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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_2D0,
> #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,
> 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_2D0,
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, 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_2D0,
> #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,
> 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_2D0,
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, 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_2D0,
> #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,
> 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_2D0,
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, 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_2D0,
> #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,
> 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_2D0,
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, 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_2D0,
> #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,
> 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_2D0,
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, 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_2D0,
> #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,
> 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_2D0,
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, 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_2D0,
> #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,
> 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_2D0,
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, 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_2D0,
> #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,
> 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_2D0,
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, 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_2D0,
> #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,
> 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 exp 1 $eq_no = 1
> array_tmp1[1] := exp(array_x[1]);
> #emit pre div CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_2D0[1] / array_tmp1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[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;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre exp ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1[1] * array_x[2] / 1;
> #emit pre div CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := -ats(2,array_tmp1,array_tmp2,2) / array_tmp1[1];
> #emit pre add CONST FULL $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;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre exp ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1[2] * array_x[2] / 2;
> #emit pre div CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := -ats(3,array_tmp1,array_tmp2,2) / array_tmp1[1];
> #emit pre add CONST FULL $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;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre exp ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1[3] * array_x[2] / 3;
> #emit pre div CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := -ats(4,array_tmp1,array_tmp2,2) / array_tmp1[1];
> #emit pre add CONST FULL $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;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre exp ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1[4] * array_x[2] / 4;
> #emit pre div CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := -ats(5,array_tmp1,array_tmp2,2) / array_tmp1[1];
> #emit pre add CONST FULL $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;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit exp LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
> #emit div CONST FULL $eq_no = 1 i = 1
> array_tmp2[kkk] := -ats(kkk,array_tmp1,array_tmp2,2) / array_tmp1[1];
> #emit NOT FULL - FULL add $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;
> 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_2D0,
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, 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] := exp(array_x[1]);
array_tmp2[1] := array_const_2D0[1]/array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[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;
array_tmp1[2] := array_tmp1[1]*array_x[2];
array_tmp2[2] := -ats(2, array_tmp1, array_tmp2, 2)/array_tmp1[1];
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;
array_tmp1[3] := 1/2*array_tmp1[2]*array_x[2];
array_tmp2[3] := -ats(3, array_tmp1, array_tmp2, 2)/array_tmp1[1];
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;
array_tmp1[4] := 1/3*array_tmp1[3]*array_x[2];
array_tmp2[4] := -ats(4, array_tmp1, array_tmp2, 2)/array_tmp1[1];
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;
array_tmp1[5] := 1/4*array_tmp1[4]*array_x[2];
array_tmp2[5] := -ats(5, array_tmp1, array_tmp2, 2)/array_tmp1[1];
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;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_tmp1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2[kkk] :=
-ats(kkk, array_tmp1, array_tmp2, 2)/array_tmp1[1];
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;
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/exp(x));
> end;
exact_soln_y := proc(x) return -2.0/exp(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_2D0,
> #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,
> 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/div_c_exppostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 2.0 / exp(x);");
> 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 := 1.0;");
> omniout_str(ALWAYS,"## did poorly with x_start := -5.0;");
> 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,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> 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/exp(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:= 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[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 := 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_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_2D0[1] := 2.0;
> 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 := 1.0;
> ## did poorly with x_start := -5.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> 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 ) = 2.0 / exp(x);");
> 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,"2013-05-26T00:25:49-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div_c_exp")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 2.0 / exp(x);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_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,"div_c_exp diffeq.mxt")
> ;
> logitem_str(html_log_file,"div_c_exp 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_2D0,
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, 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/div_c_exppostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 2.0 / exp(x);");
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 := 1.0;");
omniout_str(ALWAYS, "## did poorly with x_start := -5.0;");
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, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
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/exp(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 := 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[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 := 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_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 1.0;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
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 ) = 2.0 / exp(x);");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T00:25:49-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"div_c_exp");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 2.0 / exp(x);");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_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, "div_c_exp diffeq.mxt");
logitem_str(html_log_file, "div_c_exp 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/div_c_exppostode.ode#################
diff ( y , x , 1 ) = 2.0 / exp(x);
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 1.0;
## did poorly with x_start := -5.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
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/exp(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
estimated_steps = 4000000
step_error = 2.5000000000000000000000000000000e-17
est_needed_step_err = 2.5000000000000000000000000000000e-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 = 1.8243849415069638273310067493493e-183
estimated_step_error = 1.8243849415069638273310067493493e-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 = 1.2243239865597218625236973167578e-175
estimated_step_error = 1.2243239865597218625236973167578e-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 = 8.2162988862900641390800296773248e-168
estimated_step_error = 8.2162988862900641390800296773248e-168
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 = 5.5138644369995380608137065813461e-160
estimated_step_error = 5.5138644369995380608137065813461e-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 = 3.7002912379791636745607763122370e-152
estimated_step_error = 3.7002912379791636745607763122370e-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 = 2.4832226787298653605115599105896e-144
estimated_step_error = 2.4832226787298653605115599105896e-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 = 1.6664615427537387019432017630483e-136
estimated_step_error = 1.6664615427537387019432017630483e-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 = 1.1183420848978399655016352750556e-128
estimated_step_error = 1.1183420848978399655016352750556e-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 = 7.5050488983806735306293381958378e-121
estimated_step_error = 7.5050488983806735306293381958378e-121
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 = 5.0365291815697705874859661956397e-113
estimated_step_error = 5.0365291815697705874859661956397e-113
best_h = 0.001024
opt_iter = 11
bytes used=4000460, alloc=2883056, time=0.31
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.3799254723505066081712118209760e-105
estimated_step_error = 3.3799254723505066081712118209760e-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 = 2.2681865777313174344765835103479e-97
estimated_step_error = 2.2681865777313174344765835103479e-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 = 1.5220965207513085540393869716663e-89
estimated_step_error = 1.5220965207513085540393869716663e-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 = 1.0213842154249593084336319688065e-81
estimated_step_error = 1.0213842154249593084336319688065e-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 = 6.8533539022595793120966584199305e-74
estimated_step_error = 6.8533539022595793120966584199305e-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 = 4.5978133177201962413499158357203e-66
estimated_step_error = 4.5978133177201962413499158357203e-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 = 3.0836700873842923441104624010883e-58
estimated_step_error = 3.0836700873842923441104624010883e-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 = 2.0669102406911079765287947359026e-50
estimated_step_error = 2.0669102406911079765287947359026e-50
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = -0.73575888234288464319104754032291
y[1] (numeric) = -0.73575888234288464319104754032291
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = -0.72843795914304663951409259127469
y[1] (numeric) = -0.72843795914304663951409259127468
absolute error = 1e-32
relative error = 1.3728005075084582469948881583302e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.041e+11
Order of pole (six term test) = 4.329e+20
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = -0.72118988034615659656268326930804
y[1] (numeric) = -0.72118988034615659656268326930802
absolute error = 2e-32
relative error = 2.7731947639642979167991997771454e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.454e+11
Order of pole (six term test) = 1.615e+21
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = -0.71401392113829473953486123130269
y[1] (numeric) = -0.71401392113829473953486123130269
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.033e+11
Order of pole (six term test) = 3.556e+20
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = -0.70690936391756029630511653061792
y[1] (numeric) = -0.7069093639175602963051165306179
absolute error = 2e-32
relative error = 2.8292170143515595195194860071813e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.570e+11
Order of pole (six term test) = 1.354e+21
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = -0.69987549822231070934359774715362
y[1] (numeric) = -0.69987549822231070934359774715362
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 8.920e+10
Order of pole (six term test) = 5.474e+20
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = -0.69291162066011487940701669618026
y[1] (numeric) = -0.69291162066011487940701669618025
absolute error = 1e-32
relative error = 1.4431854946339791231206876424608e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = -0.68601703483741333626641097879752
y[1] (numeric) = -0.6860170348374133362664109787975
absolute error = 2e-32
relative error = 2.9153794999769966738778707729755e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.129e+11
Order of pole (six term test) = 2.911e+20
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = -0.67919105128987830243022043049529
y[1] (numeric) = -0.67919105128987830243022043049529
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
bytes used=8001312, alloc=3931440, time=0.64
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.156e+11
Order of pole (six term test) = 9.268e+20
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = -0.67243298741346668581101630178611
y[1] (numeric) = -0.6724329874134666858110163017861
absolute error = 1e-32
relative error = 1.4871370362815326581559532945679e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = -0.66574216739615910657769381286262
y[1] (numeric) = -0.66574216739615910657769381286262
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.120e+11
Order of pole (six term test) = 6.398e+20
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = -0.65911792215037813203892896763225
y[1] (numeric) = -0.65911792215037813203892896763225
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.290e+11
Order of pole (six term test) = 1.722e+21
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = -0.65255958924607896132506964748516
y[1] (numeric) = -0.65255958924607896132506964748514
absolute error = 2e-32
relative error = 3.0648542032930020449686230918988e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.093e+11
Order of pole (six term test) = 2.792e+21
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = -0.64606651284450586888117122528068
y[1] (numeric) = -0.64606651284450586888117122528067
absolute error = 1e-32
relative error = 1.5478282500623557451965061635118e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = -0.63963804363260778236032285534765
y[1] (numeric) = -0.63963804363260778236032285534764
absolute error = 1e-32
relative error = 1.5633841825930778780657781205898e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = -0.63327353875810643642039990485905
y[1] (numeric) = -0.63327353875810643642039990485904
absolute error = 1e-32
relative error = 1.5790964548448838136253503140034e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = -0.62697236176521060918551214962199
y[1] (numeric) = -0.62697236176521060918551214962198
absolute error = 1e-32
relative error = 1.5949666380580923363238956180109e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.543e+11
Order of pole (six term test) = 1.112e+21
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = -0.62073388253097001274222223091491
y[1] (numeric) = -0.6207338825309700127422222309149
absolute error = 1e-32
relative error = 1.6109963192642499637752786362050e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = -0.61455747720226247300654539383636
y[1] (numeric) = -0.61455747720226247300654539383635
absolute error = 1e-32
relative error = 1.6271871014448354239410142814865e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = -0.60844252813340809762720634865897
y[1] (numeric) = -0.60844252813340809762720634865894
absolute error = 3e-32
relative error = 4.9306218110746774164762468054117e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.213e+11
Order of pole (six term test) = 4.324e+21
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = -0.60238842382440419328995521416645
y[1] (numeric) = -0.60238842382440419328995521416643
absolute error = 2e-32
relative error = 3.3201169227365474895307674296016e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = -0.59639455885977475586320190075193
y[1] (numeric) = -0.59639455885977475586320190075191
absolute error = 2e-32
relative error = 3.3534846525490236810035894273757e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.771e+11
Order of pole (six term test) = 1.157e+21
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = -0.59046033384802841828302456864059
y[1] (numeric) = -0.59046033384802841828302456864057
absolute error = 2e-32
relative error = 3.3871877336213346338871451880633e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=12002172, alloc=4193536, time=0.99
x[1] = 1.23
y[1] (analytic) = -0.58458515536171880192188878381439
y[1] (numeric) = -0.58458515536171880192188878381436
absolute error = 3e-32
relative error = 5.1318443044345103606852285271783e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.518e+11
Order of pole (six term test) = 1.260e+21
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = -0.57876843587810127742626436986212
y[1] (numeric) = -0.5787684358781012774262643698621
absolute error = 2e-32
relative error = 3.4556134647626755980576154941220e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = -0.57300959372038020064977085329567
y[1] (numeric) = -0.57300959372038020064977085329565
absolute error = 2e-32
relative error = 3.4903429574618413761305460296723e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = -0.56730805299954074835648401695181
y[1] (numeric) = -0.56730805299954074835648401695179
absolute error = 2e-32
relative error = 3.5254214873653821649737080556228e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.504e+11
Order of pole (six term test) = 2.423e+21
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = -0.56166324355675953682950026030951
y[1] (numeric) = -0.56166324355675953682950026030948
absolute error = 3e-32
relative error = 5.3412788435332807865392070843279e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = -0.55607460090638826439862831202818
y[1] (numeric) = -0.55607460090638826439862831202815
absolute error = 3e-32
relative error = 5.3949595883539221935530776108612e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.561e+11
Order of pole (six term test) = 3.687e+21
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = -0.55054156617950467620394727427232
y[1] (numeric) = -0.55054156617950467620394727427229
absolute error = 3e-32
relative error = 5.4491798336292136357735225537672e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.171e+11
Order of pole (six term test) = 6.915e+20
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = -0.5450635860680252062446663351267
y[1] (numeric) = -0.54506358606802520624466633512667
absolute error = 3e-32
relative error = 5.5039450014288663306862348740172e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.249e+11
Order of pole (six term test) = 7.418e+20
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = -0.53964011276937370793091808153778
y[1] (numeric) = -0.53964011276937370793091808153775
absolute error = 3e-32
relative error = 5.5592605683152980355194875183368e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = -0.5342706039317007399654310472076
y[1] (numeric) = -0.53427060393170073996543104720758
absolute error = 2e-32
relative error = 3.7434213772608625685580558298259e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = -0.52895452259964792943801891542745
y[1] (numeric) = -0.52895452259964792943801891542743
absolute error = 2e-32
relative error = 3.7810433875687807458219777860331e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = -0.52369133716065198852399931102871
y[1] (numeric) = -0.52369133716065198852399931102868
absolute error = 3e-32
relative error = 5.7285652580495036905772798401179e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.077e+11
Order of pole (six term test) = 5.914e+20
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = -0.51848052129178301514346522142309
y[1] (numeric) = -0.51848052129178301514346522142307
absolute error = 2e-32
relative error = 3.8574255306969743381388389099302e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = -0.51332155390711176136717341008552
y[1] (numeric) = -0.51332155390711176136717341008549
absolute error = 3e-32
relative error = 5.8442899526928218559962546569502e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = -0.50821391910560060625202965545668
y[1] (numeric) = -0.50821391910560060625202965545666
absolute error = 2e-32
relative error = 3.9353506954704728989210772223787e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.111e+11
Order of pole (six term test) = 4.417e+20
TOP MAIN SOLVE Loop
bytes used=16003116, alloc=4259060, time=1.34
x[1] = 1.38
y[1] (analytic) = -0.50315710611951302216003002973818
y[1] (numeric) = -0.50315710611951302216003002973816
absolute error = 2e-32
relative error = 3.9749016274947481189091677809396e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = -0.49815060926333637546429785699966
y[1] (numeric) = -0.49815060926333637546429785699962
absolute error = 4e-32
relative error = 8.0297001059884037560691317177131e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = -0.49319392788321295387972247966754
y[1] (numeric) = -0.4931939278832129538797224796675
absolute error = 4e-32
relative error = 8.1103999336893491744482177904572e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.528e+10
Order of pole (six term test) = 3.441e+20
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = -0.48828656630687416347879194624471
y[1] (numeric) = -0.48828656630687416347879194624468
absolute error = 3e-32
relative error = 6.1439331061067645010611059195690e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = -0.48342803379407288877059956197097
y[1] (numeric) = -0.48342803379407288877059956197093
absolute error = 4e-32
relative error = 8.2742408805027854924486016180388e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = -0.4786178444875090590377256987904
y[1] (numeric) = -0.47861784448750905903772569879036
absolute error = 4e-32
relative error = 8.3573983838464923131607835287058e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = -0.4738555173642435134467330551028
y[1] (numeric) = -0.47385551736424351344673305510277
absolute error = 3e-32
relative error = 6.3310437254948292385099933939363e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.934e+11
Order of pole (six term test) = 2.478e+21
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = -0.46914057618759530627829783412195
y[1] (numeric) = -0.46914057618759530627829783412192
absolute error = 3e-32
relative error = 6.3946717727532260825829160133714e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.227e+11
Order of pole (six term test) = 7.772e+20
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = -0.4644725494595176419674141413649
y[1] (numeric) = -0.46447254945951764196741414136487
absolute error = 3e-32
relative error = 6.4589392925178091562339848339240e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = -0.45985097037344767750748876862291
y[1] (numeric) = -0.45985097037344767750748876862287
absolute error = 4e-32
relative error = 8.6984702821254818170163438397241e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = -0.45527537676762547715927481158951
y[1] (numeric) = -0.45527537676762547715927481158947
absolute error = 4e-32
relative error = 8.7858913618375133714675752866343e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.224e+11
Order of pole (six term test) = 8.454e+20
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = -0.45074531107887745132121401376173
y[1] (numeric) = -0.4507453110788774513212140137617
absolute error = 3e-32
relative error = 6.6556432785054969130634337810209e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.559e+11
Order of pole (six term test) = 1.206e+21
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = -0.44626032029685965786656094152802
y[1] (numeric) = -0.44626032029685965786656094152799
absolute error = 3e-32
relative error = 6.7225336055070972339030831901790e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = -0.44181995591875639023929199353893
y[1] (numeric) = -0.44181995591875639023929199353889
absolute error = 4e-32
relative error = 9.0534615886285043681686794876231e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.039e+10
Order of pole (six term test) = 2.732e+20
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = -0.43742377390442952212985753283752
y[1] (numeric) = -0.43742377390442952212985753283749
absolute error = 3e-32
relative error = 6.8583377927132388104823546351596e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.418e+11
Order of pole (six term test) = 1.448e+21
bytes used=20005336, alloc=4259060, time=1.69
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = -0.43307133463201412362786904627373
y[1] (numeric) = -0.4330713346320141236278690462737
absolute error = 3e-32
relative error = 6.9272652334496712136192795616319e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = -0.42876220285395590837633282336661
y[1] (numeric) = -0.42876220285395590837633282336659
absolute error = 2e-32
relative error = 4.6645902709881259027933867662438e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.118e+11
Order of pole (six term test) = 5.980e+20
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = -0.42449594765348611543550999515945
y[1] (numeric) = -0.42449594765348611543550999515942
absolute error = 3e-32
relative error = 7.0672052738861119882089597188767e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = -0.42027214240152947330831826638783
y[1] (numeric) = -0.42027214240152947330831826638781
absolute error = 2e-32
relative error = 4.7588212451378540618839355044150e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = -0.41609036471404093688776773145513
y[1] (numeric) = -0.41609036471404093688776773145511
absolute error = 2e-32
relative error = 4.8066481937751781736211397590791e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = -0.41195019640976693096457268007686
y[1] (numeric) = -0.41195019640976693096457268007683
absolute error = 3e-32
relative error = 7.2824337168561499747191030963601e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.254e+11
Order of pole (six term test) = 4.028e+20
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = -0.40785122346842687638409107270102
y[1] (numeric) = -0.407851223468426876384091072701
absolute error = 2e-32
relative error = 4.9037489283266221980462867706038e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = -0.4037930359893108169703585352867
y[1] (numeric) = -0.40379303598931081697035853528668
absolute error = 2e-32
relative error = 4.9530324243951148036542863564240e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = -0.39977522815028900694540718427019
y[1] (numeric) = -0.39977522815028900694540718427016
absolute error = 3e-32
relative error = 7.5042168417503815492798251679712e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = -0.39579739816722935976845242258825
y[1] (numeric) = -0.39579739816722935976845242258823
absolute error = 2e-32
relative error = 5.0530903165638672074060929249050e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.342e+10
Order of pole (six term test) = 2.889e+20
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = -0.39185914825381870010601272007459
y[1] (numeric) = -0.39185914825381870010601272007457
absolute error = 2e-32
relative error = 5.1038747185367257355366544351225e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.530e+10
Order of pole (six term test) = 7.343e+20
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = -0.38796008458178380102467698857468
y[1] (numeric) = -0.38796008458178380102467698857466
absolute error = 2e-32
relative error = 5.1551695122346810458097983038692e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.554e+11
Order of pole (six term test) = 1.051e+21
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = -0.38409981724150822847708958234667
y[1] (numeric) = -0.38409981724150822847708958234664
absolute error = 3e-32
relative error = 7.8104697407697731064859606390684e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.295e+11
Order of pole (six term test) = 8.297e+20
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = -0.38027796020304105473278211658868
y[1] (numeric) = -0.38027796020304105473278211658865
absolute error = 3e-32
relative error = 7.8889662666703481013307057089807e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 4.327e+11
Order of pole (six term test) = 6.308e+21
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = -0.37649413127749354159270234015759
y[1] (numeric) = -0.37649413127749354159270234015756
absolute error = 3e-32
relative error = 7.9682516957717506003785242832470e-30 %
Correct digits = 32
h = 0.01
bytes used=24005980, alloc=4324584, time=2.05
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.785e+10
Order of pole (six term test) = 4.463e+20
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = -0.37274795207881993302359197748017
y[1] (numeric) = -0.37274795207881993302359197748014
absolute error = 3e-32
relative error = 8.0483339566829621550348529003847e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = -0.3690390479859785352596275318049
y[1] (numeric) = -0.36903904798597853525962753180488
absolute error = 2e-32
relative error = 5.4194807051312062175548592062532e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = -0.36536704810546930044780167551788
y[1] (numeric) = -0.36536704810546930044780167551785
absolute error = 3e-32
relative error = 8.2109210875907996411862939945136e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = -0.36173158523424416756419098130371
y[1] (numeric) = -0.36173158523424416756419098130367
absolute error = 4e-32
relative error = 1.1057922955248008111757704702922e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = -0.35813229582298645160429346866125
y[1] (numeric) = -0.35813229582298645160429346866122
absolute error = 3e-32
relative error = 8.3767926964140810114692782095290e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.093e+11
Order of pole (six term test) = 5.465e+20
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = -0.35456881993975560895575438851885
y[1] (numeric) = -0.35456881993975560895575438851882
absolute error = 3e-32
relative error = 8.4609808626424811964766450767121e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.617e+11
Order of pole (six term test) = 3.610e+21
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = -0.35104080123399374339972138868441
y[1] (numeric) = -0.35104080123399374339972138868438
absolute error = 3e-32
relative error = 8.5460151340079865179056482545403e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = -0.34754788690089025336143451733274
y[1] (numeric) = -0.34754788690089025336143451733271
absolute error = 3e-32
relative error = 8.6319040140085956552997495572641e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.624e+11
Order of pole (six term test) = 1.301e+21
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = -0.34408972764610105684507989725189
y[1] (numeric) = -0.34408972764610105684507989725186
absolute error = 3e-32
relative error = 8.7186560916038829748205109366746e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = -0.34066597765081886594599981232611
y[1] (numeric) = -0.34066597765081886594599981232608
absolute error = 3e-32
relative error = 8.8062800420739016441743808737428e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = -0.33727629453719101793860222566362
y[1] (numeric) = -0.33727629453719101793860222566358
absolute error = 4e-32
relative error = 1.1859712837182291823138143164094e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.085e+11
Order of pole (six term test) = 4.528e+20
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = -0.33392033933408140469425995016587
y[1] (numeric) = -0.33392033933408140469425995016583
absolute error = 4e-32
relative error = 1.1978904932766226657916933453631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.323e+10
Order of pole (six term test) = 3.200e+20
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = -0.33059777644317307659360944086443
y[1] (numeric) = -0.33059777644317307659360944086439
absolute error = 4e-32
relative error = 1.2099294928825892167462047906055e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.915e+11
Order of pole (six term test) = 1.834e+21
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = -0.32730827360540813116539251467187
y[1] (numeric) = -0.32730827360540813116539251467183
absolute error = 4e-32
relative error = 1.2220894864461219649458081851989e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=28007268, alloc=4324584, time=2.41
x[1] = 1.82
y[1] (analytic) = -0.3240515018677615304127380290285
y[1] (numeric) = -0.32405150186776153041273802902846
absolute error = 4e-32
relative error = 1.2343716899767106254127543291799e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = -0.32082713555034552418092756975611
y[1] (numeric) = -0.32082713555034552418092756975606
absolute error = 5e-32
relative error = 1.5584716646311793259240084424932e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = -0.31763485221384138998156885278391
y[1] (numeric) = -0.31763485221384138998156885278387
absolute error = 4e-32
relative error = 1.2593076522053313634424029154050e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.328e+11
Order of pole (six term test) = 6.985e+20
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = -0.31447433262725523242001894980624
y[1] (numeric) = -0.3144743326272552324200189498062
absolute error = 4e-32
relative error = 1.2719639045203663408694443741274e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.459e+11
Order of pole (six term test) = 9.961e+20
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = -0.31134526073599461777912982348316
y[1] (numeric) = -0.31134526073599461777912982348312
absolute error = 4e-32
relative error = 1.2847473542858268086035888585819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.612e+11
Order of pole (six term test) = 1.203e+21
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = -0.30824732363026285139617165354796
y[1] (numeric) = -0.30824732363026285139617165354792
absolute error = 4e-32
relative error = 1.2976592798573422230058062648698e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.906e+11
Order of pole (six term test) = 2.082e+21
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = -0.30518021151376773723433345617434
y[1] (numeric) = -0.30518021151376773723433345617431
absolute error = 3e-32
relative error = 9.8302572932867228209524272119798e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = -0.3021436176727416904986820260546
y[1] (numeric) = -0.30214361767274169049868202605457
absolute error = 3e-32
relative error = 9.9290530215646160257013587451400e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 3.373e+11
Order of pole (six term test) = 7.765e+21
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = -0.29913723844527010528202413820747
y[1] (numeric) = -0.29913723844527010528202413820744
absolute error = 3e-32
relative error = 1.0028841663418904124108796091539e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 5.241e+11
Order of pole (six term test) = 1.465e+22
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = -0.29616077319092491005187681690838
y[1] (numeric) = -0.29616077319092491005187681690835
absolute error = 3e-32
relative error = 1.0129633197796930023720986878278e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = -0.29321392426070027430878891399001
y[1] (numeric) = -0.29321392426070027430878891398998
absolute error = 3e-32
relative error = 1.0231437703936124752419898249413e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.130e+11
Order of pole (six term test) = 8.209e+20
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = -0.29029639696724745996162616737418
y[1] (numeric) = -0.29029639696724745996162616737414
absolute error = 4e-32
relative error = 1.3779020483162586134558038467988e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = -0.28740789955540584088015289513921
y[1] (numeric) = -0.28740789955540584088015289513918
absolute error = 3e-32
relative error = 1.0438126455955908151697802188814e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.975e+10
Order of pole (six term test) = 5.599e+20
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = -0.28454814317302714370230801772766
y[1] (numeric) = -0.28454814317302714370230801772763
absolute error = 3e-32
relative error = 1.0543031370883940001436322900347e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = -0.28171684184208999229594292219192
y[1] (numeric) = -0.28171684184208999229594292219189
absolute error = 3e-32
relative error = 1.0648990597734949007162153208123e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=32008792, alloc=4324584, time=2.76
x[1] = 1.97
y[1] (analytic) = -0.27891371243010186730539604907824
y[1] (numeric) = -0.27891371243010186730539604907821
absolute error = 3e-32
relative error = 1.0756014732519919919816751155846e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = -0.27613847462178562095502707959073
y[1] (numeric) = -0.2761384746217856209550270795907
absolute error = 3e-32
relative error = 1.0864114477741518312768652129717e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = -0.27339085089104771573759642680838
y[1] (numeric) = -0.27339085089104771573759642680834
absolute error = 4e-32
relative error = 1.4631067524619133022870341667028e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.060e+11
Order of pole (six term test) = 2.184e+21
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = -0.27067056647322538378799898994497
y[1] (numeric) = -0.27067056647322538378799898994493
absolute error = 4e-32
relative error = 1.4778112197861300454460854921150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.323e+10
Order of pole (six term test) = 4.994e+20
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = -0.26797734933760993163516210074751
y[1] (numeric) = -0.26797734933760993163516210074747
absolute error = 4e-32
relative error = 1.4926634694638388564699529574731e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.462e+11
Order of pole (six term test) = 1.636e+21
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = -0.2653109301602434426396855294633
y[1] (numeric) = -0.26531093016024344263968552946326
absolute error = 4e-32
relative error = 1.5076649867323844222274857354120e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.134e+11
Order of pole (six term test) = 7.992e+20
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = -0.2626710422969861567647978241762
y[1] (numeric) = -0.26267104229698615676479782417617
absolute error = 3e-32
relative error = 1.1421129538169961775025024484204e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = -0.2600574217568518343961621541422
y[1] (numeric) = -0.26005742175685183439616215414217
absolute error = 3e-32
relative error = 1.1535913798318497053412857342226e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.439e+11
Order of pole (six term test) = 1.242e+21
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = -0.25746980717560843772469303348974
y[1] (numeric) = -0.25746980717560843772469303348971
absolute error = 3e-32
relative error = 1.1651851659460157724366996217866e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.583e+11
Order of pole (six term test) = 9.150e+20
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = -0.25490793978964148973852270144483
y[1] (numeric) = -0.2549079397896414897385227014448
absolute error = 3e-32
relative error = 1.1768954715477673160289443122434e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.425e+11
Order of pole (six term test) = 9.866e+20
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = -0.25237156341007749713823574894352
y[1] (numeric) = -0.25237156341007749713823574894349
absolute error = 3e-32
relative error = 1.1887234676774231318025234081519e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = -0.24986042439716484949609962897764
y[1] (numeric) = -0.24986042439716484949609962897761
absolute error = 3e-32
relative error = 1.2006703371444528816359975891804e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = -0.24737427163490963272785765185998
y[1] (numeric) = -0.24737427163490963272785765185995
absolute error = 3e-32
relative error = 1.2127372746457590262460161074663e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = -0.24491285650596382043729475214525
y[1] (numeric) = -0.24491285650596382043729475214522
absolute error = 3e-32
relative error = 1.2249254868851475110174591115718e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.026e+11
Order of pole (six term test) = 6.151e+20
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = -0.24247593286676333193178390681564
y[1] (numeric) = -0.24247593286676333193178390681561
absolute error = 3e-32
relative error = 1.2372361926939991521878330499885e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=36009520, alloc=4324584, time=3.11
x[1] = 2.12
y[1] (analytic) = -0.24006325702291347069389640532458
y[1] (numeric) = -0.24006325702291347069389640532455
absolute error = 3e-32
relative error = 1.2496706231531537906250974174170e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.051e+11
Order of pole (six term test) = 1.605e+21
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = -0.23767458770481928183241092954488
y[1] (numeric) = -0.23767458770481928183241092954485
absolute error = 3e-32
relative error = 1.2622300217160194017158710932124e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = -0.23530968604355839152815844137813
y[1] (numeric) = -0.2353096860435583915281584413781
absolute error = 3e-32
relative error = 1.2749156443329184723775983595065e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = -0.23296831554699391573854142836567
y[1] (numeric) = -0.23296831554699391573854142836565
absolute error = 2e-32
relative error = 8.5848583971778938662399876124018e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.437e+11
Order of pole (six term test) = 1.070e+21
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = -0.23065024207612504943169198345969
y[1] (numeric) = -0.23065024207612504943169198345967
absolute error = 2e-32
relative error = 8.6711376584634548838689864354102e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.595e+11
Order of pole (six term test) = 4.384e+21
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = -0.22835523382167297138948422676448
y[1] (numeric) = -0.22835523382167297138948422676446
absolute error = 2e-32
relative error = 8.7582840407408343822424252687579e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.217e+11
Order of pole (six term test) = 9.605e+20
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = -0.2260830612808997231503695594535
y[1] (numeric) = -0.22608306128089972315036955945348
absolute error = 2e-32
relative error = 8.8463062587208823266150074163391e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.116e+11
Order of pole (six term test) = 5.118e+20
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = -0.22383349723465774396061136811429
y[1] (numeric) = -0.22383349723465774396061136811427
absolute error = 2e-32
relative error = 8.9352131146987488146044744309985e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = -0.22160631672466776666828885169988
y[1] (numeric) = -0.22160631672466776666828885169986
absolute error = 2e-32
relative error = 9.0250134994341209264717771668886e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.757e+10
Order of pole (six term test) = 3.047e+20
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = -0.21940129703102280233072422159711
y[1] (numeric) = -0.21940129703102280233072422159709
absolute error = 2e-32
relative error = 9.1157163930403061028202043735619e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.826e+11
Order of pole (six term test) = 1.642e+21
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = -0.21721821764991596391504727554914
y[1] (numeric) = -0.21721821764991596391504727554912
absolute error = 2e-32
relative error = 9.2073308658822509587921440290796e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.535e+11
Order of pole (six term test) = 4.801e+21
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = -0.21505686027158990185570719310607
y[1] (numeric) = -0.21505686027158990185570719310605
absolute error = 2e-32
relative error = 9.2998660794835853373932485946045e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = -0.2129170087585056463941117721627
y[1] (numeric) = -0.21291700875850564639411177216268
absolute error = 2e-32
relative error = 9.3933312874427823071052091710136e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = -0.2107984491237286735664353784814
y[1] (numeric) = -0.21079844912372867356643537848138
absolute error = 2e-32
relative error = 9.4877358363585257205503690445116e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 3.097e+10
Order of pole (six term test) = 3.894e+20
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = -0.20870096950953003342818271727923
y[1] (numeric) = -0.20870096950953003342818271727921
absolute error = 2e-32
relative error = 9.5830891667643778717351852852968e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.429e+10
Order of pole (six term test) = 4.334e+20
TOP MAIN SOLVE Loop
bytes used=40010420, alloc=4324584, time=3.47
x[1] = 2.27
y[1] (analytic) = -0.20662436016620040061049843066899
y[1] (numeric) = -0.20662436016620040061049843066897
absolute error = 2e-32
relative error = 9.6794008140728407194171550561075e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 4.311e+11
Order of pole (six term test) = 1.077e+22
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = -0.20456841343107492859562313519417
y[1] (numeric) = -0.20456841343107492859562313519415
absolute error = 2e-32
relative error = 9.7766804095289050835042636318176e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = -0.20253292370776681017944409869335
y[1] (numeric) = -0.20253292370776681017944409869333
absolute error = 2e-32
relative error = 9.8749376811731831702012210539709e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = -0.20051768744560746745988138759597
y[1] (numeric) = -0.20051768744560746745988138759596
absolute error = 1e-32
relative error = 4.9870912274073603699788075784545e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = -0.19852250311929131535297509114374
y[1] (numeric) = -0.19852250311929131535297509114372
absolute error = 2e-32
relative error = 1.0074424655013586200245455289684e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = -0.19654717120872306309606247764772
y[1] (numeric) = -0.1965471712087230630960624776477
absolute error = 2e-32
relative error = 1.0175674306073334882894211461532e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = -0.19459149417906553845140142910307
y[1] (numeric) = -0.19459149417906553845140142910306
absolute error = 1e-32
relative error = 5.1389707665217238766190693680524e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.084e+11
Order of pole (six term test) = 5.491e+20
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = -0.19265527646098603937603364791825
y[1] (numeric) = -0.19265527646098603937603364791824
absolute error = 1e-32
relative error = 5.1906182813659223978910849912131e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = -0.1907383244310992377765931935996
y[1] (numeric) = -0.19073832443109923777659319359959
absolute error = 1e-32
relative error = 5.2427848623637871642843537695544e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = -0.18884044639260467962313819571542
y[1] (numeric) = -0.1888404463926046796231381957154
absolute error = 2e-32
relative error = 1.0590951452433780516028994407103e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = -0.18696145255611694515588165595398
y[1] (numeric) = -0.18696145255611694515588165595397
absolute error = 1e-32
relative error = 5.3486961420555261889655796190901e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = -0.18510115502068655218486709261196
y[1] (numeric) = -0.18510115502068655218486709261195
absolute error = 1e-32
relative error = 5.4024514319656293150976451646436e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.917e+11
Order of pole (six term test) = 2.955e+21
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = -0.18325936775500970455710302844059
y[1] (numeric) = -0.18325936775500970455710302844058
absolute error = 1e-32
relative error = 5.4567469715209868709689093790961e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = -0.18143590657882500675034444015938
y[1] (numeric) = -0.18143590657882500675034444015938
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = -0.17963058914449528424947775826781
y[1] (numeric) = -0.17963058914449528424947775826781
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.720e+11
Order of pole (six term test) = 1.974e+21
TOP MAIN SOLVE Loop
bytes used=44011380, alloc=4390108, time=3.84
x[1] = 2.42
y[1] (analytic) = -0.17784323491877266787219852147351
y[1] (numeric) = -0.17784323491877266787219852147352
absolute error = 1e-32
relative error = 5.6229296574409230399807946027656e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.094e+11
Order of pole (six term test) = 9.655e+20
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = -0.17607366516474511853721843978805
y[1] (numeric) = -0.17607366516474511853721843978805
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.819e+11
Order of pole (six term test) = 1.166e+21
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = -0.1743217029239625871124340741545
y[1] (numeric) = -0.17432170292396258711243407415451
absolute error = 1e-32
relative error = 5.7365203713974166946836126510321e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = -0.17258717299874102194414703303231
y[1] (numeric) = -0.17258717299874102194414703303231
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.981e+12
Order of pole (six term test) = 2.107e+23
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = -0.17086990193464245445334189841079
y[1] (numeric) = -0.17086990193464245445334189841079
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.325e+11
Order of pole (six term test) = 8.155e+20
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = -0.16916971800312941079298153170792
y[1] (numeric) = -0.16916971800312941079298153170791
absolute error = 1e-32
relative error = 5.9112234258231804442181766503214e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.528e+11
Order of pole (six term test) = 9.466e+20
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = -0.16748645118439191499303078395017
y[1] (numeric) = -0.16748645118439191499303078395017
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = -0.1658199331503453662792122341894
y[1] (numeric) = -0.16581993315034536627921223418939
absolute error = 1e-32
relative error = 6.0306380602223588640486996748391e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = -0.16416999724779759033905734893432
y[1] (numeric) = -0.16416999724779759033905734893431
absolute error = 1e-32
relative error = 6.0912469803517367190350879755840e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = -0.16253647848178338122635216367639
y[1] (numeric) = -0.16253647848178338122635216367638
absolute error = 1e-32
relative error = 6.1524650302552058181472092470256e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = -0.16091921349906486734428000303859
y[1] (numeric) = -0.16091921349906486734428000303858
absolute error = 1e-32
relative error = 6.2142983317887717199316412325979e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = -0.15931804057179605153010981297284
y[1] (numeric) = -0.15931804057179605153010981297283
absolute error = 1e-32
relative error = 6.2767530683341157040160116000376e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.293e+11
Order of pole (six term test) = 7.872e+20
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = -0.15773279958134989168182564520009
y[1] (numeric) = -0.15773279958134989168182564520008
absolute error = 1e-32
relative error = 6.3398354854169380920722045280718e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = -0.15616333200230630462128247910557
y[1] (numeric) = -0.15616333200230630462128247910557
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = -0.15460948088659949198093132207952
y[1] (numeric) = -0.15460948088659949198093132207952
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=48012564, alloc=4390108, time=4.19
x[1] = 2.57
y[1] (analytic) = -0.15307109084782300283349165501697
y[1] (numeric) = -0.15307109084782300283349165501696
absolute error = 1e-32
relative error = 6.5329122204672792491111002445234e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 7.763e+10
Order of pole (six term test) = 8.138e+20
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = -0.15154800804569096355775503214886
y[1] (numeric) = -0.15154800804569096355775503214885
absolute error = 1e-32
relative error = 6.5985690798291787552905072689246e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = -0.15004008017065392105055739728929
y[1] (numeric) = -0.15004008017065392105055739728929
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 3.362e+11
Order of pole (six term test) = 6.164e+21
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = -0.14854715642866776085642114033995
y[1] (numeric) = -0.14854715642866776085642114033995
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = -0.14706908752611417709398724772342
y[1] (numeric) = -0.14706908752611417709398724772342
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.362e+11
Order of pole (six term test) = 1.002e+21
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = -0.14560572565487118621366387301155
y[1] (numeric) = -0.14560572565487118621366387301155
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.636e+11
Order of pole (six term test) = 1.250e+21
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = -0.14415692447753219162542581259969
y[1] (numeric) = -0.14415692447753219162542581259968
absolute error = 1e-32
relative error = 6.9368849510649528444746669083753e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.391e+11
Order of pole (six term test) = 9.504e+20
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = -0.14272253911277212109091017917259
y[1] (numeric) = -0.14272253911277212109091017917259
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = -0.14130242612085917348135255637331
y[1] (numeric) = -0.14130242612085917348135255637331
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.161e+10
Order of pole (six term test) = 1.622e+20
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = -0.13989644348931072606396584367654
y[1] (numeric) = -0.13989644348931072606396584367653
absolute error = 1e-32
relative error = 7.1481445493388005623048727555502e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.273e+11
Order of pole (six term test) = 6.113e+20
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = -0.13850445061869196789553697891176
y[1] (numeric) = -0.13850445061869196789553697891175
absolute error = 1e-32
relative error = 7.2199845964014406892841951652971e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = -0.13712630830855583917474638648806
y[1] (numeric) = -0.13712630830855583917474638648804
absolute error = 2e-32
relative error = 1.4585093295880789692431122279052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 7.678e+11
Order of pole (six term test) = 2.810e+22
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = -0.13576187874352287053542862700309
y[1] (numeric) = -0.13576187874352287053542862700308
absolute error = 1e-32
relative error = 7.3658379602212855063587398183621e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = -0.13441102547949953025310340171193
y[1] (numeric) = -0.13441102547949953025310340171192
absolute error = 1e-32
relative error = 7.4398658624364170559344965097343e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.669e+11
Order of pole (six term test) = 2.011e+21
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = -0.13307361343003370118801281601234
y[1] (numeric) = -0.13307361343003370118801281601233
absolute error = 1e-32
relative error = 7.5146377574377011322438273249617e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.258e+11
Order of pole (six term test) = 8.514e+20
bytes used=52013996, alloc=4390108, time=4.55
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = -0.13174950885280592300098873189073
y[1] (numeric) = -0.13174950885280592300098873189072
absolute error = 1e-32
relative error = 7.5901611224769479838955124903649e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = -0.13043857933625504875511446038598
y[1] (numeric) = -0.13043857933625504875511446038597
absolute error = 1e-32
relative error = 7.6664435099535978828949226134720e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = -0.12914069378633697845769563692426
y[1] (numeric) = -0.12914069378633697845769563692425
absolute error = 1e-32
relative error = 7.7434925481699673623583983715462e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = -0.1278557224134151454048600511159
y[1] (numeric) = -0.12785572241341514540486005111589
absolute error = 1e-32
relative error = 7.8213159420940858051063490230785e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.456e+11
Order of pole (six term test) = 1.229e+21
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = -0.12658353671928144436649625986908
y[1] (numeric) = -0.12658353671928144436649625986906
absolute error = 2e-32
relative error = 1.5799842948260397334859256656509e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = -0.12532400948430630369353354844936
y[1] (numeric) = -0.12532400948430630369353354844935
absolute error = 1e-32
relative error = 7.9793170048970143889936526760817e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.104e+11
Order of pole (six term test) = 4.790e+20
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = -0.12407701475471661634406565854311
y[1] (numeric) = -0.1240770147547166163440656585431
absolute error = 1e-32
relative error = 8.0595104740137728142197930833716e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = -0.12284242783000025761081913621326
y[1] (numeric) = -0.12284242783000025761081913621325
absolute error = 1e-32
relative error = 8.1405099008942137326412384061343e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 7.113e+11
Order of pole (six term test) = 3.585e+22
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = -0.12162012525043592999124277636788
y[1] (numeric) = -0.12162012525043592999124277636787
absolute error = 1e-32
relative error = 8.2223233855485249357490080054626e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.962e+10
Order of pole (six term test) = 4.332e+20
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = -0.12040998478474708817431334210487
y[1] (numeric) = -0.12040998478474708817431334210486
absolute error = 1e-32
relative error = 8.3049591093933499858020907441889e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.466e+11
Order of pole (six term test) = 9.572e+20
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = -0.11921188541787870952626780936569
y[1] (numeric) = -0.11921188541787870952626780936568
absolute error = 1e-32
relative error = 8.3884253360699366980536000522470e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.394e+11
Order of pole (six term test) = 6.240e+20
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = -0.11802570733889568774212465157395
y[1] (numeric) = -0.11802570733889568774212465157394
absolute error = 1e-32
relative error = 8.4727304122705081519229603507370e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.240e+11
Order of pole (six term test) = 3.048e+21
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = -0.11685133192900163949227461081453
y[1] (numeric) = -0.11685133192900163949227461081452
absolute error = 1e-32
relative error = 8.5578827685729388689038868581297e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.965e+10
Order of pole (six term test) = 7.144e+20
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = -0.1156886417496769259348212535548
y[1] (numeric) = -0.11568864174967692593482125355479
absolute error = 1e-32
relative error = 8.6438909202838196255215153767232e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = -0.11453752053093470288593752994038
y[1] (numeric) = -0.11453752053093470288593752994037
absolute error = 1e-32
relative error = 8.7307634682899952085225341249847e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
bytes used=56015400, alloc=4390108, time=4.91
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = -0.11339785315969382524346871484118
y[1] (numeric) = -0.11339785315969382524346871484117
absolute error = 1e-32
relative error = 8.8185090999186602667834537903410e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.705e+11
Order of pole (six term test) = 1.052e+21
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = -0.11226952566826744294453481233074
y[1] (numeric) = -0.11226952566826744294453481233073
absolute error = 1e-32
relative error = 8.9071365898060992702389555618283e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.215e+11
Order of pole (six term test) = 2.350e+20
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = -0.11115242522296613730713531516097
y[1] (numeric) = -0.11115242522296613730713531516096
absolute error = 1e-32
relative error = 8.9966548007751574505501623563636e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = -0.11004644011281445805989306166835
y[1] (numeric) = -0.11004644011281445805989306166835
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.129e+11
Order of pole (six term test) = 7.500e+20
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = -0.10895145973837973270423724734572
y[1] (numeric) = -0.10895145973837973270423724734572
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = -0.10786737460071203108065245281805
y[1] (numeric) = -0.10786737460071203108065245281805
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.173e+10
Order of pole (six term test) = -1.856e+21
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = -0.10679407629039417912623358620798
y[1] (numeric) = -0.10679407629039417912623358620799
absolute error = 1e-32
relative error = 9.3638152483364578899453675304496e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = -0.10573145747670072681579747643322
y[1] (numeric) = -0.10573145747670072681579747643322
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = -0.10467941189686478617431100509864
y[1] (numeric) = -0.10467941189686478617431100509864
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.422e+11
Order of pole (six term test) = 3.946e+21
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = -0.10363783434545166603549268832574
y[1] (numeric) = -0.10363783434545166603549268832574
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 5.285e+11
Order of pole (six term test) = 1.987e+22
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = -0.10260662066383824090120823479189
y[1] (numeric) = -0.10260662066383824090120823479189
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = -0.10158566772979700182977879769406
y[1] (numeric) = -0.10158566772979700182977879769406
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.006e+11
Order of pole (six term test) = 6.159e+20
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = -0.10057487344718374774961076493595
y[1] (numeric) = -0.10057487344718374774961076493595
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = -0.099574136735727885958684831300122
y[1] (numeric) = -0.099574136735727885958684831300123
absolute error = 1e-33
relative error = 1.0042768461593833870464264827291e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = -0.098583357520924320831446190234969
y[1] (numeric) = -0.09858335752092432083144619023497
absolute error = 1e-33
relative error = 1.0143699962620465300790761327945e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
bytes used=60018092, alloc=4390108, time=5.26
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = -0.097602436724025919913543080119995
y[1] (numeric) = -0.097602436724025919913543080119995
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.536e+11
Order of pole (six term test) = 1.458e+21
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = -0.096631276252135556642683519477524
y[1] (numeric) = -0.096631276252135556642683519477524
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = -0.095669778988396738891625658216285
y[1] (numeric) = -0.095669778988396738891625658216281
absolute error = 4e-33
relative error = 4.1810486470185511681611757055732e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = -0.094717848782281842387981540479467
y[1] (numeric) = -0.094717848782281842387981540479467
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = -0.093775390439976977826083093679625
y[1] (numeric) = -0.093775390439976977826083093679622
absolute error = 3e-33
relative error = 3.1991335743040351878649138007971e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.278e+10
Order of pole (six term test) = 1.252e+21
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = -0.092842309714862530149608892870319
y[1] (numeric) = -0.092842309714862530149608892870318
absolute error = 1e-33
relative error = 1.0770951337501208363479760143213e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.292e+11
Order of pole (six term test) = 8.148e+20
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = -0.091918513298088418050967052756972
y[1] (numeric) = -0.091918513298088418050967052756969
absolute error = 3e-33
relative error = 3.2637603594295616766579582390159e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = -0.091003908809243131205530209038912
y[1] (numeric) = -0.091003908809243131205530209038908
absolute error = 4e-33
relative error = 4.3954155951526842213086355764994e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.410e+10
Order of pole (six term test) = 2.397e+20
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = -0.090098404787115612136670184356672
y[1] (numeric) = -0.090098404787115612136670184356668
absolute error = 4e-33
relative error = 4.4395902562883266809655948762514e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = -0.089201910680549058892080384870443
y[1] (numeric) = -0.089201910680549058892080384870443
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.631e+11
Order of pole (six term test) = 4.087e+21
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = -0.088314336839385733904031703200168
y[1] (numeric) = -0.088314336839385733904031703200167
absolute error = 1e-33
relative error = 1.1323189821587697850912318873809e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 5.089e+11
Order of pole (six term test) = -4.235e+22
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = -0.087435594505501873506901935547708
y[1] (numeric) = -0.087435594505501873506901935547705
absolute error = 3e-33
relative error = 3.4310969313661215935771353041843e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.988e+10
Order of pole (six term test) = -4.255e+19
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = -0.086565595803931801595459532304399
y[1] (numeric) = -0.086565595803931801595459532304398
absolute error = 1e-33
relative error = 1.1551933429361091392289542290008e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 8.049e+10
Order of pole (six term test) = 7.190e+20
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = -0.085704253734080359827870913912309
y[1] (numeric) = -0.085704253734080359827870913912308
absolute error = 1e-33
relative error = 1.1668032290471356861690043782105e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.686e+11
Order of pole (six term test) = 8.117e+21
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = -0.08485148216102277560912865346997
y[1] (numeric) = -0.084851482161022775609128653469967
absolute error = 3e-33
relative error = 3.5355893893602186360284587210425e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
bytes used=64021980, alloc=4390108, time=5.62
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = -0.084007195806891097834448734719998
y[1] (numeric) = -0.084007195806891097834448734719999
absolute error = 1e-33
relative error = 1.1903742178214335158820658201116e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.427e+11
Order of pole (six term test) = 1.414e+21
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = -0.083171310242346339029033231003973
y[1] (numeric) = -0.083171310242346339029033231003971
absolute error = 2e-33
relative error = 2.4046753552064495691167646951714e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.138e+11
Order of pole (six term test) = 1.580e+21
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = -0.082343741878135471091305809546969
y[1] (numeric) = -0.082343741878135471091305809546968
absolute error = 1e-33
relative error = 1.2144213721547277802153549148086e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.412e+11
Order of pole (six term test) = 1.067e+21
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = -0.081524407956732430332158524288851
y[1] (numeric) = -0.081524407956732430332158524288849
absolute error = 2e-33
relative error = 2.4532530197109348643560263727964e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = -0.080713226544062295903747969588037
y[1] (numeric) = -0.080713226544062295903747969588035
absolute error = 2e-33
relative error = 2.4779086224587695927974479188157e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.501e+10
Order of pole (six term test) = 2.013e+20
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = -0.079910116521307814028787133448768
y[1] (numeric) = -0.079910116521307814028787133448768
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.237e+11
Order of pole (six term test) = 8.621e+20
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = -0.079114997576797448675927960221868
y[1] (numeric) = -0.079114997576797448675927960221866
absolute error = 2e-33
relative error = 2.5279656970962892860199012888142e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 8.165e+10
Order of pole (six term test) = -7.832e+20
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = -0.078327790197974147479542180731511
y[1] (numeric) = -0.07832779019797414747954218073151
absolute error = 1e-33
relative error = 1.2766860873675761853412664752027e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = -0.077548415663444019773799670535193
y[1] (numeric) = -0.077548415663444019773799670535192
absolute error = 1e-33
relative error = 1.2895169958596531044540053834688e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.686e+11
Order of pole (six term test) = 2.967e+21
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = -0.076776796035104131602221620427345
y[1] (numeric) = -0.076776796035104131602221620427345
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = -0.076012854150348630475649281811054
y[1] (numeric) = -0.076012854150348630475649281811053
absolute error = 1e-33
relative error = 1.3155669671632946210386362329574e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = -0.075256513614352420484609166127661
y[1] (numeric) = -0.075256513614352420484609166127661
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 3.434e+11
Order of pole (six term test) = 5.307e+21
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = -0.07450769879243161612715564269026
y[1] (numeric) = -0.07450769879243161612715564269026
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = -0.073766334802480010891207409483032
y[1] (numeric) = -0.07376633480248001089120740948303
absolute error = 2e-33
relative error = 2.7112638920657887426818372110231e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = -0.073032347507480804231933106715629
y[1] (numeric) = -0.073032347507480804231933106715628
absolute error = 1e-33
relative error = 1.3692562735951608549059492421654e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.029e+10
Order of pole (six term test) = 7.954e+20
bytes used=68024824, alloc=4390108, time=6.00
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = -0.072305663508092838110643563374324
y[1] (numeric) = -0.072305663508092838110643563374323
absolute error = 1e-33
relative error = 1.3830175279258375527155453482934e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = -0.071586210135310601712666409183133
y[1] (numeric) = -0.071586210135310601712666409183131
absolute error = 2e-33
relative error = 2.7938341703236505652149863987642e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = -0.070873915443197270338558156312127
y[1] (numeric) = -0.070873915443197270338558156312126
absolute error = 1e-33
relative error = 1.4109563352704306463280552558300e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 3.651e+10
Order of pole (six term test) = -5.666e+20
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = -0.070168708201690051766487050931066
y[1] (numeric) = -0.070168708201690051766487050931064
absolute error = 2e-33
relative error = 2.8502733643767278370041893023457e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = -0.069470517889477120614427368210285
y[1] (numeric) = -0.069470517889477120614427368210282
absolute error = 3e-33
relative error = 4.3183786318864016628350882152315e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = -0.068779274686945428389665462380541
y[1] (numeric) = -0.068779274686945428389665462380539
absolute error = 2e-33
relative error = 2.9078527057797073771687539613154e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = -0.068094909469198684000745677908606
y[1] (numeric) = -0.068094909469198684000745677908603
absolute error = 3e-33
relative error = 4.4056156669934154230769597849129e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = -0.067417353799144806524088947411793
y[1] (numeric) = -0.067417353799144806524088947411792
absolute error = 1e-33
relative error = 1.4832976135184425829824754411972e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = -0.066746539920652158964800262941896
y[1] (numeric) = -0.066746539920652158964800262941894
absolute error = 2e-33
relative error = 2.9964100047397013348162753033730e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.408e+11
Order of pole (six term test) = 2.457e+20
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = -0.066082400751773878629337943842434
y[1] (numeric) = -0.066082400751773878629337943842432
absolute error = 2e-33
relative error = 3.0265244259400081344601532358897e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.649e+11
Order of pole (six term test) = 9.379e+20
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = -0.065424869878039626537435557928615
y[1] (numeric) = -0.065424869878039626537435557928612
absolute error = 3e-33
relative error = 4.5854122531575315453421861683226e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = -0.064773881545814085042627460724618
y[1] (numeric) = -0.064773881545814085042627460724615
absolute error = 3e-33
relative error = 4.6314964124515562570589568858681e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = -0.064129370655721539505605401547277
y[1] (numeric) = -0.064129370655721539505605401547275
absolute error = 2e-33
relative error = 3.1186958168309462222678998645337e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = -0.06349127275613588647309399855947
y[1] (numeric) = -0.063491272756135886473093998559467
absolute error = 3e-33
relative error = 4.7250588463121898173058737405767e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = -0.062859524036735417357637959073097
y[1] (numeric) = -0.062859524036735417357637959073094
absolute error = 3e-33
relative error = 4.7725464772001536839720195823920e-30 %
Correct digits = 32
h = 0.01
bytes used=72025664, alloc=4390108, time=6.35
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 8.008e+11
Order of pole (six term test) = 3.316e+22
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = -0.062234061322121733091297992320118
y[1] (numeric) = -0.062234061322121733091297992320116
absolute error = 2e-33
relative error = 3.2136742444753152582914967864034e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.182e+11
Order of pole (six term test) = 2.308e+21
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = -0.061614822065502151639403195435717
y[1] (numeric) = -0.061614822065502151639403195435714
absolute error = 3e-33
relative error = 4.8689583113795695841186218479486e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.029e+11
Order of pole (six term test) = 8.614e+20
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = -0.061001744342434976609846609938077
y[1] (numeric) = -0.061001744342434976609846609938074
absolute error = 3e-33
relative error = 4.9178921559347830221497349142520e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = -0.060394766844637001479572584727239
y[1] (numeric) = -0.060394766844637001479572584727238
absolute error = 1e-33
relative error = 1.6557725979346156875326624675194e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = -0.059793828873852630183518163993323
y[1] (numeric) = -0.059793828873852630183518163993322
absolute error = 1e-33
relative error = 1.6724133891972455935728870658204e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = -0.059198870335784000972958310966756
y[1] (numeric) = -0.059198870335784000972958310966755
absolute error = 1e-33
relative error = 1.6892214231924776941045504281515e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = -0.058609831734081506550582555054073
y[1] (numeric) = -0.058609831734081506550582555054072
absolute error = 1e-33
relative error = 1.7061983807377182540227991646582e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.872e+10
Order of pole (six term test) = 5.377e+19
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = -0.05802665416439410952930865344351
y[1] (numeric) = -0.05802665416439410952930865344351
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.320e+11
Order of pole (six term test) = 7.542e+20
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = -0.057449279308478858241421061568647
y[1] (numeric) = -0.057449279308478858241421061568648
absolute error = 1e-33
relative error = 1.7406658743801010712670834455867e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.896e+11
Order of pole (six term test) = 4.778e+21
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = -0.056877649428369013844706373088932
y[1] (numeric) = -0.056877649428369013844706373088933
absolute error = 1e-33
relative error = 1.7581598572553305739867046315485e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = -0.056311707360600205533436432653193
y[1] (numeric) = -0.056311707360600205533436432653194
absolute error = 1e-33
relative error = 1.7758296575814237079292689384975e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.280e+11
Order of pole (six term test) = 1.608e+21
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = -0.055751396510494036464908666394755
y[1] (numeric) = -0.055751396510494036464908666394756
absolute error = 1e-33
relative error = 1.7936770423531379650961145659917e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = -0.055196660846498568757372606584414
y[1] (numeric) = -0.055196660846498568757372606584414
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = -0.054647444894585121603126124871106
y[1] (numeric) = -0.054647444894585121603126124871106
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = -0.054103693732700822171923333263377
y[1] (numeric) = -0.054103693732700822171923333263377
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
bytes used=76026804, alloc=4390108, time=6.71
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.627e+11
Order of pole (six term test) = 2.164e+21
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = -0.053565352985276354555161603984964
y[1] (numeric) = -0.053565352985276354555161603984964
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.366e+11
Order of pole (six term test) = 3.161e+21
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = -0.053032368817788357521165235770362
y[1] (numeric) = -0.053032368817788357521165235770362
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.871e+11
Order of pole (six term test) = 2.230e+21
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = -0.052504687931375927316809944658597
y[1] (numeric) = -0.052504687931375927316809944658597
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.959e+11
Order of pole (six term test) = 2.367e+21
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = -0.051982257557510687161282079114776
y[1] (numeric) = -0.051982257557510687161282079114776
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = -0.051465025452719890434480311840354
y[1] (numeric) = -0.051465025452719890434480311840354
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.181e+11
Order of pole (six term test) = 7.316e+20
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = -0.050952939893362029865981219773543
y[1] (numeric) = -0.050952939893362029865981219773542
absolute error = 1e-33
relative error = 1.9625952930152249947053771534425e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = -0.050445949670454430281133975316452
y[1] (numeric) = -0.050445949670454430281133975316452
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = -0.049944004084552307659248404512019
y[1] (numeric) = -0.049944004084552307659248404512018
absolute error = 1e-33
relative error = 2.0022423478643360070810260687583e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.360e+11
Order of pole (six term test) = 9.884e+20
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = -0.049447052940678782405514765966805
y[1] (numeric) = -0.049447052940678782405514765966805
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.240e+11
Order of pole (six term test) = 1.020e+21
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = -0.048955046543305339833757439474213
y[1] (numeric) = -0.048955046543305339833757439474213
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 6.969e+10
Order of pole (six term test) = 6.642e+20
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = -0.048467935691382235901887836166041
y[1] (numeric) = -0.048467935691382235901887836166041
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = -0.047985671673418351236488733125186
y[1] (numeric) = -0.047985671673418351236488733125186
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = -0.047508206262610001427832355579656
y[1] (numeric) = -0.047508206262610001427832355579656
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.260e+11
Order of pole (six term test) = 9.875e+20
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = -0.047035491712018216472302370200866
y[1] (numeric) = -0.047035491712018216472302370200865
absolute error = 1e-33
relative error = 2.1260541000031391527759086310802e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = -0.046567480749794007086145084511088
y[1] (numeric) = -0.046567480749794007086145084511087
absolute error = 1e-33
relative error = 2.1474212989381512456123660353175e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.239e+10
Order of pole (six term test) = 4.354e+20
bytes used=80028892, alloc=4390108, time=7.06
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = -0.046104126574451140413202269518292
y[1] (numeric) = -0.046104126574451140413202269518291
absolute error = 1e-33
relative error = 2.1690032417925808677583263344546e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = -0.045645382850185952400257012152537
y[1] (numeric) = -0.045645382850185952400257012152536
absolute error = 1e-33
relative error = 2.1908020867786984745046437920212e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = -0.045191203702243728817329962734743
y[1] (numeric) = -0.045191203702243728817329962734741
absolute error = 2e-33
relative error = 4.4256400275983368846390927167131e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = -0.044741543712331191557166645081646
y[1] (numeric) = -0.044741543712331191557166645081644
absolute error = 2e-33
relative error = 4.4701184493300823037557828729065e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.147e+11
Order of pole (six term test) = 8.314e+20
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = -0.044296357914074631458722837151075
y[1] (numeric) = -0.044296357914074631458722837151073
absolute error = 2e-33
relative error = 4.5150438866318718558957830086431e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = -0.043855601788523233464145468835525
y[1] (numeric) = -0.043855601788523233464145468835524
absolute error = 1e-33
relative error = 2.2802104160424368546127846612959e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = -0.043419231259697144438017493467177
y[1] (numeric) = -0.043419231259697144438017493467177
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.156e+11
Order of pole (six term test) = 7.291e+20
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = -0.04298720269017983845193870167105
y[1] (numeric) = -0.042987202690179838451938701671049
absolute error = 1e-33
relative error = 2.3262737219894604529581623205560e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = -0.042559472876754338767297894474697
y[1] (numeric) = -0.042559472876754338767297894474696
absolute error = 1e-33
relative error = 2.3496531615789640432415238120581e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.187e+11
Order of pole (six term test) = 6.967e+20
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = -0.042135999046082860134798199089125
y[1] (numeric) = -0.042135999046082860134798199089124
absolute error = 1e-33
relative error = 2.3732675684426763580710055832070e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = -0.041716738850429439371365169807746
y[1] (numeric) = -0.041716738850429439371365169807745
absolute error = 1e-33
relative error = 2.3971193040409625066602092677123e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = -0.041301650363425126473930878432624
y[1] (numeric) = -0.041301650363425126473930878432622
absolute error = 2e-33
relative error = 4.8424215071345176604216766568584e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.776e+11
Order of pole (six term test) = 1.793e+21
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = -0.040890692075875312785676353468485
y[1] (numeric) = -0.040890692075875312785676353468484
absolute error = 1e-33
relative error = 2.4455443261865942332146407278608e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.276e+11
Order of pole (six term test) = 3.117e+21
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = -0.040483822891608776944055087487307
y[1] (numeric) = -0.040483822891608776944055087487306
absolute error = 1e-33
relative error = 2.4701224552765086939880743270610e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.345e+11
Order of pole (six term test) = 6.070e+20
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = -0.04008100212336803351173327510709
y[1] (numeric) = -0.040081002123368033511733275107089
absolute error = 1e-33
relative error = 2.4949475986703930464915145741440e-30 %
Correct digits = 32
h = 0.01
bytes used=84030688, alloc=4455632, time=7.42
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.823e+10
Order of pole (six term test) = 5.409e+20
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = -0.039682189488740573321885154718708
y[1] (numeric) = -0.039682189488740573321885154718707
absolute error = 1e-33
relative error = 2.5200222389032743676139702306284e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = -0.039287345106130588658487339147276
y[1] (numeric) = -0.039287345106130588658487339147274
absolute error = 2e-33
relative error = 5.0906977669201430973337148919991e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = -0.038896429490770780440773257808341
y[1] (numeric) = -0.038896429490770780440773257808339
absolute error = 2e-33
relative error = 5.1418601300526917537017237808153e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.038e+11
Order of pole (six term test) = 6.966e+20
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = -0.038509403550773848589242650711833
y[1] (numeric) = -0.038509403550773848589242650711832
absolute error = 1e-33
relative error = 2.5967683417415717019629951461350e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = -0.038126228583223270718972279600075
y[1] (numeric) = -0.038126228583223270718972279600074
absolute error = 1e-33
relative error = 2.6228662974549525156215756559254e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.267e+11
Order of pole (six term test) = 9.481e+20
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = -0.037746866270302978234839492009752
y[1] (numeric) = -0.037746866270302978234839492009751
absolute error = 1e-33
relative error = 2.6492265419838080248302375028925e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.704e+11
Order of pole (six term test) = 1.479e+21
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = -0.037371278675465542793042879942699
y[1] (numeric) = -0.037371278675465542793042879942697
absolute error = 2e-33
relative error = 5.3517034227491161176072934038621e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = -0.03699942823963848994437299661867
y[1] (numeric) = -0.036999428239638489944372996618669
absolute error = 1e-33
relative error = 2.7027444681663294076630948882394e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = -0.036631277777468360587436042546482
y[1] (numeric) = -0.036631277777468360587436042546481
absolute error = 1e-33
relative error = 2.7299075016572119539055130601431e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.436e+11
Order of pole (six term test) = 4.496e+20
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = -0.036266790473602144634845884059948
y[1] (numeric) = -0.036266790473602144634845884059947
absolute error = 1e-33
relative error = 2.7573435281731907224809331267541e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = -0.035905929879005715032652207912938
y[1] (numeric) = -0.035905929879005715032652207912936
absolute error = 2e-33
relative error = 5.5701105826795614858150315907712e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 8.789e+10
Order of pole (six term test) = 5.390e+19
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = -0.035548659907318893973338772871938
y[1] (numeric) = -0.035548659907318893973338772871937
absolute error = 1e-33
relative error = 2.8130455623563918871367194411499e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = -0.035194944831246786805975603183958
y[1] (numeric) = -0.035194944831246786805975603183956
absolute error = 2e-33
relative error = 5.6826342805469022397620692052799e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.746e+11
Order of pole (six term test) = 4.439e+21
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = -0.034844749278987022773908907373465
y[1] (numeric) = -0.034844749278987022773908907373463
absolute error = 2e-33
relative error = 5.7397457045446197477205057110728e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = -0.034498038230692545301085182050658
bytes used=88032504, alloc=4455632, time=7.79
y[1] (numeric) = -0.034498038230692545301085182050656
absolute error = 2e-33
relative error = 5.7974311078959290818741032291737e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = -0.034154777014969598103090448554437
y[1] (numeric) = -0.034154777014969598103090448554435
absolute error = 2e-33
relative error = 5.8556962591892367028532192341084e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = -0.033814931305410556918597371718443
y[1] (numeric) = -0.033814931305410556918597371718441
absolute error = 2e-33
relative error = 5.9145469849882263960123061503387e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.263e+11
Order of pole (six term test) = 2.428e+21
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = -0.033478467117161260141504088950542
y[1] (numeric) = -0.03347846711716126014150408895054
absolute error = 2e-33
relative error = 5.9739891704145204952943682133228e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.224e+12
Order of pole (six term test) = 8.054e+22
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = -0.033145350803522495083967396166902
y[1] (numeric) = -0.033145350803522495083967396166901
absolute error = 1e-33
relative error = 3.0170143798680984748743609854062e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.525e+11
Order of pole (six term test) = 1.438e+21
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = -0.032815549052585300016124489678115
y[1] (numeric) = -0.032815549052585300016124489678114
absolute error = 1e-33
relative error = 3.0473358784811105424495723619863e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = -0.032489028883899745509903311888252
y[1] (numeric) = -0.032489028883899745509903311888251
absolute error = 1e-33
relative error = 3.0779621132214257513169545877563e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = -0.032165757645176861962279857041206
y[1] (numeric) = -0.032165757645176861962279857041204
absolute error = 2e-33
relative error = 6.2177922934760801607080332059942e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = -0.031845703009023383487986359852932
y[1] (numeric) = -0.03184570300902338348798635985293
absolute error = 2e-33
relative error = 6.2802821449201672763710634207786e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 5.509e+11
Order of pole (six term test) = 1.434e+22
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = -0.031528832969708981653338582022219
y[1] (numeric) = -0.031528832969708981653338582022217
absolute error = 2e-33
relative error = 6.3434000298123323081212027004717e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.077e+11
Order of pole (six term test) = 6.233e+20
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = -0.031215115839965665771861598480226
y[1] (numeric) = -0.031215115839965665771861598480224
absolute error = 2e-33
relative error = 6.4071522599936628851995347043460e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.667e+11
Order of pole (six term test) = 2.298e+21
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = -0.030904520247819029699076470646538
y[1] (numeric) = -0.030904520247819029699076470646537
absolute error = 1e-33
relative error = 3.2357726053701520881190269631465e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.057e+11
Order of pole (six term test) = 6.943e+20
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = -0.030597015133451028248486648885946
y[1] (numeric) = -0.030597015133451028248486648885944
absolute error = 2e-33
relative error = 6.5365853214009918165243590001587e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = -0.030292569746093969503791341104983
y[1] (numeric) = -0.030292569746093969503791341104981
absolute error = 2e-33
relative error = 6.6022790960409921477070149341098e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = -0.029991153640955412423968720457457
y[1] (numeric) = -0.029991153640955412423968720457456
absolute error = 1e-33
relative error = 3.3343165520462570822510867326997e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=92033272, alloc=4455632, time=8.15
x[1] = 4.21
y[1] (analytic) = -0.029692736676173662228426886608675
y[1] (numeric) = -0.029692736676173662228426886608674
absolute error = 1e-33
relative error = 3.3678269905058291050690669799292e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = -0.029397289009803559109224000018468
y[1] (numeric) = -0.029397289009803559109224000018467
absolute error = 1e-33
relative error = 3.4016742144709835579774241916368e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 7.638e+11
Order of pole (six term test) = 3.454e+22
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = -0.029104781096832258846716960143819
y[1] (numeric) = -0.029104781096832258846716960143818
absolute error = 1e-33
relative error = 3.4358616086923230704126457106698e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = -0.028815183686224706904213334652431
y[1] (numeric) = -0.02881518368622470690421333465243
absolute error = 1e-33
relative error = 3.4703925919377593664755781815585e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.578e+11
Order of pole (six term test) = 1.631e+21
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = -0.028528467817998510546573891712003
y[1] (numeric) = -0.028528467817998510546573891712002
absolute error = 1e-33
relative error = 3.5052706173343929050865939997547e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = -0.028244604820327916467539980915243
y[1] (numeric) = -0.028244604820327916467539980915242
absolute error = 1e-33
relative error = 3.5404991727138284676469924348244e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = -0.027963566306676604321135135556967
y[1] (numeric) = -0.027963566306676604321135135556966
absolute error = 1e-33
relative error = 3.5760817809609612250531655166339e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.227e+11
Order of pole (six term test) = 9.588e+20
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = -0.027685324172959009434104689735196
y[1] (numeric) = -0.027685324172959009434104689735195
absolute error = 1e-33
relative error = 3.6120220003662681629608861258165e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = -0.027409850594729890829299081946433
y[1] (numeric) = -0.027409850594729890829299081946432
absolute error = 1e-33
relative error = 3.6483234249816400947358218836380e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.343e+10
Order of pole (six term test) = 4.427e+20
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = -0.027137118024401863514461149051535
y[1] (numeric) = -0.027137118024401863514461149051534
absolute error = 1e-33
relative error = 3.6849896849797898455880975585326e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = -0.026867099188490616787327558519805
y[1] (numeric) = -0.026867099188490616787327558519804
absolute error = 1e-33
relative error = 3.7220244470172725490088272640191e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.475e+11
Order of pole (six term test) = 3.523e+21
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = -0.026599767084887543076579230029926
y[1] (numeric) = -0.026599767084887543076579230029925
absolute error = 1e-33
relative error = 3.7594314146011543578407780233068e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.298e+11
Order of pole (six term test) = 1.009e+21
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = -0.026335094980159504579252024594645
y[1] (numeric) = -0.026335094980159504579252024594644
absolute error = 1e-33
relative error = 3.7972143284593662371598300446997e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.678e+11
Order of pole (six term test) = 1.997e+21
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = -0.02607305640687546766902124030864
y[1] (numeric) = -0.02607305640687546766902124030864
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = -0.025813625160959737736572931083345
y[1] (numeric) = -0.025813625160959737736572931083345
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.277e+11
Order of pole (six term test) = 5.468e+20
TOP MAIN SOLVE Loop
bytes used=96034072, alloc=4455632, time=8.51
x[1] = 4.36
y[1] (analytic) = -0.025556775299071529783340440515445
y[1] (numeric) = -0.025556775299071529783340440515445
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = -0.025302481136010612723481826091564
y[1] (numeric) = -0.025302481136010612723481826091564
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = -0.025050717242148767956366401183318
y[1] (numeric) = -0.025050717242148767956366401183318
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.885e+11
Order of pole (six term test) = 3.882e+21
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = -0.024801458440886805353287185162491
y[1] (numeric) = -0.024801458440886805353287185162491
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.294e+11
Order of pole (six term test) = 6.589e+20
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = -0.024554679806136882357878772473083
y[1] (numeric) = -0.024554679806136882357878772473084
absolute error = 1e-33
relative error = 4.0725434332484058722200405863091e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 7.687e+10
Order of pole (six term test) = -2.019e+20
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = -0.024310356659829874430052588037247
y[1] (numeric) = -0.024310356659829874430052588037248
absolute error = 1e-33
relative error = 4.1134731752100837737522525468043e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = -0.024068464569447547568416724299946
y[1] (numeric) = -0.024068464569447547568416724299947
absolute error = 1e-33
relative error = 4.1548142679171884226716892830652e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = -0.023828979345579286126376072142976
y[1] (numeric) = -0.023828979345579286126376072142977
absolute error = 1e-33
relative error = 4.1965708455134415548690703088832e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = -0.023591877039503131592658288741304
y[1] (numeric) = -0.023591877039503131592658288741305
absolute error = 1e-33
relative error = 4.2387470836914000596451934215616e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.221e+11
Order of pole (six term test) = 4.244e+20
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = -0.023357133940790890438127847222936
y[1] (numeric) = -0.023357133940790890438127847222937
absolute error = 1e-33
relative error = 4.2813472001100287151552613561508e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 7.628e+11
Order of pole (six term test) = 3.216e+22
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = -0.0231247265749370715376770994238
y[1] (numeric) = -0.023124726574937071537677099423801
absolute error = 1e-33
relative error = 4.3243754548164695996142170277851e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = -0.022894631701011416058960648775872
y[1] (numeric) = -0.022894631701011416058960648775872
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = -0.022666826309334785069005675152334
y[1] (numeric) = -0.022666826309334785069005675152334
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.985e+11
Order of pole (six term test) = 2.252e+21
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = -0.02244128761917817244552210591857
y[1] (numeric) = -0.02244128761917817244552210591857
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = -0.022217993076484612992286268573861
y[1] (numeric) = -0.022217993076484612992286268573861
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.306e+11
Order of pole (six term test) = 1.170e+21
TOP MAIN SOLVE Loop
bytes used=100035188, alloc=4455632, time=8.87
x[1] = 4.51
y[1] (analytic) = -0.021996920351613757947511147117173
y[1] (numeric) = -0.021996920351613757947511147117173
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = -0.02177804733710889234087455248789
y[1] (numeric) = -0.02177804733710889234087455248789
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 6.878e+10
Order of pole (six term test) = -2.119e+20
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = -0.021561352145486170899080084826662
y[1] (numeric) = -0.021561352145486170899080084826661
absolute error = 1e-33
relative error = 4.6379280541055870013511501164876e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 9.136e+10
Order of pole (six term test) = 8.250e+20
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = -0.021346813107045851421699134099529
y[1] (numeric) = -0.021346813107045851421699134099529
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.766e+11
Order of pole (six term test) = 1.787e+21
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = -0.021134408767705306748807525018684
y[1] (numeric) = -0.021134408767705306748807525018684
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 3.213e+11
Order of pole (six term test) = 4.734e+21
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = -0.020924117886853598619807740544615
y[1] (numeric) = -0.020924117886853598619807740544616
absolute error = 1e-33
relative error = 4.7791739915033139608756513610844e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = -0.020715919435227398879034745114834
y[1] (numeric) = -0.020715919435227398879034745114834
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.164e+11
Order of pole (six term test) = 1.611e+21
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = -0.020509792592808045618495896619257
y[1] (numeric) = -0.020509792592808045618495896619257
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = -0.02030571674673952396160676205756
y[1] (numeric) = -0.02030571674673952396160676205756
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = -0.0201036714892671632842661886631
y[1] (numeric) = -0.0201036714892671632842661886631
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 3.272e+11
Order of pole (six term test) = 6.122e+21
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = -0.01990363661569684474127497995891
y[1] (numeric) = -0.01990363661569684474127497995891
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.498e+11
Order of pole (six term test) = 4.762e+21
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = -0.019705592122374515017150152549829
y[1] (numeric) = -0.019705592122374515017150152549829
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = -0.019509518204685804251026110923004
y[1] (numeric) = -0.019509518204685804251026110923003
absolute error = 1e-33
relative error = 5.1257032055246734965527914165879e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = -0.019315395255075548095768239755011
y[1] (numeric) = -0.019315395255075548095768239755011
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = -0.019123203861087015861854421299449
y[1] (numeric) = -0.01912320386108701586185442129945
absolute error = 1e-33
relative error = 5.2292492788557096461499025048955e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = -0.018932924803420648667204884013348
y[1] (numeric) = -0.018932924803420648667204884013348
absolute error = 0
bytes used=104036280, alloc=4455632, time=9.22
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 5.245e+11
Order of pole (six term test) = 1.509e+22
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = -0.018744539054012113465157641806389
y[1] (numeric) = -0.01874453905401211346515764180639
absolute error = 1e-33
relative error = 5.3348871216225414486381892417709e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = -0.01855802777412948075439069447478
y[1] (numeric) = -0.01855802777412948075439069447478
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.487e+11
Order of pole (six term test) = 1.148e+21
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = -0.018373372312489335686976291012424
y[1] (numeric) = -0.018373372312489335686976291012424
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = -0.018190554203391634184108148582775
y[1] (numeric) = -0.018190554203391634184108148582777
absolute error = 2e-33
relative error = 1.0994717245212349887972870045537e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = -0.018009555164873117543558908122057
y[1] (numeric) = -0.018009555164873117543558908122058
absolute error = 1e-33
relative error = 5.5526079952849589742821503111034e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = -0.017830357096879100878789746029528
y[1] (numeric) = -0.017830357096879100878789746029528
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 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = -0.017652942079453452567032538193552
y[1] (numeric) = -0.017652942079453452567032538193554
absolute error = 2e-33
relative error = 1.1329556234865986705646433913828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.016e+11
Order of pole (six term test) = 2.362e+21
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = -0.017477292370946583702781029082076
y[1] (numeric) = -0.017477292370946583702781029082077
absolute error = 1e-33
relative error = 5.7217100840079339178806801033004e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.395e+11
Order of pole (six term test) = 1.020e+21
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = -0.017303390406241268354143007914501
y[1] (numeric) = -0.017303390406241268354143007914502
absolute error = 1e-33
relative error = 5.7792142263593829066707133568264e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 8.205e+10
Order of pole (six term test) = -1.367e+19
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = -0.017131218794996117202600639084614
y[1] (numeric) = -0.017131218794996117202600639084616
absolute error = 2e-33
relative error = 1.1674592589898991484904834409238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = -0.016960760319906528912079146021476
y[1] (numeric) = -0.016960760319906528912079146021477
absolute error = 1e-33
relative error = 5.8959620980335333216738313696793e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.421e+11
Order of pole (six term test) = 2.379e+21
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = -0.016791997934982945321011543333507
y[1] (numeric) = -0.016791997934982945321011543333509
absolute error = 2e-33
relative error = 1.1910435004481384760580862199534e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 2.135e+11
Order of pole (six term test) = 2.381e+21
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = -0.016624914763846238281483831586441
y[1] (numeric) = -0.016624914763846238281483831586442
absolute error = 1e-33
relative error = 6.0150684331607733023126828828634e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = -0.016459494098040057682724053532149
y[1] (numeric) = -0.01645949409804005768272405353215
absolute error = 1e-33
relative error = 6.0755208759367440378524058148940e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.730e+11
Order of pole (six term test) = 1.712e+21
TOP MAIN SOLVE Loop
bytes used=108037072, alloc=4455632, time=9.59
x[1] = 4.81
y[1] (analytic) = -0.016295719395359971892331179358986
y[1] (numeric) = -0.016295719395359971892331179358987
absolute error = 1e-33
relative error = 6.1365808758632593875535481668830e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = -0.016133574278199233527895556245215
y[1] (numeric) = -0.016133574278199233527895556245216
absolute error = 1e-33
relative error = 6.1982545389911955058345899621240e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = -0.01597304253191100513420955114174
y[1] (numeric) = -0.015973042531911005134209551141741
absolute error = 1e-33
relative error = 6.2605480327382600768966762355853e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = -0.015814108103186880987271291363368
y[1] (numeric) = -0.015814108103186880987271291363369
absolute error = 1e-33
relative error = 6.3234675865057392250239252983628e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.124e+11
Order of pole (six term test) = 4.369e+20
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = -0.015656755098451542875910667028563
y[1] (numeric) = -0.015656755098451542875910667028565
absolute error = 2e-33
relative error = 1.2774038984602885668761799019549e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = -0.015500967782273389325277966639986
y[1] (numeric) = -0.015500967782273389325277966639987
absolute error = 1e-33
relative error = 6.4512101053689105733583411344149e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 3.475e+11
Order of pole (six term test) = 7.806e+21
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = -0.015346730575790979323793014607349
y[1] (numeric) = -0.01534673057579097932379301460735
absolute error = 1e-33
relative error = 6.5160458448229415445939479591788e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = -0.015194028055155133196616204361159
y[1] (numeric) = -0.015194028055155133196616204361161
absolute error = 2e-33
relative error = 1.3163066388583022228325601109699e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = -0.015042844949986534834430520561019
y[1] (numeric) = -0.015042844949986534834430520561021
absolute error = 2e-33
relative error = 1.3295357405128278224310585398182e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.225e+11
Order of pole (six term test) = 5.398e+20
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = -0.014893166141848681036472092840257
y[1] (numeric) = -0.014893166141848681036472092840259
absolute error = 2e-33
relative error = 1.3428977968493548484005862777435e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.111e+11
Order of pole (six term test) = 2.264e+20
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = -0.014744976662736025261471037686311
y[1] (numeric) = -0.014744976662736025261471037686313
absolute error = 2e-33
relative error = 1.3563941440846520375077355696288e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = -0.014598261693577164599617798133888
y[1] (numeric) = -0.01459826169357716459961779813389
absolute error = 2e-33
relative error = 1.3700261318646899129907518322816e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 1.016e+11
Order of pole (six term test) = 1.078e+21
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = -0.014453006562752920283004829557022
y[1] (numeric) = -0.014453006562752920283004829557024
absolute error = 2e-33
relative error = 1.3837951233996065063205819382868e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = -0.014309196744629163541359738704192
y[1] (numeric) = -0.014309196744629163541359738704194
absolute error = 2e-33
relative error = 1.3977024956000295070162563718432e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
Radius of convergence (six term test) for eq 1 = 7.714e+10
Order of pole (six term test) = 6.149e+20
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = -0.014166817858104240084432800094696
y[1] (numeric) = -0.014166817858104240084432800094698
absolute error = 2e-33
relative error = 1.4117496392147684728431889649845e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=112038200, alloc=4455632, time=9.95
x[1] = 4.96
y[1] (analytic) = -0.014025855665170847952276604894962
y[1] (numeric) = -0.014025855665170847952276604894964
absolute error = 2e-33
relative error = 1.4259379589698908697301579351366e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = -0.013886296069492224920004431120137
y[1] (numeric) = -0.013886296069492224920004431120138
absolute error = 1e-33
relative error = 7.2013443685459792456242850418413e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = -0.013748125114992503074581296546882
y[1] (numeric) = -0.013748125114992503074581296546884
absolute error = 2e-33
relative error = 1.4547438165360998102828140547844e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = -0.013611328984461089597930665007658
y[1] (numeric) = -0.01361132898446108959793066500766
absolute error = 2e-33
relative error = 1.4693642349569479361641444906233e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 702
Order of pole (three term test) = -1.760e+04
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = 2.0 / exp(x);
Iterations = 400
Total Elapsed Time = 9 Seconds
Elapsed Time(since restart) = 9 Seconds
Time to Timeout = 2 Minutes 50 Seconds
Percent Done = 100.2 %
> quit
bytes used=112982704, alloc=4455632, time=10.03