 0.6850909401426869585493232471189
y[1] (numeric) = 0.68509094014268695854932324711884
absolute error = 6e-32
relative error = 8.7579613864844762458398821962122e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 0.6789390059971149172014732679482
y[1] (numeric) = 0.67893900599711491720147326794814
absolute error = 6e-32
relative error = 8.8373181493500704753702101804559e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 0.672879177183394894524357941723
y[1] (numeric) = 0.67287917718339489452435794172292
absolute error = 8e-32
relative error = 1.1889207262271366272577509609043e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 0.6669110596876917275639112103343
y[1] (numeric) = 0.66691105968769172756391121033427
absolute error = 3e-32
relative error = 4.4983509516319495653819418900390e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 0.6610342503251148775240895223366
y[1] (numeric) = 0.66103425032511487752408952233649
absolute error = 1.1e-31
relative error = 1.6640590097396461058646163382819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 0.6552483367800365828344626110016
y[1] (numeric) = 0.65524833678003658283446261100157
absolute error = 3e-32
relative error = 4.5784168102468365467824666066804e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 0.6495528976473230783311593885136
y[1] (numeric) = 0.64955289764732307833115938851349
absolute error = 1.1e-31
relative error = 1.6934725470153297427241367605211e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 0.6439475024744747574636100964996
y[1] (numeric) = 0.64394750247447475746361009649953
absolute error = 7e-32
relative error = 1.0870451353722690938278465704151e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 0.6384317118046710635459807234666
y[1] (numeric) = 0.63843171180467106354598072346654
absolute error = 6e-32
relative error = 9.3980294040213765074550308448807e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 0.6330050772207158056000451688413
y[1] (numeric) = 0.63300507722071580560004516884119
absolute error = 1.1e-31
relative error = 1.7377427758236648444897403539725e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 0.6276671413898785042945318408633
y[1] (numeric) = 0.62766714138987850429453184086327
absolute error = 3e-32
relative error = 4.7796033951322224420615047706139e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 0.6224174381096272838837184173962
y[1] (numeric) = 0.6224174381096272838837184173961
absolute error = 1.0e-31
relative error = 1.6066387905794319233172811479377e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 0.6172554923542487368941915264245
y[1] (numeric) = 0.61725549235424873689419152642442
absolute error = 8e-32
relative error = 1.2960597514470919768024807608486e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 0.6121808203223500996121524280115
y[1] (numeric) = 0.61218082032235009961215242801142
absolute error = 8e-32
relative error = 1.3068034368975358978783035927723e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 0.6071929294852389881933049814358
y[1] (numeric) = 0.60719292948523898819330498143573
absolute error = 7e-32
relative error = 1.1528460988395240772912730487331e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 0.6022913186361758574620312210822
y[1] (numeric) = 0.60229131863617585746203122108214
absolute error = 6e-32
relative error = 9.9619566385023728558896124778868e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 0.5974754779404942571950182023822
y[1] (numeric) = 0.59747547794049425719501820238216
absolute error = 4e-32
relative error = 6.6948354328918268263912582242656e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 0.5927448889865838739054744961337
y[1] (numeric) = 0.59274488898658387390547449613361
absolute error = 9e-32
relative error = 1.5183597812858922960406794776133e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = 0.588099024837731259866243636084
y[1] (numeric) = 0.58809902483773125986624363608392
absolute error = 8e-32
relative error = 1.3603151275769189073843417601790e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=12003892, alloc=4390108, time=0.48
x[1] = 0.58
y[1] (analytic) = 0.58353735008481306534211267195
y[1] (numeric) = 0.58353735008481306534211267194991
absolute error = 9e-32
relative error = 1.5423177280240781601294160493920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 0.5790593208998365047520034775093
y[1] (numeric) = 0.57905932089983650475200347750925
absolute error = 5e-32
relative error = 8.6346939243291813341822545309234e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 0.5746643850903217027590475010446
y[1] (numeric) = 0.57466438509032170275904750104455
absolute error = 5e-32
relative error = 8.7007305998511378027606434457198e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 0.5703519821545204820992534213452
y[1] (numeric) = 0.5703519821545204820992534213451
absolute error = 1.0e-31
relative error = 1.7533032781309397329261946605194e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 0.5661215433374660713160003456393
y[1] (numeric) = 0.56612154333746607131600034563923
absolute error = 7e-32
relative error = 1.2364835930342413053375754955958e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 0.5619724916878481274762910342229
y[1] (numeric) = 0.56197249168784812747629103422287
absolute error = 3e-32
relative error = 5.3383395884551101812714856795641e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.58
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 0.5579042421157073864138892207397
y[1] (numeric) = 0.5579042421157073864138892207396
absolute error = 1.0e-31
relative error = 1.7924222913375939187057342696076e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 0.5539162014509441710823954293201
y[1] (numeric) = 0.55391620145094417108239542932002
absolute error = 8e-32
relative error = 1.4442617816638271030487911596172e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 0.5500077685026349072161829087698
y[1] (numeric) = 0.55000776850263490721618290876968
absolute error = 1.2e-31
relative error = 2.1817873650529195984031730415193e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 0.5461783341191507146970578551619
y[1] (numeric) = 0.54617833411915071469705785516181
absolute error = 9e-32
relative error = 1.6478134407353878135505839274880e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 0.5424272812490720628176059159557
y[1] (numeric) = 0.54242728124907206281760591595561
absolute error = 9e-32
relative error = 1.6592085817061577622047609656693e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.17
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 0.5387539850028933980264606845022
y[1] (numeric) = 0.53875398500289339802646068450216
absolute error = 4e-32
relative error = 7.4245390500053894791429415055099e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 0.5351578127155115737441400098081
y[1] (numeric) = 0.53515781271551157374414000980806
absolute error = 4e-32
relative error = 7.4744307285791023948517216728152e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 0.5316381240094918334585420558604
y[1] (numeric) = 0.53163812400949183345854205586037
absolute error = 3e-32
relative error = 5.6429361712713405587991832667478e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 0.528194270859105020554513037748
y[1] (numeric) = 0.52819427085910502055451303774798
absolute error = 2e-32
relative error = 3.7864855988441737767727175056595e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 0.5248255976551296112098678414497
y[1] (numeric) = 0.52482559765512961120986784144959
absolute error = 1.1e-31
relative error = 2.0959343540305472972625648217509e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 0.5215314412704120902085754393012
y[1] (numeric) = 0.52153144127041209020857543930109
absolute error = 1.1e-31
relative error = 2.1091729336978825374161909507476e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.26
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 0.5183111311261791136881612469999
y[1] (numeric) = 0.51831113112617911368816124699984
absolute error = 6e-32
relative error = 1.1576058548006261498579136476086e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.63
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 0.515163989259094827660311633333
y[1] (numeric) = 0.51516398925909482766031163333292
absolute error = 8e-32
relative error = 1.5529035737737691835832167240913e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.01
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 0.5120893303890566366287094346757
y[1] (numeric) = 0.51208933038905663662870943467558
absolute error = 1.2e-31
relative error = 2.3433411492645386186692935814969e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.39
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 0.5090864619877226427837349762354
y[1] (numeric) = 0.50908646198772264278373497623536
absolute error = 4e-32
relative error = 7.8572114928808807966726908606078e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.21
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 0.506154684347763903087219138915
y[1] (numeric) = 0.50615468434776390308721913891497
absolute error = 3e-32
relative error = 5.9270418565143393797324927547233e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.83
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 0.5032932906528345790792500183577
y[1] (numeric) = 0.5032932906528345790792500183576
absolute error = 1.0e-31
relative error = 1.9869130357427862085023691031676e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.45
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=16004576, alloc=4390108, time=0.64
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 0.5005015670482529824503607593199
y[1] (numeric) = 0.50050156704825298245036075931982
absolute error = 8e-32
relative error = 1.5983965938769430410333549535385e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.09
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 0.4977787927123864483334420215631
y[1] (numeric) = 0.49777879271238644833344202156299
absolute error = 1.1e-31
relative error = 2.2098169229069051435666913427745e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 0.4951242399287328978875370821356
y[1] (numeric) = 0.49512423992873289788753708213547
absolute error = 1.3e-31
relative error = 2.6256036266516039727067954172373e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = 0.4925371741586918820773289631291
y[1] (numeric) = 0.49253717415869188207732896312907
absolute error = 3e-32
relative error = 6.0909108132281237709860143993000e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.03
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 0.4900168541150178296045839705385
y[1] (numeric) = 0.49001685411501782960458397053846
absolute error = 4e-32
relative error = 8.1629845308567921954885630375910e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.69
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 0.4875625318359481537279693357761
y[1] (numeric) = 0.48756253183594815372796933577607
absolute error = 3e-32
relative error = 6.1530568985752587412277326543068e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.36
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 0.4851734527599988052223361945172
y[1] (numeric) = 0.4851734527599988052223361945171
absolute error = 1.0e-31
relative error = 2.0611185428867042996913652822289e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.03
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 0.4828488558014197919845013942779
y[1] (numeric) = 0.48284885580141979198450139427784
absolute error = 6e-32
relative error = 1.2426248768967999927070343729129e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.71
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 0.4805879734263031197964469426198
y[1] (numeric) = 0.48058797342630311979644694261968
absolute error = 1.2e-31
relative error = 2.4969413850386682431795987959761e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.39
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 0.4783900317293355435152838485929
y[1] (numeric) = 0.4783900317293355435152838485928
absolute error = 1.0e-31
relative error = 2.0903445591980519652238997765662e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 0.4762542505111884534788217738253
y[1] (numeric) = 0.47625425051118845347882177382525
absolute error = 5e-32
relative error = 1.0498593964533103877956428476113e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.77
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 0.4741798433565371582025952933256
y[1] (numeric) = 0.47417984335653715820259529332555
absolute error = 5e-32
relative error = 1.0544522442385822658826662592945e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.47
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 0.472166017712701761505092915567
y[1] (numeric) = 0.47216601771270176150509291556694
absolute error = 6e-32
relative error = 1.2707394803771778728436504077003e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.17
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 0.470211974968901770039010184776
y[1] (numeric) = 0.47021197496890177003901018477591
absolute error = 9e-32
relative error = 1.9140303690894366451859536605748e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.88
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 0.4683169105361165058338190262395
y[1] (numeric) = 0.46831691053611650583381902623947
absolute error = 3e-32
relative error = 6.4059185831356832973495847815496e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 0.4664800139275433378749491996481
y[1] (numeric) = 0.46648001392754333787494919964807
absolute error = 3e-32
relative error = 6.4311436941132899334075601029712e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 0.4647004688396456869634722451501
y[1] (numeric) = 0.46470046883964568696347224515007
absolute error = 3e-32
relative error = 6.4557714079587270423953009666421e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 0.4629774532337826991233417326401
y[1] (numeric) = 0.46297745323378269912334173263999
absolute error = 1.1e-31
relative error = 2.3759256359392294032810810887588e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 0.4613101394184124246568735913464
y[1] (numeric) = 0.46131013941841242465687359134632
absolute error = 8e-32
relative error = 1.7341912341414911778129435244533e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 0.459697694131860282599063392557
y[1] (numeric) = 0.45969769413186028259906339255696
absolute error = 4e-32
relative error = 8.7013705986800856431071470386247e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 0.4581392786256445337932686442208
y[1] (numeric) = 0.45813927862564453379326864422076
absolute error = 4e-32
relative error = 8.7309693506294754999419725049129e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 0.4566340487483504301103861919662
y[1] (numeric) = 0.45663404874835043011038619196613
absolute error = 7e-32
relative error = 1.5329562084096093554904649256233e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 0.4551811550300446524664977001626
y[1] (numeric) = 0.45518115503004465246649770016259
absolute error = 1e-32
relative error = 2.1969275066626914213270321474112e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
bytes used=20006008, alloc=4390108, time=0.81
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 0.4537797427672215962655265790078
y[1] (numeric) = 0.45377974276722159626552657900777
absolute error = 3e-32
relative error = 6.6111368958550666143050463547972e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 0.4524289521082730097091504271879
y[1] (numeric) = 0.45242895210827300970915042718784
absolute error = 6e-32
relative error = 1.3261750761176111318081266008646e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 0.4511279181394724380813624600436
y[1] (numeric) = 0.45112791813947243808136246004353
absolute error = 7e-32
relative error = 1.5516663275616325616235196550016e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 0.4498757709714658756349069318241
y[1] (numeric) = 0.44987577097146587563490693182402
absolute error = 8e-32
relative error = 1.7782686946497977551400273998995e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 0.448671635826259976086475211474
y[1] (numeric) = 0.44867163582625997608647521147391
absolute error = 9e-32
relative error = 2.0059213200375091643010971452527e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 0.4475146331246991229721029261249
y[1] (numeric) = 0.4475146331246991229721029261248
absolute error = 1.0e-31
relative error = 2.2345638018977400760840458780943e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 0.4464038785744226122286299482153
y[1] (numeric) = 0.44640387857442261222862994821523
absolute error = 7e-32
relative error = 1.5680867340029145581324564906951e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 0.4453384832582931513562624880664
y[1] (numeric) = 0.44533848325829315135626248806637
absolute error = 3e-32
relative error = 6.7364490444451919223862992191953e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 0.4443175537232878323860112060389
y[1] (numeric) = 0.44431755372328783238601120603882
absolute error = 8e-32
relative error = 1.8005140541852734154029347193041e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 0.4433401920698426896287841643465
y[1] (numeric) = 0.44334019206984268962878416434641
absolute error = 9e-32
relative error = 2.0300437814990982866627060554155e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 0.4424054960416419078248132591774
y[1] (numeric) = 0.44240549604164190782481325917737
absolute error = 3e-32
relative error = 6.7811092467025357067418170881515e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 0.4415125591158427018474232811901
y[1] (numeric) = 0.44151255911584270184742328119003
absolute error = 7e-32
relative error = 1.5854588630543036526302881528762e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 0.440660470593726845548360376606
y[1] (numeric) = 0.44066047059372684554836037660594
absolute error = 6e-32
relative error = 1.3615925185927976907337547229455e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 0.4398483156917697846673380649495
y[1] (numeric) = 0.43984831569176978466733806494944
absolute error = 6e-32
relative error = 1.3641066217483458041890119491228e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 0.4390751756331182269704005332872
y[1] (numeric) = 0.43907517563311822697040053328718
absolute error = 2e-32
relative error = 4.5550286397224082272917241325797e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 0.4383401277394670619343204416495
y[1] (numeric) = 0.43834012773946706193432044164948
absolute error = 2e-32
relative error = 4.5626669187556677853561592709009e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 0.4376422455233264223616266443769
y[1] (numeric) = 0.43764224552332642236162664437687
absolute error = 3e-32
relative error = 6.8549141009288130490342809719642e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 0.4369805987806696612969892863352
y[1] (numeric) = 0.43698059878066966129698928633516
absolute error = 4e-32
relative error = 9.1537244700598011867621918081838e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 0.4363542536839529795244770255648
y[1] (numeric) = 0.43635425368395297952447702556475
absolute error = 5e-32
relative error = 1.1458579715419595698360326238852e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 0.4357622728754974017604527545023
y[1] (numeric) = 0.43576227287549740176045275450228
absolute error = 2e-32
relative error = 4.5896584548323769246052574685806e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 0.4352037155612237634223065843026
y[1] (numeric) = 0.43520371556122376342230658430256
absolute error = 4e-32
relative error = 9.1910980007184391568292556285828e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 0.434677637604731334552461447562
y[1] (numeric) = 0.4346776376047313345524614475619
absolute error = 1.0e-31
relative error = 2.3005554311706678480361957679571e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=24007092, alloc=4390108, time=0.98
x[1] = 1.26
y[1] (analytic) = 0.4341830916217106731136575108235
y[1] (numeric) = 0.43418309162171067311365751082345
absolute error = 5e-32
relative error = 1.1515879122156912921945894709488e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 0.433719127074681266448862983912
y[1] (numeric) = 0.43371912707468126644886298391198
absolute error = 2e-32
relative error = 4.6112792246204623287365718398905e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 0.4332847903680444872206131064074
y[1] (numeric) = 0.43328479036804448722061310640735
absolute error = 5e-32
relative error = 1.1539754247438173551741166172085e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = 0.4328791249434423586133939099388
y[1] (numeric) = 0.43287912494344235861339390993876
absolute error = 4e-32
relative error = 9.2404548279444483039185938719841e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 0.4325011713754125930020158907071
y[1] (numeric) = 0.43250117137541259300201589070707
absolute error = 3e-32
relative error = 6.9363973985540701958385658059172e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 0.4321499674673303386618230213838
y[1] (numeric) = 0.43214996746733033866182302138375
absolute error = 5e-32
relative error = 1.1570057564282912649503636891646e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = 0.4318245483476270404260172705726
y[1] (numeric) = 0.43182454834762704042601727057259
absolute error = 1e-32
relative error = 2.3157553312485163021517410537735e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 0.4315239465662767924842150139894
y[1] (numeric) = 0.43152394656627679248421501398937
absolute error = 3e-32
relative error = 6.9521054946581898365220113729114e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = 0.4312471921915405347673605076999
y[1] (numeric) = 0.4312471921915405347673605076998
absolute error = 1.0e-31
relative error = 2.3188556774552752183297382574709e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 0.4309933129069584185799778269894
y[1] (numeric) = 0.43099331290695841857997782698932
absolute error = 8e-32
relative error = 1.8561772910214541322885183990195e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 0.4307613341085806423240247476081
y[1] (numeric) = 0.43076133410858064232402474760809
absolute error = 1e-32
relative error = 2.3214711275546685298208220906602e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 0.4305502790024270343118016103547
y[1] (numeric) = 0.43055027900242703431180161035464
absolute error = 6e-32
relative error = 1.3935654655483750570264345567853e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = 0.4303591687021656367908499264018
y[1] (numeric) = 0.43035916870216563679084992640174
absolute error = 6e-32
relative error = 1.3941843084450142055690930966603e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 0.430187022327000523403836782196
y[1] (numeric) = 0.43018702232700052340383678219589
absolute error = 1.1e-31
relative error = 2.5570273925275474820938321269548e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 0.4300328570997590613832519647964
y[1] (numeric) = 0.4300328570997590613832519647963
absolute error = 1.0e-31
relative error = 2.3254037069265614484426977037248e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 0.4298956884451688098364374506391
y[1] (numeric) = 0.42989568844516880983643745063903
absolute error = 7e-32
relative error = 1.6283019783979102070507062851874e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 0.4297745300883142265130178970241
y[1] (numeric) = 0.42977453008831422651301789702404
absolute error = 6e-32
relative error = 1.3960808703035663788394339656528e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 0.4296683941532633374661023754251
y[1] (numeric) = 0.42966839415326333746610237542503
absolute error = 7e-32
relative error = 1.6291633490507774882949038898853e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 0.4295762912618545070224798438708
y[1] (numeric) = 0.42957629126185450702247984387078
absolute error = 2e-32
relative error = 4.6557504235746352398558284701503e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 0.429497230632633429467133372752
y[1] (numeric) = 0.42949723063263342946713337275193
absolute error = 7e-32
relative error = 1.6298126043069615670129627529513e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 0.4294302201799304488253518908766
y[1] (numeric) = 0.42943022017993044882535189087657
absolute error = 3e-32
relative error = 6.9860011220053532390504908983495e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 0.4293742666130682990930253985376
y[1] (numeric) = 0.42937426661306829909302539853754
absolute error = 6e-32
relative error = 1.3973822994396902456650916352040e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=28008432, alloc=4455632, time=1.14
x[1] = 1.48
y[1] (analytic) = 0.4293283755356903442237734593522
y[1] (numeric) = 0.42932837553569034422377345935211
absolute error = 9e-32
relative error = 2.0962974992673933350480609932254e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 0.4292915515451993851316815154363
y[1] (numeric) = 0.42929155154519938513168151543623
absolute error = 7e-32
relative error = 1.6305934684258471316023925352389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 0.4292627983322970899118101485657
y[1] (numeric) = 0.42926279833229708991181014856568
absolute error = 2e-32
relative error = 4.6591505431406563050295596390306e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 0.4292411187806140934184044850838
y[1] (numeric) = 0.42924111878061409341840448508376
absolute error = 4e-32
relative error = 9.3187717229029197052670851604818e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = 0.4292255150664208032738707298473
y[1] (numeric) = 0.42922551506642080327387072984723
absolute error = 7e-32
relative error = 1.6308443357373058523925028541972e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 0.4292149887584089413110109929239
y[1] (numeric) = 0.42921498875840894131101099292384
absolute error = 6e-32
relative error = 1.3979008555493861087745462769129e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 0.4292085409175338423775231929236
y[1] (numeric) = 0.42920854091753384237752319292356
absolute error = 4e-32
relative error = 9.3194790379731554021075800314714e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 0.4292051721969075263560872253044
y[1] (numeric) = 0.4292051721969075263560872253044
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = 0.4292038829417325541760793362391
y[1] (numeric) = 0.42920388294173255417607933623905
absolute error = 5e-32
relative error = 1.1649475223127897858372150083120e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 0.4292036732892666745145914663546
y[1] (numeric) = 0.4292036732892666745145914663546
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 0.4292035432688082648053890569827
y[1] (numeric) = 0.42920354326880826480538905698268
absolute error = 2e-32
relative error = 4.6597937770224998362784526554099e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.008874
Order of pole (three term test) = -0.8949
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 0.4292024929016925680950273462434
y[1] (numeric) = 0.42920249290169256809502734624336
absolute error = 4e-32
relative error = 9.3196103614341936289442045994422e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01851
Order of pole (three term test) = -0.9018
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 0.4291995223012887262057704629465
y[1] (numeric) = 0.42919952230128872620577046294646
absolute error = 4e-32
relative error = 9.3196748648571119128955245394513e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02814
Order of pole (three term test) = -0.9135
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = 0.429193631772987609585327609601
y[1] (numeric) = 0.42919363177298760958532760960098
absolute error = 2e-32
relative error = 4.6599013870221060338671001548356e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03776
Order of pole (three term test) = -0.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 0.4291838219141704451437442747123
y[1] (numeric) = 0.42918382191417044514374427471229
absolute error = 1e-32
relative error = 2.3300039492168537559055532820444e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04737
Order of pole (three term test) = -0.9513
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 0.4291690937141482452979716974198
y[1] (numeric) = 0.42916909371414824529797169741976
absolute error = 4e-32
relative error = 9.3203356406280138552692958625135e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05696
Order of pole (three term test) = -0.9775
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 0.4291484486540620443644927074566
y[1] (numeric) = 0.42914844865406204436449270745656
absolute error = 4e-32
relative error = 9.3207840143549323810932896216134e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06652
Order of pole (three term test) = -1.008
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 0.4291208888067339523596145973413
y[1] (numeric) = 0.42912088880673395235961459734123
absolute error = 7e-32
relative error = 1.6312419606197816356456569666309e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07606
Order of pole (three term test) = -1.044
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 0.4290854169364590411852579316506
y[1] (numeric) = 0.42908541693645904118525793165057
absolute error = 3e-32
relative error = 6.9916149129912143232658759852391e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08556
Order of pole (three term test) = -1.085
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = 0.4290410365987280840947823424486
y[1] (numeric) = 0.42904103659872808409478234244856
absolute error = 4e-32
relative error = 9.3231175080837435713130684862058e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09503
Order of pole (three term test) = -1.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 0.4289867522398711762480047341728
y[1] (numeric) = 0.42898675223987117624800473417277
absolute error = 3e-32
relative error = 6.9932229476460088580628546435112e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1045
Order of pole (three term test) = -1.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 0.4289215692966122720763904698331
y[1] (numeric) = 0.42892156929661227207639046983303
absolute error = 7e-32
relative error = 1.6319999974539139409110273121303e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1139
Order of pole (three term test) = -1.235
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 0.4288444942955246840876428573349
y[1] (numeric) = 0.42884449429552468408764285733482
absolute error = 8e-32
relative error = 1.8654780710527326541348011491729e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1232
Order of pole (three term test) = -1.294
NO COMPLEX POLE (six term test) for Equation 1
bytes used=32009296, alloc=4455632, time=1.30
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 0.4287545349523775976426897830511
y[1] (numeric) = 0.42875453495237759764268978305105
absolute error = 5e-32
relative error = 1.1661684232810172885282219967766e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1325
Order of pole (three term test) = -1.358
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 0.4286507002713636671363782803312
y[1] (numeric) = 0.42865070027136366713637828033113
absolute error = 7e-32
relative error = 1.6330312759476530527313870487702e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1417
Order of pole (three term test) = -1.427
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 0.4285320006441977709049483513426
y[1] (numeric) = 0.42853200064419777090494835134251
absolute error = 9e-32
relative error = 2.1001932146188854336964712475544e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1509
Order of pole (three term test) = -1.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 0.4283974479490770150673773153451
y[1] (numeric) = 0.42839744794907701506737731534503
absolute error = 7e-32
relative error = 1.6339966620977816548616813781038e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1601
Order of pole (three term test) = -1.578
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 0.4282460556494920903826769439426
y[1] (numeric) = 0.42824605564949209038267694394257
absolute error = 3e-32
relative error = 7.0053184621866535774580119305864e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1691
Order of pole (three term test) = -1.661
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 0.4280768388928801010698001765041
y[1] (numeric) = 0.42807683889288010106980017650403
absolute error = 7e-32
relative error = 1.6352204473626396055734332664361e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1781
Order of pole (three term test) = -1.748
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 0.4278888146091090003894858417304
y[1] (numeric) = 0.42788881460910900038948584173033
absolute error = 7e-32
relative error = 1.6359390012086991137739707600837e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.187
Order of pole (three term test) = -1.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 0.4276810016087837846265532903126
y[1] (numeric) = 0.42768100160878378462655329031256
absolute error = 4e-32
relative error = 9.3527652267774882721965400966639e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1959
Order of pole (three term test) = -1.936
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = 0.4274524206813646149351702644646
y[1] (numeric) = 0.42745242068136461493517026446454
absolute error = 6e-32
relative error = 1.4036649951440030239756947461555e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2047
Order of pole (three term test) = -2.036
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 0.4272020946930870553166743065306
y[1] (numeric) = 0.42720209469308705531667430653051
absolute error = 9e-32
relative error = 2.1067312430819963311993091116237e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2133
Order of pole (three term test) = -2.141
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 0.426929048684674634787749850842
y[1] (numeric) = 0.4269290486846746347877498508419
absolute error = 1.0e-31
relative error = 2.3423095783266545144975693171604e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2219
Order of pole (three term test) = -2.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 0.4266323099688339625641710448309
y[1] (numeric) = 0.42663230996883396256417104483079
absolute error = 1.1e-31
relative error = 2.5783326163936257215130812668222e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2305
Order of pole (three term test) = -2.363
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 0.4263109082275226468298375836185
y[1] (numeric) = 0.42631090822752264682983758361845
absolute error = 5e-32
relative error = 1.1728529351473910582018739731581e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2389
Order of pole (three term test) = -2.481
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = 0.4259638756089802903802829832816
y[1] (numeric) = 0.42596387560898029038028298328152
absolute error = 8e-32
relative error = 1.8780935328289941371588555916828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2472
Order of pole (three term test) = -2.603
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = 0.4255902468245128601219498354748
y[1] (numeric) = 0.42559024682451286012194983547473
absolute error = 7e-32
relative error = 1.6447745342449935859524196283399e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2554
Order of pole (three term test) = -2.729
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 0.4251890592450207520709354882891
y[1] (numeric) = 0.42518905924502075207093548828905
absolute error = 5e-32
relative error = 1.1759474735493334169612906451548e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2636
Order of pole (three term test) = -2.859
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 0.4247593529972608991251480648099
y[1] (numeric) = 0.42475935299726089912514806480982
absolute error = 8e-32
relative error = 1.8834193864241027688190008022772e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2716
Order of pole (three term test) = -2.993
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 0.4243001710598332954793137595222
y[1] (numeric) = 0.42430017105983329547931375952217
absolute error = 3e-32
relative error = 7.0704661572642889866662761460040e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2795
Order of pole (three term test) = -3.131
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 0.4238105593588823391103824155512
y[1] (numeric) = 0.42381055935888233911038241555116
absolute error = 4e-32
relative error = 9.4381791856507382981714214099092e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2873
Order of pole (three term test) = -3.273
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = 0.4232895668635034222788336950803
y[1] (numeric) = 0.42328956686350342227883369508024
absolute error = 6e-32
relative error = 1.4174693802303889985221174254793e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.295
Order of pole (three term test) = -3.419
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 0.4227362456808452294663389393975
y[1] (numeric) = 0.42273624568084522946633893939746
absolute error = 4e-32
relative error = 9.4621647442549674761136802052484e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3025
Order of pole (three term test) = -3.569
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 0.422149651150898232599236603159
y[1] (numeric) = 0.42214965115089823259923660315898
absolute error = 2e-32
relative error = 4.7376564082131528786652670203714e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.31
Order of pole (three term test) = -3.723
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=36010256, alloc=4455632, time=1.47
x[1] = 1.93
y[1] (analytic) = 0.4215288419409599047872890647119
y[1] (numeric) = 0.42152884194095990478728906471181
absolute error = 9e-32
relative error = 2.1350852194499555374281534847491e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3173
Order of pole (three term test) = -3.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 0.4208728801397672061350676858407
y[1] (numeric) = 0.42087288013976720613506768584066
absolute error = 4e-32
relative error = 9.5040573739786808166200008969328e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3245
Order of pole (three term test) = -4.041
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 0.4201808313512869284558284591307
y[1] (numeric) = 0.42018083135128692845582845913062
absolute error = 8e-32
relative error = 1.9039421608720889181869676047239e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3315
Order of pole (three term test) = -4.205
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 0.4194517647881545199315652154474
y[1] (numeric) = 0.41945176478815451993156521544738
absolute error = 2e-32
relative error = 4.7681287048824470067825467139568e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3385
Order of pole (three term test) = -4.373
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 0.4186847533647520459146398138793
y[1] (numeric) = 0.41868475336475204591463981387924
absolute error = 6e-32
relative error = 1.4330591099344111003125323211898e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3453
Order of pole (three term test) = -4.545
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = 0.4178788737899159781524738599072
y[1] (numeric) = 0.41787887378991597815247385990713
absolute error = 7e-32
relative error = 1.6751265591663227384241229565700e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3519
Order of pole (three term test) = -4.719
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 0.4170332066592655417336357161303
y[1] (numeric) = 0.41703320665926554173363571613023
absolute error = 7e-32
relative error = 1.6785234097003953085483545770189e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3584
Order of pole (three term test) = -4.898
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 0.4161468365471423869975682295008
y[1] (numeric) = 0.4161468365471423869975682295007
absolute error = 1.0e-31
relative error = 2.4029979617223809897546004014198e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3648
Order of pole (three term test) = -5.079
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 0.4152188520981523925173823401654
y[1] (numeric) = 0.41521885209815239251738234016537
absolute error = 3e-32
relative error = 7.2251054711042807175351614082125e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.371
Order of pole (three term test) = -5.263
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 0.4142483461183004450517028740902
y[1] (numeric) = 0.41424834611830044505170287409014
absolute error = 6e-32
relative error = 1.4484065069233924367079556536574e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3771
Order of pole (three term test) = -5.451
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 0.4132344156657090830635167316961
y[1] (numeric) = 0.41323441566570908306351673169604
absolute error = 6e-32
relative error = 1.4519603819382197039308892513967e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.383
Order of pole (three term test) = -5.641
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 0.4121761621409119320172702052914
y[1] (numeric) = 0.41217616214091193201727020529131
absolute error = 9e-32
relative error = 2.1835323889796281630828398908724e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3888
Order of pole (three term test) = -5.835
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 0.4110726913767129021859299941674
y[1] (numeric) = 0.41107269137671290218592999416735
absolute error = 5e-32
relative error = 1.2163298863893462542924965598861e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3944
Order of pole (three term test) = -6.031
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 0.4099231137276021631231096264879
y[1] (numeric) = 0.40992311372760216312310962648785
absolute error = 5e-32
relative error = 1.2197409300814756957188814753382e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3999
Order of pole (three term test) = -6.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 0.4087265441587199532773271390117
y[1] (numeric) = 0.40872654415871995327732713901168
absolute error = 2e-32
relative error = 4.8932471565226848588094282943864e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4052
Order of pole (three term test) = -6.432
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 0.4074821023343593284415688497724
y[1] (numeric) = 0.4074821023343593284415688497723
absolute error = 1.0e-31
relative error = 2.4540955155361652460845067855160e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4103
Order of pole (three term test) = -6.636
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 0.4061889127059989988370663118704
y[1] (numeric) = 0.4061889127059989988370663118704
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4153
Order of pole (three term test) = -6.843
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 0.4048461045998574516209385237192
y[1] (numeric) = 0.40484610459985745162093852371912
absolute error = 8e-32
relative error = 1.9760595221502884236515672750757e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4201
Order of pole (three term test) = -7.053
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 0.4034528123039596034784101570717
y[1] (numeric) = 0.40345281230395960347841015707164
absolute error = 6e-32
relative error = 1.4871627652652538596313401702366e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4247
Order of pole (three term test) = -7.265
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 0.4020081751547072767069018829839
y[1] (numeric) = 0.40200817515470727670690188298384
absolute error = 6e-32
relative error = 1.4925069615041990440109645080858e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4292
Order of pole (three term test) = -7.479
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 0.4005113376229448418165262096097
y[1] (numeric) = 0.40051133762294484181652620960967
absolute error = 3e-32
relative error = 7.4904246601485805005942576540935e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4335
Order of pole (three term test) = -7.695
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 0.3989614493995114201544499120086
y[1] (numeric) = 0.39896144939951142015444991200855
absolute error = 5e-32
relative error = 1.2532539190254212932639112344712e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4376
Order of pole (three term test) = -7.913
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=40011404, alloc=4455632, time=1.64
x[1] = 2.15
y[1] (analytic) = 0.397357665480271091404153882264
y[1] (numeric) = 0.39735766548027109140415388226398
absolute error = 2e-32
relative error = 5.0332488177437727217204456503726e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4415
Order of pole (three term test) = -8.133
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 0.3956991462506126030096987439834
y[1] (numeric) = 0.39569914625061260300969874398332
absolute error = 8e-32
relative error = 2.0217379986292085087287888777691e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4453
Order of pole (three term test) = -8.356
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 0.3939850575694101316244699944165
y[1] (numeric) = 0.39398505756941013162446999441646
absolute error = 4e-32
relative error = 1.0152669303442559842027348529979e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4489
Order of pole (three term test) = -8.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 0.3922145708524367005782248676625
y[1] (numeric) = 0.39221457085243670057822486766244
absolute error = 6e-32
relative error = 1.5297748849461756212907860494959e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4523
Order of pole (three term test) = -8.806
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 0.390386863155221912090205163797
y[1] (numeric) = 0.3903868631552219120902051637969
absolute error = 1.0e-31
relative error = 2.5615616056280805474685076488349e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4555
Order of pole (three term test) = -9.033
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 0.3885011172553457085241426126549
y[1] (numeric) = 0.38850111725534570852414261265488
absolute error = 2e-32
relative error = 5.1479903433211564184748924015970e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.83
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4586
Order of pole (three term test) = -9.262
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 0.3865565217341599333776091775186
y[1] (numeric) = 0.38655652173415993337760917751859
absolute error = 1e-32
relative error = 2.5869438071147414608406587002201e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.12
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4615
Order of pole (three term test) = -9.493
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 0.3845522710579295199177144375002
y[1] (numeric) = 0.38455227105792951991771443750011
absolute error = 9e-32
relative error = 2.3403840459036651373662607495936e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4641
Order of pole (three term test) = -9.725
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 0.3824875656583851934119039106856
y[1] (numeric) = 0.38248756565838519341190391068559
absolute error = 1e-32
relative error = 2.6144640761816023052532468235415e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4666
Order of pole (three term test) = -9.958
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 0.3803616120126796317507622663104
y[1] (numeric) = 0.3803616120126796317507622663104
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4689
Order of pole (three term test) = -10.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 0.3781736227227390889133890573964
y[1] (numeric) = 0.37817362272273908891338905739636
absolute error = 4e-32
relative error = 1.0577152291059260050299501524257e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.34
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4711
Order of pole (three term test) = -10.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 0.3759228165940025461791265687448
y[1] (numeric) = 0.3759228165940025461791265687448
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.473
Order of pole (three term test) = -10.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 0.3736084187135405172361343481243
y[1] (numeric) = 0.37360841871354051723613434812426
absolute error = 4e-32
relative error = 1.0706396857365649744701392088148e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4747
Order of pole (three term test) = -10.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 0.3712296605275456953713983504607
y[1] (numeric) = 0.37122966052754569537139835046065
absolute error = 5e-32
relative error = 1.3468751373192050955855529073967e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4763
Order of pole (three term test) = -11.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 0.368785779918187693742031018189
y[1] (numeric) = 0.3687857799181876937420310181889
absolute error = 1.0e-31
relative error = 2.7116012993284132483366434720788e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4776
Order of pole (three term test) = -11.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 0.366276021279824193317880571166
y[1] (numeric) = 0.36627602127982419331788057116597
absolute error = 3e-32
relative error = 8.1905443591899441646914604364461e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4788
Order of pole (three term test) = -11.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 0.363699635594560877444164323471
y[1] (numeric) = 0.36369963559456087744416432347099
absolute error = 1e-32
relative error = 2.7495215890586253446683572123640e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4798
Order of pole (three term test) = -11.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 0.3610558805071525970936361660082
y[1] (numeric) = 0.36105588050715259709363616600818
absolute error = 2e-32
relative error = 5.5393087551730917073292082154673e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4806
Order of pole (three term test) = -12.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 0.358344020399238276754180427816
y[1] (numeric) = 0.35834402039923827675418042781595
absolute error = 5e-32
relative error = 1.3953072230504640449327768195660e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = -12.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 0.3555633264629021375231055720614
y[1] (numeric) = 0.3555633264629021375231055720613
absolute error = 1.0e-31
relative error = 2.8124385322521035022834599053856e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -12.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 0.3527130767735538813471291122589
y[1] (numeric) = 0.35271307677355388134712911225887
absolute error = 3e-32
relative error = 8.5054969536217019035034297392716e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 0.3497925563621205484503630346451
y[1] (numeric) = 0.34979255636212054845036303464505
absolute error = 5e-32
relative error = 1.4294186394360494576169483813085e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 0.3468010572865428288247166088224
y[1] (numeric) = 0.3468010572865428288247166088223
bytes used=44012204, alloc=4455632, time=1.80
absolute error = 1.0e-31
relative error = 2.8834975528167275865792623242474e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -13.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 0.3437378787025686782111476073675
y[1] (numeric) = 0.34373787870256867821114760736748
absolute error = 2e-32
relative error = 5.8183869858886588751306068983702e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.07
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4813
Order of pole (three term test) = -13.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 0.3406023269338371592691582926181
y[1] (numeric) = 0.34060232693383715926915829261801
absolute error = 9e-32
relative error = 2.6423777197941082070923791971943e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4807
Order of pole (three term test) = -13.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 0.3373937155412454996088222273348
y[1] (numeric) = 0.33739371554124549960882222733473
absolute error = 7e-32
relative error = 2.0747274408388523471192763657496e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4799
Order of pole (three term test) = -14.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 0.334111365391592430037344395568
y[1] (numeric) = 0.3341113653915924300373443955679
absolute error = 1.0e-31
relative error = 2.9930140174308598205823227427816e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.96
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.479
Order of pole (three term test) = -14.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 0.3307546047254909387435325689107
y[1] (numeric) = 0.33075460472549093874353256891069
absolute error = 1e-32
relative error = 3.0233895030122039095556589628512e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4779
Order of pole (three term test) = -14.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 0.3273227692245436502013552441779
y[1] (numeric) = 0.32732276922454365020135524417785
absolute error = 5e-32
relative error = 1.5275442071584077546426840772550e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4765
Order of pole (three term test) = -14.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 0.3238152020777741113106750925374
y[1] (numeric) = 0.32381520207777411131067509253735
absolute error = 5e-32
relative error = 1.5440905701515203357354170475968e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.475
Order of pole (three term test) = -14.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 0.3202312540473073417019030673365
y[1] (numeric) = 0.32023125404730734170190306733644
absolute error = 6e-32
relative error = 1.8736459743287979931653780762234e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4733
Order of pole (three term test) = -15.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = 0.3165702835332930802042763146862
y[1] (numeric) = 0.31657028353329308020427631468615
absolute error = 5e-32
relative error = 1.5794280954593009793384037105888e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.23
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4714
Order of pole (three term test) = -15.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 0.3128316566380652352072155840616
y[1] (numeric) = 0.3128316566380652352072155840615
absolute error = 1.0e-31
relative error = 3.1966074365580058947981961922107e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4693
Order of pole (three term test) = -15.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 0.3090147472295311230231920335903
y[1] (numeric) = 0.30901474722953112302319203359028
absolute error = 2e-32
relative error = 6.4721830201664536190227813557779e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.467
Order of pole (three term test) = -15.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 0.3051189370037841553810913325716
y[1] (numeric) = 0.30511893700378415538109133257152
absolute error = 8e-32
relative error = 2.6219283793259879363519724314459e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4646
Order of pole (three term test) = -16.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 0.3011436155469337148335027904674
y[1] (numeric) = 0.3011436155469337148335027904673
absolute error = 1.0e-31
relative error = 3.3206747491020555880615396829046e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.94
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4619
Order of pole (three term test) = -16.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 0.2970881803961460351419175078784
y[1] (numeric) = 0.29708818039614603514191750787836
absolute error = 4e-32
relative error = 1.3464015951985311107070934416683e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4591
Order of pole (three term test) = -16.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 0.2929520370998899826026642604518
y[1] (numeric) = 0.2929520370998899826026642604518
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4561
Order of pole (three term test) = -16.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 0.288734599277381713785655172555
y[1] (numeric) = 0.28873459927738171378565517255494
absolute error = 6e-32
relative error = 2.0780329115444584100321255398755e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4529
Order of pole (three term test) = -17.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 0.2844352886772222652697043558066
y[1] (numeric) = 0.28443528867722226526970435580651
absolute error = 9e-32
relative error = 3.1641643488945628010684280014190e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4495
Order of pole (three term test) = -17.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 0.2800535352352222116643104758323
y[1] (numeric) = 0.28005353523522221166431047583223
absolute error = 7e-32
relative error = 2.4995220982018915917527454920209e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.446
Order of pole (three term test) = -17.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 0.2755887771314076095002881233824
y[1] (numeric) = 0.27558877713140760950028812338239
absolute error = 1e-32
relative error = 3.6285947868014053171012101593521e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4422
Order of pole (three term test) = -17.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 0.2710404608462015264423637215671
y[1] (numeric) = 0.27104046084620152644236372156707
absolute error = 3e-32
relative error = 1.1068458157995503001067707443303e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4383
Order of pole (three term test) = -17.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 0.2664080412157755377176324945692
y[1] (numeric) = 0.26640804121577553771763249456918
absolute error = 2e-32
relative error = 7.5072809021560742850849606753346e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4342
Order of pole (three term test) = -18.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 0.2616909814865656546563597454083
y[1] (numeric) = 0.26169098148656565465635974540826
absolute error = 4e-32
relative error = 1.5285203858679198340220367664097e-29 %
Correct digits = 31
h = 0.01
bytes used=48013260, alloc=4455632, time=1.97
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.43
Order of pole (three term test) = -18.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 0.2568887533689472337977021516452
y[1] (numeric) = 0.25688875336894723379770215164515
absolute error = 5e-32
relative error = 1.9463678087996829545529466354954e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4255
Order of pole (three term test) = -18.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 0.2520008370900634991141674487226
y[1] (numeric) = 0.2520008370900634991141674487226
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4209
Order of pole (three term test) = -18.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 0.2470267214458023945466136767484
y[1] (numeric) = 0.2470267214458023945466136767483
absolute error = 1.0e-31
relative error = 4.0481450514631866185265307877401e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4161
Order of pole (three term test) = -19.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 0.2419659038519165692078483901949
y[1] (numeric) = 0.24196590385191656920784839019488
absolute error = 2e-32
relative error = 8.2656273803932411077974685536160e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4112
Order of pole (three term test) = -19.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 0.236817890394281383298907316266
y[1] (numeric) = 0.23681789039428138329890731626594
absolute error = 6e-32
relative error = 2.5335923692295869030190351571857e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4061
Order of pole (three term test) = -19.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 0.2315821958782859089793023660538
y[1] (numeric) = 0.23158219587828590897930236605376
absolute error = 4e-32
relative error = 1.7272484980245652429339827633388e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4008
Order of pole (three term test) = -19.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 0.2262583438773519871323110038826
y[1] (numeric) = 0.22625834387735198713231100388254
absolute error = 6e-32
relative error = 2.6518359045589160864067034308684e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3954
Order of pole (three term test) = -19.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 0.2208458667805764881600628584297
y[1] (numeric) = 0.22084586678057648816006285842969
absolute error = 1e-32
relative error = 4.5280448965502239304752531772373e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3898
Order of pole (three term test) = -20.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 0.2153443058394920126220458186207
y[1] (numeric) = 0.21534430583949201262204581862061
absolute error = 9e-32
relative error = 4.1793536006975714277245536016126e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3841
Order of pole (three term test) = -20.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 0.2097532112139413556859348843289
y[1] (numeric) = 0.20975321121394135568593488432882
absolute error = 8e-32
relative error = 3.8140059709695046908079693628289e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3782
Order of pole (three term test) = -20.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 0.2040721420170611479825272819433
y[1] (numeric) = 0.20407214201706114798252728194328
absolute error = 2e-32
relative error = 9.8004557615355111721041793984088e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3722
Order of pole (three term test) = -20.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 0.1983006663593701745381845937161
y[1] (numeric) = 0.19830066635937017453818459371603
absolute error = 7e-32
relative error = 3.5299931808167791755740883881645e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.366
Order of pole (three term test) = -20.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 0.1924383613919579629896287999871
y[1] (numeric) = 0.19243836139195796298962879998702
absolute error = 8e-32
relative error = 4.1571752857038833500804850301628e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3596
Order of pole (three term test) = -21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 0.1864848133487693222582611248928
y[1] (numeric) = 0.18648481334876932225826112489274
absolute error = 6e-32
relative error = 3.2174201707131108185218789412739e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3532
Order of pole (three term test) = -21.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 0.1804396175879806032653732517793
y[1] (numeric) = 0.18043961758798060326537325177923
absolute error = 7e-32
relative error = 3.8794141184581418520344985212835e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3465
Order of pole (three term test) = -21.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 0.1743023786324635440966594895267
y[1] (numeric) = 0.17430237863246354409665948952667
absolute error = 3e-32
relative error = 1.7211469077687358161090552180450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3398
Order of pole (three term test) = -21.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 0.1680727102093326532652331971401
y[1] (numeric) = 0.16807271020933265326523319714006
absolute error = 4e-32
relative error = 2.3799223532589231126639893781862e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3329
Order of pole (three term test) = -21.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 0.1617502352885721763677772078291
y[1] (numeric) = 0.16175023528857217636777720782903
absolute error = 7e-32
relative error = 4.3276598562664083715101906476794e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3258
Order of pole (three term test) = -21.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 0.1553345861207387834693516691176
y[1] (numeric) = 0.15533458612073878346935166911755
absolute error = 5e-32
relative error = 3.2188581595817880613638656793052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3187
Order of pole (three term test) = -22.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 0.1488254042737362069795396196241
y[1] (numeric) = 0.14882540427373620697953961962405
absolute error = 5e-32
relative error = 3.3596414700835919596640443618781e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3114
Order of pole (three term test) = -22.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 0.1422223406686581525867881173662
y[1] (numeric) = 0.14222234066865815258678811736611
absolute error = 9e-32
relative error = 6.3281197297741771942522801781255e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.304
Order of pole (three term test) = -22.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 0.1355250556146958989897204783588
y[1] (numeric) = 0.13552505561469589898972047835879
absolute error = 1e-32
relative error = 7.3787093867206886589777604273651e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2965
Order of pole (three term test) = -22.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=52014652, alloc=4455632, time=2.14
x[1] = 2.82
y[1] (analytic) = 0.12873321884310709569453606376
y[1] (numeric) = 0.12873321884310709569453606375999
absolute error = 1e-32
relative error = 7.7680027656167326519698481109811e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2888
Order of pole (three term test) = -22.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = 0.1218465095402423620270251127245
y[1] (numeric) = 0.12184650954024236202702511272448
absolute error = 2e-32
relative error = 1.6414093498012416244944179857052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.281
Order of pole (three term test) = -22.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 0.1148646163796263847268194935862
y[1] (numeric) = 0.11486461637962638472681949358619
absolute error = 1e-32
relative error = 8.7059011862714119626435241173836e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2732
Order of pole (three term test) = -22.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 0.1077872375530903060408541071749
y[1] (numeric) = 0.10778723755309030604085410717488
absolute error = 2e-32
relative error = 1.8555072431603097036381293193752e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2652
Order of pole (three term test) = -23.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 0.1006140808009522891031731663928
y[1] (numeric) = 0.10061408080095228910317316639272
absolute error = 8e-32
relative error = 7.9511733708790011053946961438090e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2571
Order of pole (three term test) = -23.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 0.0933448634412432425696937587379
y[1] (numeric) = 0.09334486344124324256969375873789
absolute error = 1.0e-32
relative error = 1.0712962268453677961268388894773e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2489
Order of pole (three term test) = -23.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = 0.0859793123979747819598179047655
y[1] (numeric) = 0.085979312397974781959817904765478
absolute error = 2.2e-32
relative error = 2.5587550523977211626610187598430e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2406
Order of pole (three term test) = -23.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 0.0785171642284466009323155072093
y[1] (numeric) = 0.078517164228446600932315507209236
absolute error = 6.4e-32
relative error = 8.1510839863996179153029399388928e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2322
Order of pole (three term test) = -23.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = 0.0709581651495905217811066693455
y[1] (numeric) = 0.070958165149590521781106669345485
absolute error = 1.5e-32
relative error = 2.1139216280998439101148941391699e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2237
Order of pole (three term test) = -23.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 0.0633020710633485907678471066028
y[1] (numeric) = 0.063302071063348590767847106602705
absolute error = 9.5e-32
relative error = 1.5007407878476864679833374769290e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2151
Order of pole (three term test) = -23.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = 0.0555486475810826805029317351583
y[1] (numeric) = 0.055548647581082680502931735158218
absolute error = 8.2e-32
relative error = 1.4761835538895358439877848266890e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2065
Order of pole (three term test) = -23.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 0.0476976700470131584350196046763
y[1] (numeric) = 0.047697670047013158435019604676278
absolute error = 2.2e-32
relative error = 4.6123846255625742480749714097407e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1977
Order of pole (three term test) = -23.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = 0.0397489235606842776017633813283
y[1] (numeric) = 0.039748923560684277601763381328274
absolute error = 2.6e-32
relative error = 6.5410576365183988586856498704531e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1889
Order of pole (three term test) = -24.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 0.031702202998454043121389404702
y[1] (numeric) = 0.031702202998454043121389404701921
absolute error = 7.9e-32
relative error = 2.4919403867249361939277520267643e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.18
Order of pole (three term test) = -24.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 0.0235573130340064054563873229762
y[1] (numeric) = 0.023557313034006405456387322976111
absolute error = 8.9e-32
relative error = 3.7780200089680482554478297640419e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1711
Order of pole (three term test) = -24.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = 0.0153140681578837292470763748061
y[1] (numeric) = 0.015314068157883729247076374806096
absolute error = 4e-33
relative error = 2.6119774045414495130814691184547e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.162
Order of pole (three term test) = -24.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 0.0069722926960375844844419643954
y[1] (numeric) = 0.0069722926960375844844419643953548
absolute error = 4.52e-32
relative error = 6.4828029990318047301241079468969e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1529
Order of pole (three term test) = -24.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = -0.0014681791726039950414158127892
y[1] (numeric) = -0.0014681791726039950414158127892073
absolute error = 7.3e-33
relative error = 4.9721451824252203494790109983734e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1438
Order of pole (three term test) = -24.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = -0.0100075033995545427284272052687
y[1] (numeric) = -0.010007503399554542728427205268786
absolute error = 8.6e-32
relative error = 8.5935519146391756598368313718463e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1345
Order of pole (three term test) = -24.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = -0.0186458260511741377683744258176
y[1] (numeric) = -0.01864582605117413776837442581763
absolute error = 3.0e-32
relative error = 1.6089391758597299445795199207813e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1253
Order of pole (three term test) = -24.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = -0.027383283294062890860533466737
y[1] (numeric) = -0.027383283294062890860533466737011
absolute error = 1.1e-32
relative error = 4.0170493369525801287718168196055e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1159
Order of pole (three term test) = -24.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = -0.0362200013814443976723926912916
y[1] (numeric) = -0.03622000138144439767239269129162
absolute error = 2.0e-32
relative error = 5.5218109434545888227098046895603e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1066
Order of pole (three term test) = -24.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=56015980, alloc=4455632, time=2.31
x[1] = 3.04
y[1] (analytic) = -0.0451560966405405216907550451568
y[1] (numeric) = -0.045156096640540521690755045156862
absolute error = 6.2e-32
relative error = 1.3730150436505456018789735445771e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09716
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = -0.0541916754609387689744177984351
y[1] (numeric) = -0.05419167546093876897441779843513
absolute error = 3.0e-32
relative error = 5.5359056063184333140653685140977e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08771
Order of pole (three term test) = -24.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = -0.0633268342839534180612607282068
y[1] (numeric) = -0.063326834283953418061260728206895
absolute error = 9.5e-32
relative error = 1.5001539406505962533069871661187e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07822
Order of pole (three term test) = -24.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = -0.0725616595929814689078863372732
y[1] (numeric) = -0.072561659592981468907886337273277
absolute error = 7.7e-32
relative error = 1.0611664676898849464489079296756e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06871
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = -0.0818962279048543752588814626402
y[1] (numeric) = -0.081896227904854375258881462640253
absolute error = 5.3e-32
relative error = 6.4716045361178888076065378290814e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05916
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = -0.0913306057621864252652564819142
y[1] (numeric) = -0.091330605762186425265256481914289
absolute error = 8.9e-32
relative error = 9.7448165658448566809894210437354e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04959
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = -0.1008648497267205355076239454585
y[1] (numeric) = -0.10086484972672053550762394545858
absolute error = 8e-32
relative error = 7.9314052632556354668104199415439e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04001
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = -0.1104990063736721238391691632832
y[1] (numeric) = -0.11049900637367212383916916328321
absolute error = 1e-32
relative error = 9.0498551327993069194674628190650e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0304
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = -0.1202331122870716266564150260244
y[1] (numeric) = -0.12023311228707162665641502602445
absolute error = 5e-32
relative error = 4.1585881833133232517686014487989e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02079
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = -0.1300671940561061263421727608608
y[1] (numeric) = -0.13006719405610612634217276086083
absolute error = 3e-32
relative error = 2.3065001300065811544886011726131e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01116
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = -0.140001268272460454714885693655
y[1] (numeric) = -0.14000126827246045471488569365499
absolute error = 1e-32
relative error = 7.1427924356647364439923500669696e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.001534
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = -0.1500353415286580383718053432053
y[1] (numeric) = -0.15003534152865803837180534320532
absolute error = 2e-32
relative error = 1.3330192604107098518837596529979e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = -0.160169410417401651840082905726
y[1] (numeric) = -0.16016941041740165184008290572609
absolute error = 9e-32
relative error = 5.6190504644713310385352692548079e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = -0.1704034615319141444599116498647
y[1] (numeric) = -0.17040346153191414445991164986476
absolute error = 6e-32
relative error = 3.5210552333036294255854658983897e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = -0.1807374714672791069273158461397
y[1] (numeric) = -0.18073747146727910692731584613973
absolute error = 3e-32
relative error = 1.6598660895525048928839412956076e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = -0.1911714068227813434310491703005
y[1] (numeric) = -0.19117140682278134343104917030056
absolute error = 6e-32
relative error = 3.1385446703136346642812699908770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = -0.2017052242052469153383392777164
y[1] (numeric) = -0.20170522420524691533833927771646
absolute error = 6e-32
relative error = 2.9746378774476597165638255273052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = -0.2123388702333824224278933347958
y[1] (numeric) = -0.2123388702333824224278933347958
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = -0.2230722815431130877456572625241
y[1] (numeric) = -0.22307228154311308774565726252418
absolute error = 8e-32
relative error = 3.5862815158654497839341107263930e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = -0.233905384793919112279291505415
y[1] (numeric) = -0.2339053847939191122792915054151
absolute error = 1.0e-31
relative error = 4.2752329147148270839391901792863e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = -0.2448380966761696658211761562575
y[1] (numeric) = -0.24483809667616966582117615625757
absolute error = 7e-32
relative error = 2.8590321910803013220019796335742e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = -0.2558703239194537806269707748284
y[1] (numeric) = -0.25587032391945378062697077482844
absolute error = 4e-32
relative error = 1.5632918811089528725491325053395e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = -0.2670019633019073147873054328283
y[1] (numeric) = -0.26700196330190731478730543282838
absolute error = 8e-32
relative error = 2.9962326497779922547890534379932e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=60017300, alloc=4521156, time=2.48
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = -0.2782329016605350526240382595053
y[1] (numeric) = -0.2782329016605350526240382595053
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = -0.2895630159025269099096415838683
y[1] (numeric) = -0.28956301590252690990964158386833
absolute error = 3e-32
relative error = 1.0360439128075195958404259653322e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = -0.3009921730175671122986248744605
y[1] (numeric) = -0.30099217301756711229862487446056
absolute error = 6e-32
relative error = 1.9934073168240876144259430920296e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = -0.3125202300911351160634089488972
y[1] (numeric) = -0.31252023009113511606340894889719
absolute error = 1e-32
relative error = 3.1997928572764281741801027489061e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = -0.3241470343187969410536619294145
y[1] (numeric) = -0.32414703431879694105366192941451
absolute error = 1e-32
relative error = 3.0850197414316157011063128906887e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = -0.3358724230214854867577104152688
y[1] (numeric) = -0.33587242302148548675771041526884
absolute error = 4e-32
relative error = 1.1909283781074587481175572804932e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = -0.3476962236617683034471532851407
y[1] (numeric) = -0.34769622366176830344715328514077
absolute error = 7e-32
relative error = 2.0132516615450662043204279664245e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = -0.3596182538611011916411200989301
y[1] (numeric) = -0.35961825386110119164112009893012
absolute error = 2e-32
relative error = 5.5614529533099818341221628225524e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = -0.3716383214180659045446056247285
y[1] (numeric) = -0.3716383214180659045446056247285
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = -0.3837562243275901297058346922217
y[1] (numeric) = -0.38375622432759012970583469222171
absolute error = 1e-32
relative error = 2.6058209264284369879591321136608e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = -0.3959717508011478279105082340292
y[1] (numeric) = -0.39597175080114782791050823402918
absolute error = 2e-32
relative error = 5.0508653608584708052526746157886e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = -0.4082846792879379092958746500094
y[1] (numeric) = -0.40828467928793790929587465000946
absolute error = 6e-32
relative error = 1.4695628575787364855047803969858e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = -0.4206947784970391288346639253275
y[1] (numeric) = -0.42069477849703912883466392532756
absolute error = 6e-32
relative error = 1.4262121392225048269732118717962e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = -0.4332018074205389857177984602343
y[1] (numeric) = -0.43320180742053898571779846023434
absolute error = 4e-32
relative error = 9.2335718168343722388859369484583e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = -0.445805515357634313765216359047
y[1] (numeric) = -0.44580551535763431376521635904707
absolute error = 7e-32
relative error = 1.5701914307597690108885413230013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = -0.4585056419397011528258498543986
y[1] (numeric) = -0.45850564193970115282584985439862
absolute error = 2e-32
relative error = 4.3619964882853575869875520376383e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = -0.4713019171563313942005103587744
y[1] (numeric) = -0.47130191715633139420051035877447
absolute error = 7e-32
relative error = 1.4852475123028391706475012931769e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = -0.4841940613823335964448349870275
y[1] (numeric) = -0.48419406138233359644483498702754
absolute error = 4e-32
relative error = 8.2611504746265044094873626465198e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = -0.4971817854056952714932148600522
y[1] (numeric) = -0.49718178540569527149321486005228
absolute error = 8e-32
relative error = 1.6090694057651531835115002756588e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = -0.510264790456503844898394624218
y[1] (numeric) = -0.510264790456503844898394624218
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = -0.5234427682368233981148199464733
y[1] (numeric) = -0.52344276823682339811481994647335
absolute error = 5e-32
relative error = 9.5521426666034845559608632497757e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = -0.5367154009515242051764018526177
y[1] (numeric) = -0.53671540095152420517640185261775
absolute error = 5e-32
relative error = 9.3159242144638902039118890239370e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=64019308, alloc=4521156, time=2.65
x[1] = 3.49
y[1] (analytic) = -0.5500823613400619808407213272332
y[1] (numeric) = -0.55008236134006198084072132723326
absolute error = 6e-32
relative error = 1.0907457540327835349187017981835e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = -0.5635433127092036623013423733282
y[1] (numeric) = -0.56354331270920366230134237332827
absolute error = 7e-32
relative error = 1.2421405492947618786524677576335e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = -0.5770979089666964519173336942424
y[1] (numeric) = -0.57709790896669645191733369424245
absolute error = 5e-32
relative error = 8.6640410965144275184819031114097e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = -0.5907457946558767540837834877278
y[1] (numeric) = -0.59074579465587675408378348772779
absolute error = 1e-32
relative error = 1.6927754865906805059069236622072e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = -0.604486604991215545378460985316
y[1] (numeric) = -0.60448660499121554537846098531601
absolute error = 1e-32
relative error = 1.6542963760372028284164795514243e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = -0.6183199658947966234772311138702
y[1] (numeric) = -0.61831996589479662347723111387026
absolute error = 6e-32
relative error = 9.7037138228540778820247810258349e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = -0.6322454940337240870437291772895
y[1] (numeric) = -0.63224549403372408704372917728955
absolute error = 5e-32
relative error = 7.9083204976282505718708645078196e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = -0.6462627968584553058764793868963
y[1] (numeric) = -0.64626279685845530587647938689636
absolute error = 6e-32
relative error = 9.2841488465165696497262932724068e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = -0.6603714726420555480483865639633
y[1] (numeric) = -0.66037147264205554804838656396328
absolute error = 2e-32
relative error = 3.0285984220340026746680535994075e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = -0.674571110520370338608599145451
y[1] (numeric) = -0.674571110520370338608599145451
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = -0.6888612905331115326443501606522
y[1] (numeric) = -0.68886129053311153264435016065218
absolute error = 2e-32
relative error = 2.9033421205192047187600121574191e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = -0.7032415836658529941297082747341
y[1] (numeric) = -0.70324158366585299412970827473408
absolute error = 2e-32
relative error = 2.8439728913276337572401084972268e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = -0.7177115518929316810283503064616
y[1] (numeric) = -0.7177115518929316810283503064616
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = -0.732270748221249846577595727932
y[1] (numeric) = -0.73227074822124984657759572793202
absolute error = 2e-32
relative error = 2.7312302244192823224438584799313e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = -0.746918716734973976570076455602
y[1] (numeric) = -0.74691871673497397657007645560201
absolute error = 1e-32
relative error = 1.3388337681124488270074274874001e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = -0.7616549926411259927765627558659
y[1] (numeric) = -0.76165499264112599277656275586593
absolute error = 3e-32
relative error = 3.9387912230407052420243521864590e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = -0.7764791023160621634275955254717
y[1] (numeric) = -0.77647910231606216342759552547175
absolute error = 5e-32
relative error = 6.4393233315437941262487144896753e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = -0.7913905633528350729016090798401
y[1] (numeric) = -0.7913905633528350729016090798401
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = -0.8063888846094339144620438135202
y[1] (numeric) = -0.80638888460943391446204381352022
absolute error = 2e-32
relative error = 2.4801929170547523593322339543679e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = -0.8214735662578982820543751314638
y[1] (numeric) = -0.82147356625789828205437513146387
absolute error = 7e-32
relative error = 8.5212723665442674703799462699580e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = -0.8366440998343005498248069716278
y[1] (numeric) = -0.83664409983430054982480697162787
absolute error = 7e-32
relative error = 8.3667595353703772664612408071827e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = -0.8518999682895918411643298936456
y[1] (numeric) = -0.85189996828959184116432989364563
absolute error = 3e-32
relative error = 3.5215402179475028276446033219075e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = -0.8672406460413065027236108273902
y[1] (numeric) = -0.86724064604130650272361082739029
absolute error = 9e-32
relative error = 1.0377742372987591446913405581965e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=68020160, alloc=4521156, time=2.81
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = -0.8826655990261199129943999105103
y[1] (numeric) = -0.88266559902611991299439991051037
absolute error = 7e-32
relative error = 7.9305231876300363489514814703110e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = -0.8981742847532543697203943020784
y[1] (numeric) = -0.89817428475325436972039430207841
absolute error = 1e-32
relative error = 1.1133696621861302776334866835528e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = -0.9137661523587277155933226437975
y[1] (numeric) = -0.9137661523587277155933226437975
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = -0.9294406426604392774168875977093
y[1] (numeric) = -0.92944064266043927741688759770932
absolute error = 2e-32
relative error = 2.1518318741422604068984305519930e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = -0.9451971882140876101905548624369
y[1] (numeric) = -0.94519718821408761019055486243694
absolute error = 4e-32
relative error = 4.2319211799157385009878450724463e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = -0.9610352133699144543853782538038
y[1] (numeric) = -0.96103521336991445438537825380382
absolute error = 2e-32
relative error = 2.0810891964997905080398700880350e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.53
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = -0.9769541343302692320634197407623
y[1] (numeric) = -0.97695413433026923206341974076232
absolute error = 2e-32
relative error = 2.0471790125245324563386030179976e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = -0.9929533592079883254391227481598
y[1] (numeric) = -0.99295335920798832543912274815988
absolute error = 8e-32
relative error = 8.0567731865886011232866094824093e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = -1.0090322880855833000034318256493
y[1] (numeric) = -1.0090322880855833000034318256493
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.47
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = -1.025190313075232153437669625635
y[1] (numeric) = -1.0251903130752321534376696256351
absolute error = 1e-31
relative error = 9.7542864699953168828023519408051e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = -1.0414268183795675912422723433438
y[1] (numeric) = -1.0414268183795675912422723433439
absolute error = 1e-31
relative error = 9.6022109508949786990876429426039e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.12
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = -1.0577411803532562503034774729765
y[1] (numeric) = -1.0577411803532562503034774729766
absolute error = 1e-31
relative error = 9.4541086096886925047009608042986e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.45
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = -1.0741327675653627125269230597523
y[1] (numeric) = -1.0741327675653627125269230597524
absolute error = 1e-31
relative error = 9.3098360854087656908545545604140e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = -1.0906009408624920721887649260472
y[1] (numeric) = -1.0906009408624920721887649260473
absolute error = 1e-31
relative error = 9.1692567146435696046221277276597e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.14
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = -1.1071450534327047428001953906352
y[1] (numeric) = -1.1071450534327047428001953906353
absolute error = 1e-31
relative error = 9.0322401468488581598243078491540e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = -1.1237644508701971120579391906727
y[1] (numeric) = -1.1237644508701971120579391906729
absolute error = 2e-31
relative error = 1.7797323971685365271592158677858e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = -1.1404584712407415768691319229587
y[1] (numeric) = -1.1404584712407415768691319229589
absolute error = 2e-31
relative error = 1.7536806910856959605178648649884e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = -1.1572264451478794145016116973683
y[1] (numeric) = -1.1572264451478794145016116973685
absolute error = 2e-31
relative error = 1.7282702174546524575336963248517e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.57
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = -1.1740676957998598706276695153856
y[1] (numeric) = -1.1740676957998598706276695153858
absolute error = 2e-31
relative error = 1.7034792858664382881175823645110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = -1.1909815390773187704082363861256
y[1] (numeric) = -1.1909815390773187704082363861258
absolute error = 2e-31
relative error = 1.6792871546518233495808830678029e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.33
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = -1.2079672836016898848127974157074
y[1] (numeric) = -1.2079672836016898848127974157076
absolute error = 2e-31
relative error = 1.6556739798753288865036814873082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.27
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = -1.225024230804342211095410160473
y[1] (numeric) = -1.2250242308043422110954101604732
absolute error = 2e-31
relative error = 1.6326207675800944785592861931395e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=72020992, alloc=4521156, time=2.98
x[1] = 3.94
y[1] (analytic) = -1.2421516749964362537563938505644
y[1] (numeric) = -1.2421516749964362537563938505646
absolute error = 2e-31
relative error = 1.6101093290444888874566606488806e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = -1.2593489034394923204198066883598
y[1] (numeric) = -1.25934890343949232041980668836
absolute error = 2e-31
relative error = 1.5881222388312450629464340598253e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = -1.2766151964166637758559301912485
y[1] (numeric) = -1.2766151964166637758559301912487
absolute error = 2e-31
relative error = 1.5666427954279471834201023552181e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = -1.2939498273047081268827525106807
y[1] (numeric) = -1.2939498273047081268827525106809
absolute error = 2e-31
relative error = 1.5456549842940906895988613746045e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = -1.3113520626466487410979362833252
y[1] (numeric) = -1.3113520626466487410979362833254
absolute error = 2e-31
relative error = 1.5251434431448416882091394929425e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.09
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = -1.3288211622251199333299490479899
y[1] (numeric) = -1.3288211622251199333299490479901
absolute error = 2e-31
relative error = 1.5050934293151883650820579084305e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.74
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = -1.3463563791363880853608318169022
y[1] (numeric) = -1.3463563791363880853608318169025
absolute error = 3e-31
relative error = 2.2282361835908047739775467002530e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.41
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = -1.363956959865041396870317585315
y[1] (numeric) = -1.3639569598650413968703175853152
absolute error = 2e-31
relative error = 1.4663219286610720907428927363392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = -1.3816221443593407986884466192346
y[1] (numeric) = -1.3816221443593407986884466192349
absolute error = 3e-31
relative error = 2.1713606808112519067417288967605e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.76
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = -1.3993511661072244933281454781476
y[1] (numeric) = -1.3993511661072244933281454781478
absolute error = 2e-31
relative error = 1.4292338109551774431242919625047e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.44
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = -1.4171432522129585224070534208273
y[1] (numeric) = -1.4171432522129585224070534208276
absolute error = 3e-31
relative error = 2.1169348937133284765504263120032e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.13
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = -1.4349976234744256959657292715176
y[1] (numeric) = -1.4349976234744256959657292715179
absolute error = 3e-31
relative error = 2.0905957967626317344344898148424e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.82
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = -1.4529134944610451548537141522107
y[1] (numeric) = -1.4529134944610451548537141522109
absolute error = 2e-31
relative error = 1.3765444450923042037280428687759e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = -1.4708900735923147742921442269604
y[1] (numeric) = -1.4708900735923147742921442269606
absolute error = 2e-31
relative error = 1.3597209172235790946251143982340e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.22
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = -1.4889265632169685544380089817521
y[1] (numeric) = -1.4889265632169685544380089817523
absolute error = 2e-31
relative error = 1.3432495929677070833239964427856e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.92
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = -1.5070221596927410822769628863557
y[1] (numeric) = -1.5070221596927410822769628863559
absolute error = 2e-31
relative error = 1.3271204986181288854395237643258e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = -1.5251760534667310884649713203402
y[1] (numeric) = -1.5251760534667310884649713203404
absolute error = 2e-31
relative error = 1.3113240241701882470277558700875e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = -1.5433874291563560628300760061255
y[1] (numeric) = -1.5433874291563560628300760061257
absolute error = 2e-31
relative error = 1.2958509070488132465921910612713e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = -1.5616554656308898331401917272407
y[1] (numeric) = -1.5616554656308898331401917272409
absolute error = 2e-31
relative error = 1.2806922166996830514740936757006e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = -1.5799793360935749534470053079295
y[1] (numeric) = -1.5799793360935749534470053079297
absolute error = 2e-31
relative error = 1.2658393399909308324580269845786e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = -1.5983582081643016908355692264027
y[1] (numeric) = -1.5983582081643016908355692264029
absolute error = 2e-31
relative error = 1.2512839673761114307392261657974e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = -1.6167912439628453427498138283373
y[1] (numeric) = -1.6167912439628453427498138283375
absolute error = 2e-31
relative error = 1.2370180797725553384839043260372e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=76023148, alloc=4521156, time=3.14
x[1] = 4.16
y[1] (analytic) = -1.6352776001926535612316097892908
y[1] (numeric) = -1.635277600192653561231609789291
absolute error = 2e-31
relative error = 1.2230339361123629142237624707952e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = -1.6538164282251753054107794572422
y[1] (numeric) = -1.6538164282251753054107794572424
absolute error = 2e-31
relative error = 1.2093240615261865599905848161302e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = -1.6724068741847229894210819669533
y[1] (numeric) = -1.6724068741847229894210819669535
absolute error = 2e-31
relative error = 1.1958812361226238556293150752240e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = -1.6910480790338593395980987485076
y[1] (numeric) = -1.6910480790338593395980987485078
absolute error = 2e-31
relative error = 1.1826984843285195620845289907576e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = -1.7097391786593004223444551186229
y[1] (numeric) = -1.7097391786593004223444551186231
absolute error = 2e-31
relative error = 1.1697690647577655037859388244154e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = -1.7284793039583262524311770505132
y[1] (numeric) = -1.7284793039583262524311770505134
absolute error = 2e-31
relative error = 1.1570864605783096660516585994530e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = -1.7472675809256903407463615868448
y[1] (numeric) = -1.747267580925690340746361586845
absolute error = 2e-31
relative error = 1.1446443703490530985403967318545e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = -1.7661031307410194906088104104552
y[1] (numeric) = -1.7661031307410194906088104104554
absolute error = 2e-31
relative error = 1.1324366993001378882884881209487e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = -1.7849850698566951027398281302941
y[1] (numeric) = -1.7849850698566951027398281302943
absolute error = 2e-31
relative error = 1.1204575510318229464154561063283e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = -1.8039125100862072008359222794552
y[1] (numeric) = -1.8039125100862072008359222794554
absolute error = 2e-31
relative error = 1.1087012196087170387737703297844e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = -1.822884558692972342413475864514
y[1] (numeric) = -1.8228845586929723424134758645143
absolute error = 3e-31
relative error = 1.6457432730413998213644863078827e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = -1.8419003184796065332083226779057
y[1] (numeric) = -1.841900318479606533208322677906
absolute error = 3e-31
relative error = 1.6287526365576313422009405757544e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = -1.860958887877644217913179263164
y[1] (numeric) = -1.8609588878776442179131792631643
absolute error = 3e-31
relative error = 1.6120721524489939989438827237340e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = -1.8800593610376943754286253662208
y[1] (numeric) = -1.8800593610376943754286253662211
absolute error = 3e-31
relative error = 1.5956942967716492756571919276248e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = -1.899200827920024703093237603664
y[1] (numeric) = -1.8992008279200247030932376036643
absolute error = 3e-31
relative error = 1.5796117798061163867012665094386e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = -1.9183823743855648315499399031558
y[1] (numeric) = -1.9183823743855648315499399031561
absolute error = 3e-31
relative error = 1.5638175371376962801049287815783e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = -1.9376030822873194700029198405699
y[1] (numeric) = -1.9376030822873194700029198405703
absolute error = 4e-31
relative error = 2.0644062948527328351412177081287e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = -1.9568620295621823406267625493371
y[1] (numeric) = -1.9568620295621823406267625493375
absolute error = 4e-31
relative error = 2.0440889237832154309629725619021e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = -1.9761582903231417208108726455763
y[1] (numeric) = -1.9761582903231417208108726455767
absolute error = 4e-31
relative error = 2.0241293521815599893024024052150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = -1.9954909349518683727617974225641
y[1] (numeric) = -1.9954909349518683727617974225645
absolute error = 4e-31
relative error = 2.0045192538529275621681784663522e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = -2.0148590301916766017476474330366
y[1] (numeric) = -2.0148590301916766017476474330369
absolute error = 3e-31
relative error = 1.4889379132963984287109719208574e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = -2.0342616392408491469562573075772
y[1] (numeric) = -2.0342616392408491469562573075775
absolute error = 3e-31
relative error = 1.4747365541039979071044369736920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = -2.0536978218463165725557714761559
y[1] (numeric) = -2.0536978218463165725557714761562
absolute error = 3e-31
relative error = 1.4607796571079470251515678914219e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=80024836, alloc=4521156, time=3.31
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = -2.0731666343976817910966146332443
y[1] (numeric) = -2.0731666343976817910966146332445
absolute error = 2e-31
relative error = 9.6470778895255617865808878131191e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = -2.0926671300215803168808602577823
y[1] (numeric) = -2.0926671300215803168808602577825
absolute error = 2e-31
relative error = 9.5571817003661509178567446659480e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = -2.1121983586763668133522935335094
y[1] (numeric) = -2.1121983586763668133522935335096
absolute error = 2e-31
relative error = 9.4688076609117469715139970379767e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = -2.1317593672471184659313348565068
y[1] (numeric) = -2.131759367247118465931334856507
absolute error = 2e-31
relative error = 9.3819219501436129212950670300211e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = -2.1513491996409456800367096510664
y[1] (numeric) = -2.1513491996409456800367096510666
absolute error = 2e-31
relative error = 9.2964917101035691969558466848461e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = -2.1709668968826005733034876438366
y[1] (numeric) = -2.1709668968826005733034876438369
absolute error = 3e-31
relative error = 1.3818727518636278261207968033714e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = -2.1906114972103737012279432702555
y[1] (numeric) = -2.1906114972103737012279432702558
absolute error = 3e-31
relative error = 1.3694806239355262967392023395378e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = -2.2102820361722694266465863988873
y[1] (numeric) = -2.2102820361722694266465863988876
absolute error = 3e-31
relative error = 1.3572928481088102818317358718794e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = -2.2299775467224503155925613446698
y[1] (numeric) = -2.2299775467224503155925613446701
absolute error = 3e-31
relative error = 1.3453050253395170104888613075830e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = -2.2496970593179409151701985931512
y[1] (numeric) = -2.2496970593179409151701985931514
absolute error = 2e-31
relative error = 8.8900858527430194627094674203568e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = -2.2694396020155812431505179934839
y[1] (numeric) = -2.2694396020155812431505179934842
absolute error = 3e-31
relative error = 1.3219122453558924737057014831949e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = -2.2892042005692202940195181752062
y[1] (numeric) = -2.2892042005692202940195181752065
absolute error = 3e-31
relative error = 1.3104990805337668557773312676805e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = -2.3089898785271398422096416782592
y[1] (numeric) = -2.3089898785271398422096416782596
absolute error = 4e-31
relative error = 1.7323592611638137343188889410608e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = -2.3287956573296988002152788818011
y[1] (numeric) = -2.3287956573296988002152788818015
absolute error = 4e-31
relative error = 1.7176260130038969599014767355197e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = -2.3486205564071883672378692086186
y[1] (numeric) = -2.348620556407188367237869208619
absolute error = 4e-31
relative error = 1.7031273907093003994720156209098e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = -2.3684635932778881829272807804022
y[1] (numeric) = -2.3684635932778881829272807804026
absolute error = 4e-31
relative error = 1.6888585542765766149274677582496e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = -2.3883237836463136806858075749921
y[1] (numeric) = -2.3883237836463136806858075749925
absolute error = 4e-31
relative error = 1.6748147916079870513808001972386e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = -2.4082001415016448158813262073901
y[1] (numeric) = -2.4082001415016448158813262073905
absolute error = 4e-31
relative error = 1.6609915143953860509223686552978e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = -2.4280916792163263261788146856254
y[1] (numeric) = -2.4280916792163263261788146856258
absolute error = 4e-31
relative error = 1.6473842541608691112740115257729e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = -2.4479974076448296640463665993177
y[1] (numeric) = -2.4479974076448296640463665993181
absolute error = 4e-31
relative error = 1.6339886584472822696571858398737e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = -2.4679163362225667253247514756035
y[1] (numeric) = -2.4679163362225667253247514756039
absolute error = 4e-31
relative error = 1.6208004871520343723555666689326e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = -2.4878474730649454825700921787708
y[1] (numeric) = -2.4878474730649454825700921787712
absolute error = 4e-31
relative error = 1.6078156089979796118272318109625e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=84026192, alloc=4521156, time=3.48
x[1] = 4.61
y[1] (analytic) = -2.5077898250665576176888711718273
y[1] (numeric) = -2.5077898250665576176888711718277
absolute error = 4e-31
relative error = 1.5950299981354452633134118949241e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = -2.5277423980004882351846582243842
y[1] (numeric) = -2.5277423980004882351846582243846
absolute error = 4e-31
relative error = 1.5824397308697701391507807778120e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = -2.5477041966177377251279927125974
y[1] (numeric) = -2.5477041966177377251279927125978
absolute error = 4e-31
relative error = 1.5700409825089939346738727475548e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = -2.5676742247467458337459747992399
y[1] (numeric) = -2.5676742247467458337459747992403
absolute error = 4e-31
relative error = 1.5578300243265973291359888939524e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = -2.5876514853930079893074429838229
y[1] (numeric) = -2.5876514853930079893074429838233
absolute error = 4e-31
relative error = 1.5458032206344383290833656193031e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = -2.607634980838773921754162833204
y[1] (numeric) = -2.6076349808387739217541628332044
absolute error = 4e-31
relative error = 1.5339570259612627414332812330753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = -2.6276237127428186062991456798947
y[1] (numeric) = -2.6276237127428186062991456798951
absolute error = 4e-31
relative error = 1.5222879823323866254476539237295e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = -2.6476166822402755539808796320554
y[1] (numeric) = -2.6476166822402755539808796320558
absolute error = 4e-31
relative error = 1.5107927166463568320489674655736e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = -2.667612890042522465927611603558
y[1] (numeric) = -2.6676128900425224659276116035584
absolute error = 4e-31
relative error = 1.4994679381445929831635730780069e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = -2.6876113365371092628494917036729
y[1] (numeric) = -2.6876113365371092628494917036733
absolute error = 4e-31
relative error = 1.4883104359702011164775201917405e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = -2.7076110218877184970389038522753
y[1] (numeric) = -2.7076110218877184970389038522757
absolute error = 4e-31
relative error = 1.4773170768123263245212853633167e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = -2.7276109461341481509210826531746
y[1] (numeric) = -2.727610946134148150921082653175
absolute error = 4e-31
relative error = 1.4664848026325796154701934540513e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.007339
Order of pole (three term test) = -0.8943
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = -2.7476101092923068239584801849428
y[1] (numeric) = -2.7476101092923068239584801849432
absolute error = 4e-31
relative error = 1.4558106284702334449399374630207e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01698
Order of pole (three term test) = -0.9004
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = -2.767607511454211308473521317219
y[1] (numeric) = -2.7676075114542113084735213172194
absolute error = 4e-31
relative error = 1.4452916403230314086696500369671e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02661
Order of pole (three term test) = -0.9113
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = -2.7876021528879765547154963123733
y[1] (numeric) = -2.7876021528879765547154963123737
absolute error = 4e-31
relative error = 1.4349249931006009096922849153355e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03623
Order of pole (three term test) = -0.927
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = -2.8075930341377880262584087164105
y[1] (numeric) = -2.8075930341377880262584087164109
absolute error = 4e-31
relative error = 1.4247079086475936559374946784274e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04584
Order of pole (three term test) = -0.9476
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = -2.8275791561238464485775487727873
y[1] (numeric) = -2.8275791561238464485775487727876
absolute error = 3e-31
relative error = 1.0609782553753560103884704694123e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05543
Order of pole (three term test) = -0.973
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = -2.8475595202422749564132217146596
y[1] (numeric) = -2.8475595202422749564132217146599
absolute error = 3e-31
relative error = 1.0535337290315024430881900614407e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.065
Order of pole (three term test) = -1.003
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = -2.8675331284649786492901502413476
y[1] (numeric) = -2.8675331284649786492901502413479
absolute error = 3e-31
relative error = 1.0461954110381742278103216421208e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07454
Order of pole (three term test) = -1.038
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = -2.8874989834394465693202152576495
y[1] (numeric) = -2.8874989834394465693202152576498
absolute error = 3e-31
relative error = 1.0389614047332227147087011194988e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08405
Order of pole (three term test) = -1.078
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = -2.9074560885884861211739226395384
y[1] (numeric) = -2.9074560885884861211739226395387
absolute error = 3e-31
relative error = 1.0318298569580262048543543563270e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09353
Order of pole (three term test) = -1.122
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = -2.9274034482098799608617106191698
y[1] (numeric) = -2.9274034482098799608617106191701
absolute error = 3e-31
relative error = 1.0247989568484361623412040022147e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.103
Order of pole (three term test) = -1.172
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = -2.9473400675759553877192667889538
y[1] (numeric) = -2.9473400675759553877192667889542
absolute error = 4e-31
relative error = 1.3571559128871771076824201589613e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1124
Order of pole (three term test) = -1.226
NO COMPLEX POLE (six term test) for Equation 1
bytes used=88027848, alloc=4521156, time=3.64
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = -2.9672649530330562827406304097327
y[1] (numeric) = -2.9672649530330562827406304097331
absolute error = 4e-31
relative error = 1.3480427475515155716498906254833e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1217
Order of pole (three term test) = -1.284
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = -2.9871771121009076461481397184653
y[1] (numeric) = -2.9871771121009076461481397184657
absolute error = 4e-31
relative error = 1.3390568586630490105113625117771e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.131
Order of pole (three term test) = -1.348
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = -3.0070755535718627978282707459854
y[1] (numeric) = -3.0070755535718627978282707459858
absolute error = 4e-31
relative error = 1.3301960422140781408026580213539e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1403
Order of pole (three term test) = -1.416
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = -3.026959287610023315996029785628
y[1] (numeric) = -3.0269592876100233159960297856284
absolute error = 4e-31
relative error = 1.3214581432835372395559478025543e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1495
Order of pole (three term test) = -1.488
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = -3.0468273258502218021766327470316
y[1] (numeric) = -3.046827325850221802176632747032
absolute error = 4e-31
relative error = 1.3128410547137895031480888312155e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1586
Order of pole (three term test) = -1.566
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = -3.0666786814968575743104585897138
y[1] (numeric) = -3.0666786814968575743104585897142
absolute error = 4e-31
relative error = 1.3043427158294864874183555020239e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1677
Order of pole (three term test) = -1.648
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = -3.0865123694225754044943291441219
y[1] (numeric) = -3.0865123694225754044943291441223
absolute error = 4e-31
relative error = 1.2959611111969461572007166018071e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1767
Order of pole (three term test) = -1.734
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = -3.1063274062667774335675731995194
y[1] (numeric) = -3.1063274062667774335675731995198
absolute error = 4e-31
relative error = 1.2876942694225684681686692865292e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1856
Order of pole (three term test) = -1.825
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = -3.1261228105339584114335092408118
y[1] (numeric) = -3.1261228105339584114335092408122
absolute error = 4e-31
relative error = 1.2795402619888687976219358412126e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1945
Order of pole (three term test) = -1.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = -3.1458976026918544296742604464858
y[1] (numeric) = -3.1458976026918544296742604464862
absolute error = 4e-31
relative error = 1.2714972021267680881083449224025e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2033
Order of pole (three term test) = -2.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = -3.1656508052693953316674308040397
y[1] (numeric) = -3.1656508052693953316674308040402
absolute error = 5e-31
relative error = 1.5794540546535430180187357710469e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.212
Order of pole (three term test) = -2.124
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = -3.1853814429544510050452574116347
y[1] (numeric) = -3.1853814429544510050452574116352
absolute error = 5e-31
relative error = 1.5696707253252799601835466321994e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2206
Order of pole (three term test) = -2.232
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = -3.2050885426913617819484480229353
y[1] (numeric) = -3.2050885426913617819484480229358
absolute error = 5e-31
relative error = 1.5600193047401503810314612721986e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2291
Order of pole (three term test) = -2.345
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = -3.2247711337782431941159535140125
y[1] (numeric) = -3.224771133778243194115953514013
absolute error = 5e-31
relative error = 1.5504976299331490486930039227712e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2375
Order of pole (three term test) = -2.462
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = -3.2444282479640553524162533206808
y[1] (numeric) = -3.2444282479640553524162533206812
absolute error = 4e-31
relative error = 1.2328828669612531188160711284781e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2459
Order of pole (three term test) = -2.583
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = -3.264058919545427243963091597697
y[1] (numeric) = -3.2640589195454272439630915976974
absolute error = 4e-31
relative error = 1.2254680747481924744708744190963e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2541
Order of pole (three term test) = -2.709
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = sin(x) - 1,0;
Iterations = 490
Total Elapsed Time = 3 Seconds
Elapsed Time(since restart) = 3 Seconds
Time to Timeout = 2 Minutes 56 Seconds
Percent Done = 100.2 %
> quit
bytes used=90956636, alloc=4521156, time=3.76