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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
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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_0D1,
> array_const_0D2,
> #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_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
> #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_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
> #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_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
> #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_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
> #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_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
> #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_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
> #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_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
> #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_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_tmp4, array_tmp5, 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_0D1,
> array_const_0D2,
> #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_tmp4,
> array_tmp5,
> 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 mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> #emit pre exp 1 $eq_no = 1
> array_tmp4[1] := exp(array_tmp3[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0;
> #emit pre exp ID_FULL iii = 2 $eq_no = 1
> #emit pre exp 2 $eq_no = 1
> array_tmp4[2] := att(1,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0.0;
> array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre exp ID_FULL iii = 3 $eq_no = 1
> #emit pre exp 3 $eq_no = 1
> array_tmp4[3] := att(2,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0.0;
> array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre exp ID_FULL iii = 4 $eq_no = 1
> #emit pre exp 4 $eq_no = 1
> array_tmp4[4] := att(3,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0.0;
> array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre exp ID_FULL iii = 5 $eq_no = 1
> #emit pre exp 5 $eq_no = 1
> array_tmp4[5] := att(4,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0.0;
> array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0;
> #emit exp FULL $eq_no = 1
> array_tmp4[kkk] := att(kkk-1,array_tmp4,array_tmp3,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 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_0D1,
array_const_0D2, 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_tmp4, array_tmp5, 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] := array_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4[1] := exp(array_tmp3[1]);
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0);
array_tmp4[2] := att(1, array_tmp4, array_tmp3, 1);
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp3[3] := 0.;
array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4[3] := att(2, array_tmp4, array_tmp3, 1);
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp3[4] := 0.;
array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4[4] := att(3, array_tmp4, array_tmp3, 1);
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp3[5] := 0.;
array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4[5] := att(4, array_tmp4, array_tmp3, 1);
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp3[kkk] := 0.;
array_tmp3[kkk] :=
-ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0);
array_tmp4[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1);
array_tmp5[kkk] := array_tmp4[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_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 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(20.0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x + 0.2)));
> end;
exact_soln_y := proc(x)
return 20.0*exp(sqrt(0.1*x + 0.2))*sqrt(0.1*x + 0.2)
- 20.0*exp(sqrt(0.1*x + 0.2))
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, 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_0D1,
> array_const_0D2,
> #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_tmp4,
> array_tmp5,
> 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/exp_sqrtpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.0;");
> omniout_str(ALWAYS,"x_end := 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(20.0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x + 0.2)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 0.0;
> 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_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(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_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[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_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[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_0D1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D1[1] := 0.1;
> array_const_0D2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D2[1] := 0.2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> 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 ) = exp(sqrt(0.1 * x + 0.2));");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 6
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T00:55:01-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"exp_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_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,"exp_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"exp_sqrt 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_0D1,
array_const_0D2, 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_tmp4, array_tmp5, 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/exp_sqrtpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.0;");
omniout_str(ALWAYS, "x_end := 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(20.0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0\
.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x + 0.2)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.;
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_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 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_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_0D1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D1[term] := 0.; term := term + 1
end do;
array_const_0D1[1] := 0.1;
array_const_0D2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D2[term] := 0.; term := term + 1
end do;
array_const_0D2[1] := 0.2;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.;
x_end := 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 ) = exp(sqrt(0.1 * x + 0.2));")
;
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T00:55:01-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"exp_sqrt");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_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,
"exp_sqrt diffeq.mxt")
;
logitem_str(html_log_file, "exp_sqrt maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 13
> main();
##############ECHO OF PROBLEM#################
##############temp/exp_sqrtpostode.ode#################
diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 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(20.0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x + 0.2)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 5
estimated_steps = 5000000
step_error = 2.0000000000000000000000000000000e-17
est_needed_step_err = 2.0000000000000000000000000000000e-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 = 1.1720747881514179283237616825706e-168
estimated_step_error = 1.1720747881514179283237616825706e-168
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 = 7.8656589710943941872258947966958e-161
estimated_step_error = 7.8656589710943941872258947966958e-161
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 = 5.2785519865100873514387859580768e-153
estimated_step_error = 5.2785519865100873514387859580768e-153
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 = 3.5423730591446278822674423485977e-145
estimated_step_error = 3.5423730591446278822674423485977e-145
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 = 2.3772420040132886695086824055191e-137
estimated_step_error = 2.3772420040132886695086824055191e-137
best_h = 3.200000e-05
opt_iter = 6
bytes used=4000212, alloc=3014104, time=0.12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.5953343124698975884839481515087e-129
estimated_step_error = 1.5953343124698975884839481515087e-129
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 = 1.0706029616984781469063728077528e-121
estimated_step_error = 1.0706029616984781469063728077528e-121
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 = 7.1845905383248759956502325780969e-114
estimated_step_error = 7.1845905383248759956502325780969e-114
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 = 4.8213570873511815349680844202261e-106
estimated_step_error = 4.8213570873511815349680844202261e-106
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 = 3.2353700743043982097597622835816e-98
estimated_step_error = 3.2353700743043982097597622835816e-98
best_h = 0.001024
opt_iter = 11
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.1709679568904503607598873388723e-90
estimated_step_error = 2.1709679568904503607598873388723e-90
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 = 1.4565736272138751156356090546050e-82
estimated_step_error = 1.4565736272138751156356090546050e-82
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 = 9.7703626513879470649079762981020e-75
estimated_step_error = 9.7703626513879470649079762981020e-75
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 = 6.5506977943914172273692581409710e-67
estimated_step_error = 6.5506977943914172273692581409710e-67
best_h = 0.016384
opt_iter = 15
bytes used=8001068, alloc=4062488, time=0.24
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.3879592049041792774640076784827e-59
estimated_step_error = 4.3879592049041792774640076784827e-59
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 = 2.9338461747119763556594359516479e-51
estimated_step_error = 2.9338461747119763556594359516479e-51
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 = 1.9544552595886539665589391870398e-43
estimated_step_error = 1.9544552595886539665589391870398e-43
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 = 1.2927074562627636893343223036245e-35
estimated_step_error = 1.2927074562627636893343223036245e-35
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (analytic) = -17.290587327796204449202978508691
y[1] (numeric) = -17.290587327796204449202978508691
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 = 2.244
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 26.49
Order of pole (six term test) = -2.495
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (analytic) = -17.274939105918929096702966064715
y[1] (numeric) = -17.274939105918929096702966064714
absolute error = 1e-30
relative error = 5.7887324167606995074968116772733e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.255
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 26.56
Order of pole (six term test) = -2.495
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (analytic) = -17.259273422614415070350318196196
y[1] (numeric) = -17.259273422614415070350318196196
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 = 2.266
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 26.62
Order of pole (six term test) = -2.495
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (analytic) = -17.243590301745536270174986254011
y[1] (numeric) = -17.24359030174553627017498625401
absolute error = 1e-30
relative error = 5.7992563178607408549443811530080e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.277
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 26.69
Order of pole (six term test) = -2.495
TOP MAIN SOLVE Loop
bytes used=12001956, alloc=4259060, time=0.38
x[1] = 0.04
y[1] (analytic) = -17.227889766977118641339727721417
y[1] (numeric) = -17.227889766977118641339727721417
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 = 2.288
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 26.76
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (analytic) = -17.212171841778399290953205329685
y[1] (numeric) = -17.212171841778399290953205329685
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 = 2.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 26.82
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (analytic) = -17.196436549425443328923077429396
y[1] (numeric) = -17.196436549425443328923077429396
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 = 2.311
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 26.89
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (analytic) = -17.180683913003519360437335078654
y[1] (numeric) = -17.180683913003519360437335078654
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 = 2.322
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 26.95
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (analytic) = -17.16491395540943453293547915868
y[1] (numeric) = -17.16491395540943453293547915868
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 = 2.333
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.02
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (analytic) = -17.14912669935383001647922180289
y[1] (numeric) = -17.149126699353830016479221802889
absolute error = 1e-30
relative error = 5.8312007225282175374436068655586e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.345
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.08
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = -17.133322167363437773227375243985
y[1] (numeric) = -17.133322167363437773227375243985
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 = 2.356
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.15
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = -17.117500381783299449234722728327
y[1] (numeric) = -17.117500381783299449234722728326
absolute error = 1e-30
relative error = 5.8419744571129964343653237964448e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.367
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.21
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
bytes used=16002944, alloc=4390108, time=0.51
x[1] = 0.12
y[1] (analytic) = -17.101661364778948200004294489649
y[1] (numeric) = -17.101661364778948200004294489649
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 = 2.378
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.28
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = -17.085805138338554240101971725266
y[1] (numeric) = -17.085805138338554240101971725267
absolute error = 1e-30
relative error = 5.8528116872649835898390698652437e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.389
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.34
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = -17.069931724275034886668072568669
y[1] (numeric) = -17.069931724275034886668072568668
absolute error = 1e-30
relative error = 5.8582542458439171029118735638518e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.401
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.41
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = -17.054041144228129846809836582504
y[1] (numeric) = -17.054041144228129846809836582504
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 = 2.412
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.47
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = -17.038133419666442479609717921689
y[1] (numeric) = -17.038133419666442479609717921688
absolute error = 1e-30
relative error = 5.8691875181922194171475029037938e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.423
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.53
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = -17.022208571889447744816181268368
y[1] (numeric) = -17.022208571889447744816181268368
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 = 2.434
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.6
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = -17.006266622029467532176150061431
y[1] (numeric) = -17.006266622029467532176150061431
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 = 2.446
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.66
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = -16.990307591053614047802050604347
y[1] (numeric) = -16.990307591053614047802050604346
absolute error = 1e-30
relative error = 5.8857086291160391350568593097089e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.457
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.73
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
bytes used=20003920, alloc=4390108, time=0.65
x[1] = 0.2
y[1] (analytic) = -16.974331499765701916922947376822
y[1] (numeric) = -16.974331499765701916922947376821
absolute error = 1e-30
relative error = 5.8912482062330589078958149533859e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.468
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.79
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = -16.958338368808129645830712680589
y[1] (numeric) = -16.958338368808129645830712680589
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 = 2.479
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.85
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = -16.942328218663731069781344363989
y[1] (numeric) = -16.942328218663731069781344363989
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 = 2.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.92
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = -16.926301069657597398031924392916
y[1] (numeric) = -16.926301069657597398031924392915
absolute error = 1e-30
relative error = 5.9079653368131246825129296883230e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.502
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 27.98
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = -16.910256941958870452069414800018
y[1] (numeric) = -16.910256941958870452069414800017
absolute error = 1e-30
relative error = 5.9135707010975837418231759825607e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.513
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.04
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = -16.894195855582507678403236317647
y[1] (numeric) = -16.894195855582507678403236317647
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 = 2.524
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.1
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = -16.878117830391019503034667439814
y[1] (numeric) = -16.878117830391019503034667439813
absolute error = 1e-30
relative error = 5.9248312522109744880360394055679e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.535
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.17
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = -16.862022886096179580868390453317
y[1] (numeric) = -16.862022886096179580868390453316
absolute error = 1e-30
relative error = 5.9304865540454473019083935591886e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.546
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.23
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
bytes used=24004660, alloc=4390108, time=0.78
x[1] = 0.28
y[1] (analytic) = -16.845911042260708479881379620574
y[1] (numeric) = -16.845911042260708479881379620573
absolute error = 1e-30
relative error = 5.9361586173127550764936325565403e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.558
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.29
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = -16.82978231829993132679866732523
y[1] (numeric) = -16.82978231829993132679866732523
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 = 2.569
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.35
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = -16.81363673348340992833171625239
y[1] (numeric) = -16.813636733483409928331716252389
absolute error = 1e-30
relative error = 5.9475532619814270198005052348163e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.58
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.42
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = -16.79747430693654986970101654848
y[1] (numeric) = -16.797474306936549869701016548479
absolute error = 1e-30
relative error = 5.9532759611785686379762822832349e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.591
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.48
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = -16.781295057642183080178411452064
y[1] (numeric) = -16.781295057642183080178411452063
absolute error = 1e-30
relative error = 5.9590156574036347313058958038882e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.603
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.54
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = -16.765099004442126343735257865785
y[1] (numeric) = -16.765099004442126343735257865784
absolute error = 1e-30
relative error = 5.9647724104405066347175743734804e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.614
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.6
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = -16.748886166038716221558986658123
y[1] (numeric) = -16.748886166038716221558986658123
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 = 2.625
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.66
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = -16.73265656099632084219247343331
y[1] (numeric) = -16.73265656099632084219247343331
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 = 2.636
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.72
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
bytes used=28005592, alloc=4455632, time=0.92
x[1] = 0.36
y[1] (analytic) = -16.716410207742829004347775752587
y[1] (numeric) = -16.716410207742829004347775752586
absolute error = 1e-30
relative error = 5.9821456136366688007274538943127e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.647
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.78
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = -16.700147124571117027038513067224
y[1] (numeric) = -16.700147124571117027038513067224
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 = 2.659
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.85
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = -16.683867329640493771554086124214
y[1] (numeric) = -16.683867329640493771554086124213
absolute error = 1e-30
relative error = 5.9938141453774562901304500989104e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.67
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.91
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = -16.667570840978124249955013999601
y[1] (numeric) = -16.6675708409781242499550139996
absolute error = 1e-30
relative error = 5.9996745149055909376374221789981e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.681
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.97
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = -16.651257676480432225193191993324
y[1] (numeric) = -16.651257676480432225193191993323
absolute error = 1e-30
relative error = 6.0055523698517978007079309358117e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.692
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.03
Order of pole (six term test) = -2.494
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = -16.634927853914482198645434521336
y[1] (numeric) = -16.634927853914482198645434521335
absolute error = 1e-30
relative error = 6.0114477729140433094719575212960e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.703
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.09
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = -16.618581390919341171785153135328
y[1] (numeric) = -16.618581390919341171785153135328
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 = 2.715
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.15
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = -16.602218305007420559897605603032
y[1] (numeric) = -16.602218305007420559897605603032
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 = 2.726
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.21
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
bytes used=32006884, alloc=4455632, time=1.05
x[1] = 0.44
y[1] (analytic) = -16.585838613565798627161286575017
y[1] (numeric) = -16.585838613565798627161286575018
absolute error = 1e-30
relative error = 6.0292399033841162300859305322264e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.737
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.27
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = -16.569442333857523804064426298462
y[1] (numeric) = -16.569442333857523804064426298462
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 = 2.748
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.33
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = -16.553029483022899239994186996582
y[1] (numeric) = -16.553029483022899239994186996582
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 = 2.76
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.39
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = -16.536600078080748935920206326802
y[1] (numeric) = -16.536600078080748935920206326803
absolute error = 1e-30
relative error = 6.0471922600674080146122433908876e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.771
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.45
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = -16.520154135929665794387077320544
y[1] (numeric) = -16.520154135929665794387077320544
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 = 2.782
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.51
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = -16.503691673349241916525843113885
y[1] (numeric) = -16.503691673349241916525843113885
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 = 2.793
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.57
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = -16.487212707001281468486507878142
y[1] (numeric) = -16.487212707001281468486507878142
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 = 2.804
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.63
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = -16.470717253430996432576016241565
y[1] (numeric) = -16.470717253430996432576016241565
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 = 2.816
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.69
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = -16.454205329068185551453426160611
y[1] (numeric) = -16.454205329068185551453426160612
absolute error = 1e-30
relative error = 6.0774736913814286159932645250725e-30 %
Correct digits = 32
h = 0.01
bytes used=36008732, alloc=4455632, time=1.19
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.827
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.75
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = -16.437676950228396766980581499264
y[1] (numeric) = -16.437676950228396766980581499265
absolute error = 1e-30
relative error = 6.0835847001245835362909364584554e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.838
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.81
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = -16.421132133114073448747152946261
y[1] (numeric) = -16.421132133114073448747152946262
absolute error = 1e-30
relative error = 6.0897141067603225594212848210629e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.849
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.87
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = -16.404570893815684700878310418689
y[1] (numeric) = -16.40457089381568470087831041869
absolute error = 1e-30
relative error = 6.0958619794010419681592579536616e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.861
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.92
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = -16.387993248312840029486539812259
y[1] (numeric) = -16.38799324831284002948653981226
absolute error = 1e-30
relative error = 6.1020283865625279063832377174443e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.872
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.98
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = -16.371399212475388647041410487045
y[1] (numeric) = -16.371399212475388647041410487046
absolute error = 1e-30
relative error = 6.1082133971663010899694682980707e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.883
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.04
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = -16.354788802064503683997785291696
y[1] (numeric) = -16.354788802064503683997785291697
absolute error = 1e-30
relative error = 6.1144170805419855627681408970119e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.894
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.1
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = -16.338162032733751572239543862635
y[1] (numeric) = -16.338162032733751572239543862636
absolute error = 1e-30
relative error = 6.1206395064297016355508831624162e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.905
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.16
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = -16.321518920030146859258011942759
y[1] (numeric) = -16.321518920030146859258011942759
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 = 2.917
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.22
Order of pole (six term test) = -2.493
bytes used=40010784, alloc=4455632, time=1.32
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = -16.304859479395192706487746609198
y[1] (numeric) = -16.304859479395192706487746609198
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 = 2.928
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.28
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = -16.28818372616590731986304895542
y[1] (numeric) = -16.28818372616590731986304895542
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 = 2.939
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.33
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = -16.271491675575836555432623636382
y[1] (numeric) = -16.271491675575836555432623636382
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 = 2.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.39
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = -16.254783342756052937773367988941
y[1] (numeric) = -16.254783342756052937773367988942
absolute error = 1e-30
relative error = 6.1520352434943414751095736789124e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.961
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.45
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = -16.238058742736141323973664353399
y[1] (numeric) = -16.238058742736141323973664353399
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 = 2.973
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.51
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = -16.221317890445171441108198438766
y[1] (numeric) = -16.221317890445171441108198438767
absolute error = 1e-30
relative error = 6.1647272234830507657280802719381e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.984
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.57
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = -16.20456080071265752039677906955
y[1] (numeric) = -16.20456080071265752039677906955
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 = 2.995
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.62
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = -16.187787488269505246625545609635
y[1] (numeric) = -16.187787488269505246625545609636
absolute error = 1e-30
relative error = 6.1774964659293365373478813082555e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.006
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.68
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
bytes used=44012168, alloc=4455632, time=1.46
x[1] = 0.69
y[1] (analytic) = -16.17099796774894623690708025916
y[1] (numeric) = -16.17099796774894623690708025916
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 = 3.018
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.74
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = -16.154192253687460258463157277453
y[1] (numeric) = -16.154192253687460258463157277453
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 = 3.029
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.8
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = -16.137370360525685390827122934783
y[1] (numeric) = -16.137370360525685390827122934784
absolute error = 1e-30
relative error = 6.1967964895082469071830061051983e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.04
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.85
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = -16.120532302609316333679267020005
y[1] (numeric) = -16.120532302609316333679267020005
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 = 3.051
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.91
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = -16.103678094189991057445169520208
y[1] (numeric) = -16.103678094189991057445169520208
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 = 3.062
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 30.97
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = -16.086807749426165989801124028639
y[1] (numeric) = -16.086807749426165989801124028639
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 = 3.074
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.02
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = -16.06992128238397992733967772394
y[1] (numeric) = -16.06992128238397992733967772394
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 = 3.085
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.08
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = -16.053018707038106857849494432296
y[1] (numeric) = -16.053018707038106857849494432296
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 = 3.096
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.14
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
bytes used=48012980, alloc=4455632, time=1.59
x[1] = 0.77
y[1] (analytic) = -16.036100037272597874954630352403
y[1] (numeric) = -16.036100037272597874954630352402
absolute error = 1e-30
relative error = 6.2359301680315464776761126319597e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.107
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.19
Order of pole (six term test) = -2.493
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = -16.01916528688171236323647674471
y[1] (numeric) = -16.019165286881712363236476744709
absolute error = 1e-30
relative error = 6.2425225165690253506108312341693e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.118
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.25
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = -16.002214469570738628424710105644
y[1] (numeric) = -16.002214469570738628424710105643
absolute error = 1e-30
relative error = 6.2491350925308847145440792045332e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.13
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.31
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = -15.985247598956804143789309955909
y[1] (numeric) = -15.985247598956804143789309955908
absolute error = 1e-30
relative error = 6.2557679748749084893001622749257e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.141
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.36
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = -15.968264688569675580491838859144
y[1] (numeric) = -15.968264688569675580491838859142
absolute error = 2e-30
relative error = 1.2524842486056923450102236680888e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.152
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.42
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = -15.951265751852548786358577383784
y[1] (numeric) = -15.951265751852548786358577383782
absolute error = 2e-30
relative error = 1.2538189953782971198883452195449e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.163
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.47
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = -15.934250802162828874318682129465
y[1] (numeric) = -15.934250802162828874318682129463
absolute error = 2e-30
relative error = 1.2551578513679041851929241665074e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.175
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.53
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = -15.917219852772900578605264149177
y[1] (numeric) = -15.917219852772900578605264149175
absolute error = 2e-30
relative error = 1.2565008327453520794250019097824e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.186
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.59
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
bytes used=52013896, alloc=4521156, time=1.73
x[1] = 0.85
y[1] (analytic) = -15.900172916870889033744205282201
y[1] (numeric) = -15.900172916870889033744205282198
absolute error = 3e-30
relative error = 1.8867719336667389368530366706911e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.197
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.64
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = -15.883110007561411128352736899798
y[1] (numeric) = -15.883110007561411128352736899795
absolute error = 3e-30
relative error = 1.8887988552442195084423924784660e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.208
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.7
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = -15.866031137866317582835451889866
y[1] (numeric) = -15.866031137866317582835451889863
absolute error = 3e-30
relative error = 1.8908320385430956033312564281341e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.219
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.75
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = -15.848936320725425897197713726961
y[1] (numeric) = -15.848936320725425897197713726958
absolute error = 3e-30
relative error = 1.8928715084033388297276292047759e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.231
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.81
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = -15.831825568997244312393626562014
y[1] (numeric) = -15.831825568997244312393626562011
absolute error = 3e-30
relative error = 1.8949172898132264534483414919116e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.242
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.86
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = -15.814698895459686925886149060624
y[1] (numeric) = -15.814698895459686925886149060622
absolute error = 2e-30
relative error = 1.2646462719402068415364810793161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.253
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.92
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = -15.797556312810780099418933443933
y[1] (numeric) = -15.79755631281078009941893344393
absolute error = 3e-30
relative error = 1.8990278879823945507567883985678e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.264
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 31.98
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = -15.780397833669360294381459028789
y[1] (numeric) = -15.780397833669360294381459028786
absolute error = 3e-30
relative error = 1.9010927554685233006668476518111e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.275
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.03
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
bytes used=56014952, alloc=4521156, time=1.86
x[1] = 0.93
y[1] (analytic) = -15.763223470575763467589462111621
y[1] (numeric) = -15.763223470575763467589462111619
absolute error = 2e-30
relative error = 1.2687760239733177567419687198421e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.287
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.09
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = -15.746033235992506157800041773156
y[1] (numeric) = -15.746033235992506157800041773154
absolute error = 2e-30
relative error = 1.2701611701341844155737497690238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.298
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.14
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = -15.728827142304958390833688019132
y[1] (numeric) = -15.72882714230495839083368801913
absolute error = 2e-30
relative error = 1.2715506260608016774918492746988e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.309
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.19
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = -15.711605201822008528782420573926
y[1] (numeric) = -15.711605201822008528782420573923
absolute error = 3e-30
relative error = 1.9094166136838154923132386138804e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.32
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.25
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = -15.694367426776720186442870254929
y[1] (numeric) = -15.694367426776720186442870254926
absolute error = 3e-30
relative error = 1.9115138051894929964439521608758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.332
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.3
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = -15.677113829326981335824146204341
y[1] (numeric) = -15.677113829326981335824146204339
absolute error = 2e-30
relative error = 1.2757450266506485022865594932643e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.343
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.36
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = -15.659844421556145717341415495689
y[1] (numeric) = -15.659844421556145717341415495686
absolute error = 3e-30
relative error = 1.9157278445694065406993115663917e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.354
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.41
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = -15.642559215473666674116017831062
y[1] (numeric) = -15.64255921547366667411601783106
absolute error = 2e-30
relative error = 1.2785631637702825367613401005518e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.365
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.47
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
bytes used=60015772, alloc=4521156, time=2.00
x[1] = 1.01
y[1] (analytic) = -15.625258223015723523660424008836
y[1] (numeric) = -15.625258223015723523660424008834
absolute error = 2e-30
relative error = 1.2799788467201368069396515401944e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.376
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.52
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = -15.60794145604584057913023398864
y[1] (numeric) = -15.607941456045840579130233988638
absolute error = 2e-30
relative error = 1.2813989632343774681460116521169e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.388
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.58
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = -15.590608926355498930274543649205
y[1] (numeric) = -15.590608926355498930274543649204
absolute error = 1e-30
relative error = 6.4141176571335022680713207319744e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.399
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.63
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = -15.573260645664741092209266131408
y[1] (numeric) = -15.573260645664741092209266131406
absolute error = 2e-30
relative error = 1.2842525695200232452196720595716e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.41
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.68
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = -15.555896625622768628174282840611
y[1] (numeric) = -15.555896625622768628174282840609
absolute error = 2e-30
relative error = 1.2856860958472276447019956020817e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.421
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.74
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = -15.538516877808532850513560076403
y[1] (numeric) = -15.538516877808532850513560076401
absolute error = 2e-30
relative error = 1.2871241288519094652288533757328e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.433
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.79
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = -15.521121413731318702236568713069
y[1] (numeric) = -15.521121413731318702236568713067
absolute error = 2e-30
relative error = 1.2885666870891352058166326335477e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.444
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.85
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = -15.503710244831321919678483827077
y[1] (numeric) = -15.503710244831321919678483827076
absolute error = 1e-30
relative error = 6.4500689461310288599098368184940e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.455
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.9
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
bytes used=64016704, alloc=4521156, time=2.13
x[1] = 1.09
y[1] (analytic) = -15.486283382480219574974743837719
y[1] (numeric) = -15.486283382480219574974743837717
absolute error = 2e-30
relative error = 1.2914654540434273068608825983218e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.466
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 32.95
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = -15.468840837981734095301666642466
y[1] (numeric) = -15.468840837981734095301666642464
absolute error = 2e-30
relative error = 1.2929217004348891979052988428216e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.477
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.01
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = -15.451382622572190854108031482786
y[1] (numeric) = -15.451382622572190854108031482783
absolute error = 3e-30
relative error = 1.9415738211138739877218385869885e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.489
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.06
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = -15.433908747421069427871943209398
y[1] (numeric) = -15.433908747421069427871943209396
absolute error = 2e-30
relative error = 1.2958480140905266179165072495532e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.5
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.11
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = -15.416419223631548610262028046354
y[1] (numeric) = -15.416419223631548610262028046351
absolute error = 3e-30
relative error = 1.9459771795783514816679081390499e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.511
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.17
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = -15.398914062241045273961218431626
y[1] (numeric) = -15.398914062241045273961218431624
absolute error = 2e-30
relative error = 1.2987928836515207064048188397396e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.522
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.22
Order of pole (six term test) = -2.492
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = -15.381393274221747168824243603155
y[1] (numeric) = -15.381393274221747168824243603153
absolute error = 2e-30
relative error = 1.3002723253633172979587238315061e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.533
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.27
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = -15.363856870481139743485649186523
y[1] (numeric) = -15.363856870481139743485649186521
absolute error = 2e-30
relative error = 1.3017564644478280165476955802440e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.545
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.33
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
bytes used=68017908, alloc=4521156, time=2.26
x[1] = 1.17
y[1] (analytic) = -15.346304861862527076012941653629
y[1] (numeric) = -15.346304861862527076012941653627
absolute error = 2e-30
relative error = 1.3032453206180259802073135284150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.556
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.38
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = -15.328737259145546997708531686831
y[1] (numeric) = -15.32873725914554699770853168683
absolute error = 1e-30
relative error = 6.5236945685357901691974039945175e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.567
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.43
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = -15.311154073046680492703794094593
y[1] (numeric) = -15.311154073046680492703794094592
absolute error = 1e-30
relative error = 6.5311863183479520724119643315229e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.578
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.48
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = -15.293555314219755454558050637434
y[1] (numeric) = -15.293555314219755454558050637432
absolute error = 2e-30
relative error = 1.3077403905816622932589475786891e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.59
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.54
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = -15.275940993256444879673914764813
y[1] (numeric) = -15.275940993256444879673914764811
absolute error = 2e-30
relative error = 1.3092483146425472693293360554696e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.601
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.59
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = -15.25831112068675957596753126646
y[1] (numeric) = -15.258311120686759575967531266458
absolute error = 2e-30
relative error = 1.3107610561751228921636000283823e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.612
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.64
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = -15.240665706979535463887134692415
y[1] (numeric) = -15.240665706979535463887134692413
absolute error = 2e-30
relative error = 1.3122786356268482894510959075151e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.623
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.69
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = -15.223004762542915545555391103922
y[1] (numeric) = -15.22300476254291554555539110392
absolute error = 2e-30
relative error = 1.3138010735706499789762814265929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.634
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.75
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
bytes used=72018792, alloc=4521156, time=2.40
x[1] = 1.25
y[1] (analytic) = -15.205328297724826616519548299562
y[1] (numeric) = -15.20532829772482661651954829956
absolute error = 2e-30
relative error = 1.3153283907058159438142515331689e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.646
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.8
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = -15.187636322813450793327886644722
y[1] (numeric) = -15.18763632281345079332788664472
absolute error = 2e-30
relative error = 1.3168606078588980512352128958121e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.657
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.85
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = -15.16992884803769192891073857275
y[1] (numeric) = -15.169928848037691928910738572748
absolute error = 2e-30
relative error = 1.3183977459846228967548200080505e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.668
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.9
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = -15.152205883567636986528847839374
y[1] (numeric) = -15.152205883567636986528847839372
absolute error = 2e-30
relative error = 1.3199398261668111558272218110609e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.679
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 33.96
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = -15.134467439515012441860502924672
y[1] (numeric) = -15.13446743951501244186050292467
absolute error = 2e-30
relative error = 1.3214868696193055267500099713103e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.69
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.01
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = -15.116713525933635781631150488301
y[1] (numeric) = -15.116713525933635781631150488299
absolute error = 2e-30
relative error = 1.3230388976869073494352449546085e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.702
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.06
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = -15.09894415281986216604453664292
y[1] (numeric) = -15.098944152819862166044536642917
absolute error = 3e-30
relative error = 1.9868938977694829786978895193108e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.713
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.11
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = -15.08115933011302632115231200675
y[1] (numeric) = -15.081159330113026321152312006748
absolute error = 2e-30
relative error = 1.3261579937071130486295680608855e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.724
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.16
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
bytes used=76019792, alloc=4521156, time=2.54
x[1] = 1.33
y[1] (analytic) = -15.063359067695879726198960461405
y[1] (numeric) = -15.063359067695879726198960461403
absolute error = 2e-30
relative error = 1.3277251050126655669301719008968e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.735
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.21
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = -15.045543375395023159900373766807
y[1] (numeric) = -15.045543375395023159900373766805
absolute error = 2e-30
relative error = 1.3292972876411581768471019832797e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.747
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.27
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = -15.027712262981334668556909849761
y[1] (numeric) = -15.027712262981334668556909849759
absolute error = 2e-30
relative error = 1.3308745636065444284743884782392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.758
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.32
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = -15.009865740170393017864869191388
y[1] (numeric) = -15.009865740170393017864869191386
absolute error = 2e-30
relative error = 1.3324569550595432999690755417240e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.769
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.37
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = -14.992003816622896689273540773711
y[1] (numeric) = -14.99200381662289668927354077371
absolute error = 1e-30
relative error = 6.6702224214431950580131104600298e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.78
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.42
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = -14.974126501945078480737857628778
y[1] (numeric) = -14.974126501945078480737857628776
absolute error = 2e-30
relative error = 1.3356371737210902335653151979613e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.791
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.47
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = -14.956233805689115770738824597872
y[1] (numeric) = -14.956233805689115770738824597871
absolute error = 1e-30
relative error = 6.6861752296197439127520882347583e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.803
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.52
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = -14.938325737353536503484810880796
y[1] (numeric) = -14.938325737353536503484810880794
absolute error = 2e-30
relative error = 1.3388381236050879033692671297844e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.814
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.57
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
bytes used=80020688, alloc=4521156, time=2.68
x[1] = 1.41
y[1] (analytic) = -14.920402306383620952266121448836
y[1] (numeric) = -14.920402306383620952266121448835
absolute error = 1e-30
relative error = 6.7022321480712011654418397366403e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.825
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.62
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = -14.902463522171799317012568911398
y[1] (numeric) = -14.902463522171799317012568911397
absolute error = 1e-30
relative error = 6.7102999347202277321746548157190e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.836
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.68
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = -14.884509394058045211198665565117
y[1] (numeric) = -14.884509394058045211198665565116
absolute error = 1e-30
relative error = 6.7183940936555419124429555080758e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.847
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.73
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = -14.866539931330265092353158534613
y[1] (numeric) = -14.866539931330265092353158534612
absolute error = 1e-30
relative error = 6.7265147412853282698221757980917e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.859
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.78
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = -14.848555143224683689558563101497
y[1] (numeric) = -14.848555143224683689558563101497
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 = 3.87
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.83
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = -14.830555038926225480471743762438
y[1] (numeric) = -14.830555038926225480471743762438
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 = 3.881
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.88
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = -14.812539627568892269558091535786
y[1] (numeric) = -14.812539627568892269558091535787
absolute error = 1e-30
relative error = 6.7510367914143091296563211191937e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.892
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.93
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = -14.794508918236136918409100608058
y[1] (numeric) = -14.794508918236136918409100608058
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 = 3.904
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 34.98
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
bytes used=84021904, alloc=4586680, time=2.81
x[1] = 1.49
y[1] (analytic) = -14.776462919961233278205817175567
y[1] (numeric) = -14.776462919961233278205817175567
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 = 3.915
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.03
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = -14.758401641727642373598386199615
y[1] (numeric) = -14.758401641727642373598386199615
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 = 3.926
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.08
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = -14.740325092469374886494433744432
y[1] (numeric) = -14.740325092469374886494433744432
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 = 3.937
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.13
Order of pole (six term test) = -2.491
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = -14.7222332810713499874859774569
y[1] (numeric) = -14.722233281071349987485977456899
absolute error = 1e-30
relative error = 6.7924477279253457945266320880578e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.948
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.18
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = -14.704126216369750561895647077364
y[1] (numeric) = -14.704126216369750561895647077364
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 = 3.96
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.23
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = -14.68600390715237487668791958677
y[1] (numeric) = -14.686003907152374876687919586769
absolute error = 1e-30
relative error = 6.8092042350130397758682162552816e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.971
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.28
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = -14.667866362158984733769535885901
y[1] (numeric) = -14.6678663621589847337695358859
absolute error = 1e-30
relative error = 6.8176241541159537487553990982452e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.982
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.33
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = -14.649713590081650154494981006195
y[1] (numeric) = -14.649713590081650154494981006194
absolute error = 1e-30
relative error = 6.8260720173876553012656154782495e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.993
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.38
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
bytes used=88023316, alloc=4586680, time=2.96
x[1] = 1.57
y[1] (analytic) = -14.631545599565090639497597867893
y[1] (numeric) = -14.631545599565090639497597867892
absolute error = 1e-30
relative error = 6.8345479511728691792320009751232e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.004
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.43
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = -14.613362399207013047284292308001
y[1] (numeric) = -14.613362399207013047284292308
absolute error = 1e-30
relative error = 6.8430520826217552107154410162111e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.016
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.48
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = -14.595163997558446134361607775912
y[1] (numeric) = -14.595163997558446134361607775911
absolute error = 1e-30
relative error = 6.8515845396960604703477919576289e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.027
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.53
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = -14.576950403124071799002941345303
y[1] (numeric) = -14.576950403124071799002941345303
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 = 4.038
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.58
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = -14.558721624362553070120584284683
y[1] (numeric) = -14.558721624362553070120584284684
absolute error = 1e-30
relative error = 6.8687349466631795704731661885194e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.049
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.63
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = -14.540477669686858882071852131936
y[1] (numeric) = -14.540477669686858882071852131936
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 = 4.061
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.68
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = -14.522218547464585675605578637542
y[1] (numeric) = -14.522218547464585675605578637542
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 = 4.072
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.73
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = -14.503944266018275864543448371687
y[1] (numeric) = -14.503944266018275864543448371687
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 = 4.083
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.78
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = -14.485654833625733207189803065994
y[1] (numeric) = -14.485654833625733207189803065995
absolute error = 1e-30
relative error = 6.9033813899713210861096350869552e-30 %
Correct digits = 32
h = 0.01
bytes used=92024608, alloc=4586680, time=3.09
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.094
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.83
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = -14.467350258520335120873451109781
y[1] (numeric) = -14.467350258520335120873451109782
absolute error = 1e-30
relative error = 6.9121157788452973390867387645481e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.105
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.88
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = -14.449030548891341977445417526161
y[1] (numeric) = -14.449030548891341977445417526161
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 = 4.117
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.93
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = -14.430695712884203416987277816025
y[1] (numeric) = -14.430695712884203416987277816025
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 = 4.128
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 35.98
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = -14.412345758600861716425512864457
y[1] (numeric) = -14.412345758600861716425512864457
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 = 4.139
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.02
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = -14.393980694100052249197998098132
y[1] (numeric) = -14.393980694100052249197998098131
absolute error = 1e-30
relative error = 6.9473484872040291870835357235782e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.07
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = -14.375600527397601071579097439732
y[1] (numeric) = -14.375600527397601071579097439731
absolute error = 1e-30
relative error = 6.9562311368777919468564199540145e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.161
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.12
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = -14.357205266466719670739675112943
y[1] (numeric) = -14.357205266466719670739675112942
absolute error = 1e-30
relative error = 6.9651438524434920031137138687294e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.173
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.17
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = -14.338794919238296909097474288725
y[1] (numeric) = -14.338794919238296909097474288724
absolute error = 1e-30
relative error = 6.9740867739052776306745639657077e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.184
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.22
Order of pole (six term test) = -2.49
bytes used=96025948, alloc=4586680, time=3.23
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = -14.320369493601188199001553588006
y[1] (numeric) = -14.320369493601188199001553588006
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 = 4.195
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.27
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = -14.301928997402501941291637492173
y[1] (numeric) = -14.301928997402501941291637492172
absolute error = 1e-30
relative error = 6.9920637990974414811121368486428e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.206
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.32
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = -14.283473438447883260779145843697
y[1] (numeric) = -14.283473438447883260779145843696
absolute error = 1e-30
relative error = 7.0010981874214568980656587500633e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.218
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.37
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = -14.265002824501795071211145981192
y[1] (numeric) = -14.265002824501795071211145981191
absolute error = 1e-30
relative error = 7.0101633508433951489950138128552e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.229
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.42
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = -14.246517163287796501801347733196
y[1] (numeric) = -14.246517163287796501801347733195
absolute error = 1e-30
relative error = 7.0192594339964353356150670456880e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.24
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.46
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = -14.228016462488818716943369431611
y[1] (numeric) = -14.228016462488818716943369431611
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 = 4.251
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.51
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = -14.209500729747438160260678992299
y[1] (numeric) = -14.209500729747438160260678992298
absolute error = 1e-30
relative error = 7.0375449427755802154771102307651e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.262
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.56
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = -14.190969972666147253694698300678
y[1] (numeric) = -14.190969972666147253694698300678
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 = 4.274
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.61
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
bytes used=100026916, alloc=4586680, time=3.37
x[1] = 1.82
y[1] (analytic) = -14.172424198807622581887395557662
y[1] (numeric) = -14.172424198807622581887395557661
absolute error = 1e-30
relative error = 7.0559558899184913239004964932812e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.285
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.66
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = -14.153863415694990591677126289184
y[1] (numeric) = -14.153863415694990591677126289183
absolute error = 1e-30
relative error = 7.0652087746665419106258964566748e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.296
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.71
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = -14.135287630812090836096370198485
y[1] (numeric) = -14.135287630812090836096370198483
absolute error = 2e-30
relative error = 1.4148986934234017944116024943520e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.307
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.75
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = -14.116696851603736791837202051043
y[1] (numeric) = -14.116696851603736791837202051041
absolute error = 2e-30
relative error = 1.4167620237398443969029964722914e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.318
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.8
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = -14.098091085475974278734687662721
y[1] (numeric) = -14.098091085475974278734687662719
absolute error = 2e-30
relative error = 1.4186317763689471696623445134493e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.33
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.85
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = -14.07947033979633750940977129542
y[1] (numeric) = -14.079470339796337509409771295418
absolute error = 2e-30
relative error = 1.4205079819990802433493554592148e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.341
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.9
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = -14.060834621894102796811481905533
y[1] (numeric) = -14.060834621894102796811481905531
absolute error = 2e-30
relative error = 1.4223906715223029805403574297683e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.352
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.95
Order of pole (six term test) = -2.49
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = -14.042183939060539947003299288433
y[1] (numeric) = -14.042183939060539947003299288432
absolute error = 1e-30
relative error = 7.1213993801800512690844742320186e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.363
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 36.99
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
bytes used=104028452, alloc=4586680, time=3.50
x[1] = 1.9
y[1] (analytic) = -14.023518298549161364150156689029
y[1] (numeric) = -14.023518298549161364150156689027
absolute error = 2e-30
relative error = 1.4261756268445951042780403784236e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.375
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.04
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = -14.004837707575968894280686227042
y[1] (numeric) = -14.00483770757596889428068622704
absolute error = 2e-30
relative error = 1.4280779554611279665753309862228e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.386
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.09
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = -13.986142173319698434023812620538
y[1] (numeric) = -13.986142173319698434023812620536
absolute error = 2e-30
relative error = 1.4299868936090526490487870950519e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.397
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.14
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = -13.967431702922062330149547000844
y[1] (numeric) = -13.967431702922062330149547000842
absolute error = 2e-30
relative error = 1.4319024732238992600582735332865e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.408
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.18
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = -13.948706303487989595380706563134
y[1] (numeric) = -13.948706303487989595380706563132
absolute error = 2e-30
relative error = 1.4338247264550142741571182477631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.419
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.23
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = -13.929965982085863965585170440732
y[1] (numeric) = -13.929965982085863965585170440731
absolute error = 1e-30
relative error = 7.1787684283365396717251942578565e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.431
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.28
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = -13.911210745747759823107063100757
y[1] (numeric) = -13.911210745747759823107063100756
absolute error = 1e-30
relative error = 7.1884469172150959463283385680361e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.442
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.33
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = -13.892440601469676010649821768662
y[1] (numeric) = -13.89244060146967601064982176866
absolute error = 2e-30
relative error = 1.4396318525834983668809547986588e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.453
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.37
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
bytes used=108029372, alloc=4586680, time=3.64
x[1] = 1.98
y[1] (analytic) = -13.873655556211767559784344336627
y[1] (numeric) = -13.873655556211767559784344336626
absolute error = 1e-30
relative error = 7.2079056305550389443055828181862e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.464
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.42
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = -13.854855616898575357821221677558
y[1] (numeric) = -13.854855616898575357821221677557
absolute error = 1e-30
relative error = 7.2176861863527026633762670687292e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.475
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.47
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = -13.836040790419253776457328343713
y[1] (numeric) = -13.836040790419253776457328343712
absolute error = 1e-30
relative error = 7.2275010976582877557747700882950e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.487
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.52
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = -13.817211083627796285283675582438
y[1] (numeric) = -13.817211083627796285283675582438
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 = 4.498
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.56
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = -13.798366503343259072923319938145
y[1] (numeric) = -13.798366503343259072923319938145
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 = 4.509
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.61
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = -13.779507056349982698255171046757
y[1] (numeric) = -13.779507056349982698255171046757
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 = 4.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.66
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = -13.760632749397811793871657262936
y[1] (numeric) = -13.760632749397811793871657262935
absolute error = 1e-30
relative error = 7.2671076847375471553380128971985e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.532
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.7
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = -13.741743589202312843615293218743
y[1] (numeric) = -13.741743589202312843615293218742
absolute error = 1e-30
relative error = 7.2770969237539707835463405217319e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.543
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.75
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
bytes used=112030280, alloc=4586680, time=3.77
x[1] = 2.06
y[1] (analytic) = -13.722839582444990055741157005216
y[1] (numeric) = -13.722839582444990055741157005215
absolute error = 1e-30
relative error = 7.2871215464710008862394120696426e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.554
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.8
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = -13.70392073577349935295903604204
y[1] (numeric) = -13.703920735773499352959036042039
absolute error = 1e-30
relative error = 7.2971817283614516363946202330873e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.565
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.84
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = -13.684987055801860500320451392893
y[1] (numeric) = -13.684987055801860500320451392892
absolute error = 1e-30
relative error = 7.3072776460978963411024936838004e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.576
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.89
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = -13.666038549110667391631833679614
y[1] (numeric) = -13.666038549110667391631833679613
absolute error = 1e-30
relative error = 7.3174094775627287292540823943817e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.588
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.94
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = -13.647075222247296514795715035913
y[1] (numeric) = -13.647075222247296514795715035912
absolute error = 1e-30
relative error = 7.3275774018583273290486003752006e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.599
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.98
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = -13.6280970817261136162068376716
y[1] (numeric) = -13.628097081726113616206837671598
absolute error = 2e-30
relative error = 1.4675563198634648303909261676013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.61
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.03
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = -13.609104134028678584059479263449
y[1] (numeric) = -13.609104134028678584059479263448
absolute error = 1e-30
relative error = 7.3480222515129789164260840503999e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.621
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.08
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = -13.5900963856039485701559789026
y[1] (numeric) = -13.590096385603948570155978902599
absolute error = 1e-30
relative error = 7.3582995412696600615957142333368e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.632
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.12
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
bytes used=116031144, alloc=4586680, time=3.91
x[1] = 2.14
y[1] (analytic) = -13.57107384286847936954433670718
y[1] (numeric) = -13.571073842868479369544336707178
absolute error = 2e-30
relative error = 1.4737227305346867636697423865097e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.644
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.17
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = -13.55203651220662507705477905444
y[1] (numeric) = -13.552036512206625077054779054438
absolute error = 2e-30
relative error = 1.4757929542165525245242273752047e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.655
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.22
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = -13.532984399970736039551254868731
y[1] (numeric) = -13.532984399970736039551254868729
absolute error = 2e-30
relative error = 1.4778706166278628346954541938833e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.666
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.26
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = -13.513917512481355122463883222332
y[1] (numeric) = -13.51391751248135512246388322233
absolute error = 2e-30
relative error = 1.4799557553557764913001928207213e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.677
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.31
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = -13.494835856027412308922336865159
y[1] (numeric) = -13.494835856027412308922336865157
absolute error = 2e-30
relative error = 1.4820484082484844142586831418385e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.689
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.35
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = -13.475739436866417649567949859344
y[1] (numeric) = -13.475739436866417649567949859342
absolute error = 2e-30
relative error = 1.4841486134174394440816739360575e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.4
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = -13.456628261224652580883911348691
y[1] (numeric) = -13.45662826122465258088391134869
absolute error = 1e-30
relative error = 7.4312820461980467358802767683786e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.711
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.45
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = -13.437502335297359629648184131467
y[1] (numeric) = -13.437502335297359629648184131466
absolute error = 1e-30
relative error = 7.4418591717987665386165662382114e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.722
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.49
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
bytes used=120032360, alloc=4586680, time=4.05
x[1] = 2.22
y[1] (analytic) = -13.418361665248930520882699984481
y[1] (numeric) = -13.418361665248930520882699984479
absolute error = 2e-30
relative error = 1.4904949276927221890673661772789e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.733
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.54
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = -13.399206257213092706444868798839
y[1] (numeric) = -13.399206257213092706444868798837
absolute error = 2e-30
relative error = 1.4926257284257828514909251610818e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.745
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.58
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = -13.38003611729309433118343202996
y[1] (numeric) = -13.380036117293094331183432029958
absolute error = 2e-30
relative error = 1.4947642760209668172633937699003e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.756
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.63
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = -13.36085125156188765336013050944
y[1] (numeric) = -13.360851251561887653360130509438
absolute error = 2e-30
relative error = 1.4969106102174435779095733926231e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.767
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.68
Order of pole (six term test) = -2.489
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = -13.341651666062310935821481334289
y[1] (numeric) = -13.341651666062310935821481334287
absolute error = 2e-30
relative error = 1.4990647710339188427781473658434e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.778
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.72
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = -13.322437366807268824191108579594
y[1] (numeric) = -13.322437366807268824191108579592
absolute error = 2e-30
relative error = 1.5012267987710580321832008841108e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.789
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.77
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = -13.303208359779911228142489405704
y[1] (numeric) = -13.303208359779911228142489405701
absolute error = 3e-30
relative error = 2.2550951010209029839780378605845e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.801
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.81
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = -13.283964650933810721604603348272
y[1] (numeric) = -13.283964650933810721604603348269
absolute error = 3e-30
relative error = 2.2583619264517628342089661608459e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.812
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.86
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
bytes used=124033336, alloc=4586680, time=4.18
x[1] = 2.3
y[1] (analytic) = -13.26470624619313847754875192649
y[1] (numeric) = -13.264706246193138477548751926487
absolute error = 3e-30
relative error = 2.2616407361911804941940963739233e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.823
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.9
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = -13.245433151452838752803693033772
y[1] (numeric) = -13.245433151452838752803693033769
absolute error = 3e-30
relative error = 2.2649315924190383770185908854551e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.834
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 38.95
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = -13.226145372578801938148155828355
y[1] (numeric) = -13.226145372578801938148155828352
absolute error = 3e-30
relative error = 2.2682345577569190384818696485298e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.846
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = -13.206842915408036188734714026969
y[1] (numeric) = -13.206842915408036188734714026967
absolute error = 2e-30
relative error = 1.5143664635146516906898346461682e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.857
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.04
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = -13.187525785748837649706846673825
y[1] (numeric) = -13.187525785748837649706846673823
absolute error = 2e-30
relative error = 1.5165847123205700157381364434312e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.868
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.09
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = -13.168193989380959291681754680249
y[1] (numeric) = -13.168193989380959291681754680247
absolute error = 2e-30
relative error = 1.5188111609024227275107671942564e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.879
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.13
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = -13.148847532055778370585078775447
y[1] (numeric) = -13.148847532055778370585078775444
absolute error = 3e-30
relative error = 2.2815687783178363658865827267597e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.18
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = -13.129486419496462526140031019657
y[1] (numeric) = -13.129486419496462526140031019653
absolute error = 4e-30
relative error = 3.0465776590166171951712522027518e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.902
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.22
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
bytes used=128034308, alloc=4586680, time=4.32
x[1] = 2.38
y[1] (analytic) = -13.110110657398134533132559705543
y[1] (numeric) = -13.11011065739813453313255970554
absolute error = 3e-30
relative error = 2.2883102045420778544884075899260e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.913
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.27
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = -13.090720251428035719395969243693
y[1] (numeric) = -13.090720251428035719395969243689
absolute error = 4e-30
relative error = 3.0555996333079147863894709753497e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.924
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.31
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = -13.07131520722568806428286633865
y[1] (numeric) = -13.071315207225688064282866338647
absolute error = 3e-30
relative error = 2.2951018718771550852100924138983e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.935
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.36
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = -13.051895530403054991219356151912
y[1] (numeric) = -13.051895530403054991219356151908
absolute error = 4e-30
relative error = 3.0646889493425758229642120243835e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.946
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.4
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = -13.032461226544700867766022830654
y[1] (numeric) = -13.03246122654470086776602283065
absolute error = 4e-30
relative error = 3.0692590835050739105737077994092e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.958
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.45
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = -13.013012301207949226442354224563
y[1] (numeric) = -13.01301230120794922644235422456
absolute error = 3e-30
relative error = 2.3053847414879652641892612051990e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.969
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.49
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = -12.993548759923039719405868123589
y[1] (numeric) = -12.993548759923039719405868123586
absolute error = 3e-30
relative error = 2.3088380668206065073071636266012e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.98
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.54
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = -12.974070608193283819914225051936
y[1] (numeric) = -12.974070608193283819914225051932
absolute error = 4e-30
relative error = 3.0830724764777765401439817404424e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.991
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.58
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
bytes used=132036156, alloc=4586680, time=4.45
x[1] = 2.46
y[1] (analytic) = -12.954577851495219283338029474724
y[1] (numeric) = -12.954577851495219283338029474721
absolute error = 3e-30
relative error = 2.3157836823326045767007946210759e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.003
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.63
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = -12.935070495278763380333786924863
y[1] (numeric) = -12.93507049527876338033378692486
absolute error = 3e-30
relative error = 2.3192761114792417489052614343003e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.014
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.67
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = -12.915548544967364914630559517813
y[1] (numeric) = -12.91554854496736491463055951781
absolute error = 3e-30
relative error = 2.3227817150429675520657494939975e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.025
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.71
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = -12.896012005958155037730207821937
y[1] (numeric) = -12.896012005958155037730207821934
absolute error = 3e-30
relative error = 2.3263005637820080019022629930588e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.036
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.76
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = -12.876460883622096872669685058181
y[1] (numeric) = -12.876460883622096872669685058178
absolute error = 3e-30
relative error = 2.3298327289727392981094012416549e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.047
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.8
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = -12.856895183304133958844622801414
y[1] (numeric) = -12.856895183304133958844622801411
absolute error = 3e-30
relative error = 2.3333782824143865796255240662908e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.059
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.85
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = -12.837314910323337529746379138057
y[1] (numeric) = -12.837314910323337529746379138054
absolute error = 3e-30
relative error = 2.3369372964337742858563965589641e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.07
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.89
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = -12.81772006997305263531977468193
y[1] (numeric) = -12.817720069973052635319774681926
absolute error = 4e-30
relative error = 3.1206797918535050435378470579356e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.081
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.94
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
bytes used=136037104, alloc=4586680, time=4.59
x[1] = 2.54
y[1] (analytic) = -12.798110667521043120505883719354
y[1] (numeric) = -12.79811066752104312050588371935
absolute error = 4e-30
relative error = 3.1254613309065785620248664063800e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.092
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 39.98
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = -12.778486708209635471393442463572
y[1] (numeric) = -12.778486708209635471393442463569
absolute error = 3e-30
relative error = 2.3476958332418402103415895448338e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.103
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.03
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = -12.758848197255861540263650013195
y[1] (numeric) = -12.758848197255861540263650013191
absolute error = 4e-30
relative error = 3.1350792314155043786200044393458e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.115
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.07
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = -12.739195139851600160676336829311
y[1] (numeric) = -12.739195139851600160676336829308
absolute error = 3e-30
relative error = 2.3549368441772273730389905115610e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.126
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.11
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = -12.719527541163717663610627691655
y[1] (numeric) = -12.719527541163717663610627691652
absolute error = 3e-30
relative error = 2.3585781706837894799486264762990e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.137
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.16
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = -12.699845406334207305540299094042
y[1] (numeric) = -12.699845406334207305540299094039
absolute error = 3e-30
relative error = 2.3622334792388199811009973418560e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.148
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.2
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = -12.680148740480327619192993417069
y[1] (numeric) = -12.680148740480327619192993417067
absolute error = 2e-30
relative error = 1.5772685643782435903543074362208e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.159
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.25
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = -12.66043754869473969761327307828
y[1] (numeric) = -12.660437548694739697613273078278
absolute error = 2e-30
relative error = 1.5797242333115059937608409642529e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.171
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.29
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.62
bytes used=140038564, alloc=4586680, time=4.73
y[1] (analytic) = -12.640711836045643422022146884314
y[1] (numeric) = -12.640711836045643422022146884312
absolute error = 2e-30
relative error = 1.5821893782096167912747774065479e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.182
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.33
Order of pole (six term test) = -2.488
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = -12.620971607576912643840148232794
y[1] (numeric) = -12.620971607576912643840148232792
absolute error = 2e-30
relative error = 1.5846640513788287831080134835577e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.193
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.38
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = -12.601216868308229331117261418217
y[1] (numeric) = -12.601216868308229331117261418214
absolute error = 3e-30
relative error = 2.3807224582769708673114351931351e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.204
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.42
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = -12.581447623235216689490949406884
y[1] (numeric) = -12.581447623235216689490949406881
absolute error = 3e-30
relative error = 2.3844632905832297672298084626360e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.216
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.47
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = -12.561663877329571267673205907296
y[1] (numeric) = -12.561663877329571267673205907293
absolute error = 3e-30
relative error = 2.3882186542295516120220710519846e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.227
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.51
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = -12.541865635539194057348908735457
y[1] (numeric) = -12.541865635539194057348908735455
absolute error = 2e-30
relative error = 1.5946590867093250674064404256189e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.238
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.55
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = -12.522052902788320597250763224667
y[1] (numeric) = -12.522052902788320597250763224664
absolute error = 3e-30
relative error = 2.3957732995457810246539587918799e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.249
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.6
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = -12.502225683977650091060767115797
y[1] (numeric) = -12.502225683977650091060767115795
absolute error = 2e-30
relative error = 1.5997151631674027528477545859930e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.26
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.64
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = -12.482383983984473548674375830162
y[1] (numeric) = -12.482383983984473548674375830159
absolute error = 3e-30
relative error = 2.4033870483788600676028754598760e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.272
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.68
bytes used=144040208, alloc=4586680, time=4.87
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = -12.462527807662800960251373590207
y[1] (numeric) = -12.462527807662800960251373590204
absolute error = 3e-30
relative error = 2.4072162937565507916194618226266e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.283
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.73
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = -12.442657159843487512366836295536
y[1] (numeric) = -12.442657159843487512366836295533
absolute error = 3e-30
relative error = 2.4110605648462117626037926945838e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.294
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.77
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = -12.422772045334358855466481620283
y[1] (numeric) = -12.422772045334358855466481620281
absolute error = 2e-30
relative error = 1.6099466308336095759980079465212e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.305
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.81
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = -12.40287246892033543172311615599
y[1] (numeric) = -12.402872468920335431723116155988
absolute error = 2e-30
relative error = 1.6125296821455579445385803074602e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.316
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.86
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = -12.382958435363555872284784702147
y[1] (numeric) = -12.382958435363555872284784702145
absolute error = 2e-30
relative error = 1.6151229211012701406658543979588e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.328
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.9
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = -12.363029949403499472800579553202
y[1] (numeric) = -12.3630299494034994728005795532
absolute error = 2e-30
relative error = 1.6177264054080023201505142965823e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.339
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.94
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = -12.343087015757107756006854814484
y[1] (numeric) = -12.343087015757107756006854814482
absolute error = 2e-30
relative error = 1.6203401932165045076728837043369e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.35
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 40.99
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = -12.323129639118905130054789780025
y[1] (numeric) = -12.323129639118905130054789780023
absolute error = 2e-30
relative error = 1.6229643431252570639053718424640e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.361
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.03
Order of pole (six term test) = -2.487
bytes used=148041344, alloc=4586680, time=5.00
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = -12.303157824161118651159834005696
y[1] (numeric) = -12.303157824161118651159834005694
absolute error = 2e-30
relative error = 1.6255989141847560270409208852924e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.373
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.07
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = -12.283171575533796899054523089576
y[1] (numeric) = -12.283171575533796899054523089574
absolute error = 2e-30
relative error = 1.6282439659018479858771617716465e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.384
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.12
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = -12.263170897864927973628456893663
y[1] (numeric) = -12.263170897864927973628456893661
absolute error = 2e-30
relative error = 1.6308995582441151517042559871297e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.395
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.16
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = -12.243155795760556621042859952068
y[1] (numeric) = -12.243155795760556621042859952067
absolute error = 1e-30
relative error = 8.1678287582215565327934564803095e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.406
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.2
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = -12.223126273804900497512076428187
y[1] (numeric) = -12.223126273804900497512076428185
absolute error = 2e-30
relative error = 1.6362426070048493158990160613536e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.417
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.25
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = -12.203082336560465578850568889216
y[1] (numeric) = -12.203082336560465578850568889214
absolute error = 2e-30
relative error = 1.6389301857023409044361189452755e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.429
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.29
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = -12.183023988568160723791471400789
y[1] (numeric) = -12.183023988568160723791471400787
absolute error = 2e-30
relative error = 1.6416285495921894047137419348028e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.44
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.33
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = -12.162951234347411398991473397881
y[1] (numeric) = -12.16295123434741139899147339788
absolute error = 1e-30
relative error = 8.2216888050661809954404214823290e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.451
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.38
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
bytes used=152042156, alloc=4586680, time=5.14
x[1] = 2.87
y[1] (analytic) = -12.142864078396272573546762195046
y[1] (numeric) = -12.142864078396272573546762195044
absolute error = 2e-30
relative error = 1.6470578827924615870023205441789e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.462
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.42
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = -12.122762525191540790755909930698
y[1] (numeric) = -12.122762525191540790755909930696
absolute error = 2e-30
relative error = 1.6497889782497408208964037224391e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.473
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.46
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = -12.102646579188865424777936598677
y[1] (numeric) = -12.102646579188865424777936598675
absolute error = 2e-30
relative error = 1.6525311112026560657385246761539e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.485
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.5
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = -12.082516244822859129747296331499
y[1] (numeric) = -12.082516244822859129747296331496
absolute error = 3e-30
relative error = 2.4829265189570475735240004669875e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.496
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.55
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = -12.062371526507207488822201307402
y[1] (numeric) = -12.0623715265072074888222013074
absolute error = 2e-30
relative error = 1.6580487473835271800842063334217e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.507
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.59
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = -12.04221242863477787055849891279
y[1] (numeric) = -12.042212428634777870558498912788
absolute error = 2e-30
relative error = 1.6608243807792879300465771568141e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.518
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.63
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = -12.022038955577727499918235763811
y[1] (numeric) = -12.022038955577727499918235763809
absolute error = 2e-30
relative error = 1.6636113120163222758308816410446e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.53
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.67
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = -12.001851111687610751140059836333
y[1] (numeric) = -12.001851111687610751140059836331
absolute error = 2e-30
relative error = 1.6664096074749380248412536396923e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.541
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.72
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
bytes used=156043312, alloc=4586680, time=5.28
x[1] = 2.95
y[1] (analytic) = -11.981648901295485669617712526725
y[1] (numeric) = -11.981648901295485669617712526723
absolute error = 2e-30
relative error = 1.6692193340632398495062104133891e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.552
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.76
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = -11.961432328712019729853029509546
y[1] (numeric) = -11.961432328712019729853029509544
absolute error = 2e-30
relative error = 1.6720405592223548742146251177241e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.563
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.8
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = -11.941201398227594836471086597765
y[1] (numeric) = -11.941201398227594836471086597763
absolute error = 2e-30
relative error = 1.6748733509317206705389254668539e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.574
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.84
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = -11.920956114112411575207378549294
y[1] (numeric) = -11.920956114112411575207378549292
absolute error = 2e-30
relative error = 1.6777177777144365302923635618818e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.586
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.89
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = -11.900696480616592720700189275071
y[1] (numeric) = -11.90069648061659272070018927507
absolute error = 1e-30
relative error = 8.4028695432133944992991953367813e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.597
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.93
Order of pole (six term test) = -2.487
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = -11.880422501970286007845585830281
y[1] (numeric) = -11.880422501970286007845585830279
absolute error = 2e-30
relative error = 1.6834418133431818733843622415406e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.608
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 41.97
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = -11.860134182383766173397730814692
y[1] (numeric) = -11.860134182383766173397730814691
absolute error = 1e-30
relative error = 8.4316078100139182839441282520218e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.619
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.01
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = -11.839831526047536274423443530706
y[1] (numeric) = -11.839831526047536274423443530705
absolute error = 1e-30
relative error = 8.4460661268701996463521762586470e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.63
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.06
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
bytes used=160044232, alloc=4586680, time=5.41
x[1] = 3.03
y[1] (analytic) = -11.81951453713242829014713486023
y[1] (numeric) = -11.819514537132428290147134860229
absolute error = 1e-30
relative error = 8.4605843739045252191408389146980e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.642
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.1
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = -11.79918321978970301365037998317
y[1] (numeric) = -11.799183219789703013650379983169
absolute error = 1e-30
relative error = 8.4751629106224101178866147678395e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.653
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.14
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = -11.778837578151149239819462672439
y[1] (numeric) = -11.778837578151149239819462672438
absolute error = 1e-30
relative error = 8.4898020994442116303754782254987e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.664
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.18
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = -11.758477616329182255864211102399
y[1] (numeric) = -11.758477616329182255864211102398
absolute error = 1e-30
relative error = 8.5045023057345818181634837253086e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.675
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.22
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = -11.738103338416941640662334272305
y[1] (numeric) = -11.738103338416941640662334272304
absolute error = 1e-30
relative error = 8.5192638978322789181430885719969e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.686
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.27
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = -11.717714748488388379115246875363
y[1] (numeric) = -11.717714748488388379115246875362
absolute error = 1e-30
relative error = 8.5340872470803426458500380694817e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.698
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.31
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = -11.697311850598401297634025564011
y[1] (numeric) = -11.69731185059840129763402556401
absolute error = 1e-30
relative error = 8.5489727278566385854039355362608e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.709
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.35
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = -11.676894648782872826807658120024
y[1] (numeric) = -11.676894648782872826807658120023
absolute error = 1e-30
relative error = 8.5639207176047769356608551823995e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.72
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.39
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
bytes used=164045332, alloc=4586680, time=5.55
x[1] = 3.11
y[1] (analytic) = -11.656463147058804097240116297444
y[1] (numeric) = -11.656463147058804097240116297442
absolute error = 2e-30
relative error = 1.7157863193730821936799560523915e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.731
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.43
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = -11.636017349424399374477990543073
y[1] (numeric) = -11.636017349424399374477990543071
absolute error = 2e-30
relative error = 1.7188011498615841284396397829902e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.743
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.47
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = -11.615557259859159838886458097549
y[1] (numeric) = -11.615557259859159838886458097547
absolute error = 2e-30
relative error = 1.7218287123524973810217046898351e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.754
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.52
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = -11.5950828823239767162682030287
y[1] (numeric) = -11.595082882323976716268203028698
absolute error = 2e-30
relative error = 1.7248690848505124620719024636078e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.765
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.56
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = -11.574594220761223764957555637618
y[1] (numeric) = -11.574594220761223764957555637616
absolute error = 2e-30
relative error = 1.7279223460055487324219443820154e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.776
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.6
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = -11.554091279094849125060557693324
y[1] (numeric) = -11.554091279094849125060557693322
absolute error = 2e-30
relative error = 1.7309885751194105005616255585604e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.787
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.64
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = -11.533574061230466535450877574166
y[1] (numeric) = -11.533574061230466535450877574165
absolute error = 1e-30
relative error = 8.6703392607626293500061579760749e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.799
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.68
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = -11.513042571055445924071484293177
y[1] (numeric) = -11.513042571055445924071484293176
absolute error = 1e-30
relative error = 8.6858012886538476885520150251999e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.81
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.72
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
bytes used=168046804, alloc=4586680, time=5.69
x[1] = 3.19
y[1] (analytic) = -11.492496812439003377032730416866
y[1] (numeric) = -11.492496812439003377032730416865
absolute error = 1e-30
relative error = 8.7013293657618538240197059674455e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.821
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.77
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = -11.471936789232290491938980091693
y[1] (numeric) = -11.471936789232290491938980091691
absolute error = 2e-30
relative error = 1.7433847803949077610039763706150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.832
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.81
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = -11.451362505268483120818138988637
y[1] (numeric) = -11.451362505268483120818138988634
absolute error = 3e-30
relative error = 2.6197755931835846177239570248664e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.843
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.85
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = -11.430773964362869507971387359169
y[1] (numeric) = -11.430773964362869507971387359167
absolute error = 2e-30
relative error = 1.7496628016924279651545412686702e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.855
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.89
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = -11.410171170312937828004075133873
y[1] (numeric) = -11.410171170312937828004075133871
absolute error = 2e-30
relative error = 1.7528220831634969823522145199171e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.866
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.93
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = -11.389554126898463129243098826308
y[1] (numeric) = -11.389554126898463129243098826306
absolute error = 2e-30
relative error = 1.7559949913022875470884204676545e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.877
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 42.97
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = -11.368922837881593687691133834689
y[1] (numeric) = -11.368922837881593687691133834688
absolute error = 1e-30
relative error = 8.7959080579557620739786731270115e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.888
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.01
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = -11.348277307006936776613832631616
y[1] (numeric) = -11.348277307006936776613832631615
absolute error = 1e-30
relative error = 8.8119101511782323727225528635289e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.06
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
bytes used=172048844, alloc=4652204, time=5.83
x[1] = 3.27
y[1] (analytic) = -11.327617538001643856802509527325
y[1] (numeric) = -11.327617538001643856802509527324
absolute error = 1e-30
relative error = 8.8279816708608129264222626536907e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.911
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.1
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = -11.306943534575495192501906572806
y[1] (numeric) = -11.306943534575495192501906572805
absolute error = 1e-30
relative error = 8.8441230553783226932080743560592e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.922
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.14
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = -11.286255300420983897940363278493
y[1] (numeric) = -11.286255300420983897940363278492
absolute error = 1e-30
relative error = 8.8603347468375929562057548228698e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.933
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.18
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = -11.265552839213399419348085857676
y[1] (numeric) = -11.265552839213399419348085857675
absolute error = 1e-30
relative error = 8.8766171911171251704641149053370e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.944
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.22
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = -11.244836154610910457298220506121
y[1] (numeric) = -11.24483615461091045729822050612
absolute error = 1e-30
relative error = 8.8929708379072564580716734531607e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.956
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.26
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = -11.224105250254647334155070792646
y[1] (numeric) = -11.224105250254647334155070792644
absolute error = 2e-30
relative error = 1.7818792281501680683870337482290e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.967
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.3
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = -11.203360129768783811364052695703
y[1] (numeric) = -11.203360129768783811364052695701
absolute error = 2e-30
relative error = 1.7851787114168900877497584284224e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.978
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.34
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = -11.182600796760618361268843456343
y[1] (numeric) = -11.182600796760618361268843456341
absolute error = 2e-30
relative error = 1.7884927096560229928501296699326e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.989
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.38
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
bytes used=176050112, alloc=4652204, time=5.97
x[1] = 3.35
y[1] (analytic) = -11.161827254820654898092643645281
y[1] (numeric) = -11.161827254820654898092643645279
absolute error = 2e-30
relative error = 1.7918213159375180077992156253215e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.42
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = -11.141039507522682972672527215063
y[1] (numeric) = -11.141039507522682972672527215061
absolute error = 2e-30
relative error = 1.7951646241354359841262817922123e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.012
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.47
Order of pole (six term test) = -2.486
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = -11.120237558423857435488493515546
y[1] (numeric) = -11.120237558423857435488493515544
absolute error = 2e-30
relative error = 1.7985227289366224858166070686519e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.023
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.51
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = -11.099421411064777572482050112088
y[1] (numeric) = -11.099421411064777572482050112086
absolute error = 2e-30
relative error = 1.8018957258494955948486861178177e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.034
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.55
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = -11.078591068969565718112937710515
y[1] (numeric) = -11.078591068969565718112937710513
absolute error = 2e-30
relative error = 1.8052837112129481483394192078581e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.045
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.59
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = -11.057746535645945350056950637959
y[1] (numeric) = -11.057746535645945350056950637957
absolute error = 2e-30
relative error = 1.8086867822053661481692639580319e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.056
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.63
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = -11.036887814585318669902700355882
y[1] (numeric) = -11.036887814585318669902700355879
absolute error = 3e-30
relative error = 2.7181575552806476714593481860491e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.068
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.67
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = -11.016014909262843674160607715718
y[1] (numeric) = -11.016014909262843674160607715715
absolute error = 3e-30
relative error = 2.7233078610645692759862007196118e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.079
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.71
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
bytes used=180051376, alloc=4652204, time=6.11
x[1] = 3.43
y[1] (analytic) = -10.995127823137510719853384553989
y[1] (numeric) = -10.995127823137510719853384553986
absolute error = 3e-30
relative error = 2.7284812402880606857444747017451e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.09
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.75
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = -10.974226559652218588913769326337
y[1] (numeric) = -10.974226559652218588913769326334
absolute error = 3e-30
relative error = 2.7336778438945151810320197277645e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.101
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.79
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = -10.953311122233850055572307479205
y[1] (numeric) = -10.953311122233850055572307479202
absolute error = 3e-30
relative error = 2.7388978241569123751229855737594e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.113
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.83
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = -10.932381514293346960875507948664
y[1] (numeric) = -10.932381514293346960875507948661
absolute error = 3e-30
relative error = 2.7441413346924488313512317888531e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.124
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.87
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = -10.911437739225784798432755465496
y[1] (numeric) = -10.911437739225784798432755465493
absolute error = 3e-30
relative error = 2.7494085304773625441237437542379e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.135
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.91
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = -10.890479800410446815448907251941
y[1] (numeric) = -10.890479800410446815448907251937
absolute error = 4e-30
relative error = 3.6729327571492723806778565000605e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.146
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.95
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = -10.869507701210897633058545344884
y[1] (numeric) = -10.86950770121089763305854534488
absolute error = 4e-30
relative error = 3.6800194727810784963885748121161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.157
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 43.99
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = -10.84852144497505638993738540583
y[1] (numeric) = -10.848521444975056389937385405826
absolute error = 4e-30
relative error = 3.6871383997242926169548273900389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.169
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.03
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
bytes used=184052416, alloc=4652204, time=6.25
x[1] = 3.51
y[1] (analytic) = -10.827521035035269413126352817682
y[1] (numeric) = -10.827521035035269413126352817678
absolute error = 4e-30
relative error = 3.6942897520650907300247017984808e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.07
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = -10.806506474708382419964320563172
y[1] (numeric) = -10.806506474708382419964320563168
absolute error = 4e-30
relative error = 3.7014737458045538085255369851898e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.191
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.11
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = -10.785477767295812254986454371989
y[1] (numeric) = -10.785477767295812254986454371984
absolute error = 5e-30
relative error = 4.6358632486000890978075832632563e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.202
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.15
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = -10.764434916083618165606522554972
y[1] (numeric) = -10.764434916083618165606522554967
absolute error = 5e-30
relative error = 4.6449256639837906598198077352663e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.213
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.19
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = -10.743377924342572620363394553809
y[1] (numeric) = -10.743377924342572620363394553804
absolute error = 5e-30
relative error = 4.6540297057510137393963836422240e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.225
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.23
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = -10.722306795328231673474267359124
y[1] (numeric) = -10.722306795328231673474267359119
absolute error = 5e-30
relative error = 4.6631756537488067698463545436861e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.236
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.28
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = -10.70122153228100487939991651895
y[1] (numeric) = -10.701221532281004879399916518945
absolute error = 5e-30
relative error = 4.6723637903552787581501567650425e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.247
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.32
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = -10.680122138426224761090462496291
y[1] (numeric) = -10.680122138426224761090462496286
absolute error = 5e-30
relative error = 4.6815944005082115424325440931299e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.258
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.36
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.59
bytes used=188054328, alloc=4652204, time=6.38
y[1] (analytic) = -10.65900861697421583554376775324
y[1] (numeric) = -10.659008616974215835543767753235
absolute error = 5e-30
relative error = 4.6908677717340614573281971057960e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.27
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.4
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = -10.637880971120363200272629343901
y[1] (numeric) = -10.637880971120363200272629343896
absolute error = 5e-30
relative error = 4.7001841941773566013439448418179e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.281
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.44
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = -10.616739204045180684241400281519
y[1] (numeric) = -10.616739204045180684241400281514
absolute error = 5e-30
relative error = 4.7095439606304960132082528530143e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.292
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.48
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = -10.595583318914378566797554885661
y[1] (numeric) = -10.595583318914378566797554885656
absolute error = 5e-30
relative error = 4.7189473665639571794048302871955e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.303
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.52
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = -10.574413318878930868089003177283
y[1] (numeric) = -10.574413318878930868089003177278
absolute error = 5e-30
relative error = 4.7283947101569184126659582808921e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.314
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.55
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = -10.553229207075142214423651721034
y[1] (numeric) = -10.553229207075142214423651721029
absolute error = 5e-30
relative error = 4.7378862923283027612068604655535e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.326
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.59
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = -10.532030986624714281993797745609
y[1] (numeric) = -10.532030986624714281993797745604
absolute error = 5e-30
relative error = 4.7474224167682502309709177414770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.337
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.63
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = -10.510818660634811822354424615736
y[1] (numeric) = -10.51081866063481182235442461573
absolute error = 6e-30
relative error = 5.7084040679640302738207780280702e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.348
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.67
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = -10.489592232198128273011334574498
y[1] (numeric) = -10.489592232198128273011334574492
absolute error = 6e-30
relative error = 5.7199554255148395085717504992332e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.359
bytes used=192055480, alloc=4652204, time=6.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.71
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = -10.468351704392950956442303991481
y[1] (numeric) = -10.468351704392950956442303991474
absolute error = 7e-30
relative error = 6.6868215719791990538314591429660e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.37
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.75
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = -10.447097080283225870842072086924
y[1] (numeric) = -10.447097080283225870842072086918
absolute error = 6e-30
relative error = 5.7432222117699868150963821742214e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.382
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.79
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = -10.425828362918622075849971276747
y[1] (numeric) = -10.425828362918622075849971276741
absolute error = 6e-30
relative error = 5.7549384002331215953302816339539e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.393
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.83
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = -10.404545555334595676487370994298
y[1] (numeric) = -10.404545555334595676487370994292
absolute error = 6e-30
relative error = 5.7667102980040230759249777840417e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.404
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.87
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = -10.383248660552453408500832261677
y[1] (numeric) = -10.383248660552453408500832261671
absolute error = 6e-30
relative error = 5.7785382938915022404353220605732e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.415
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.91
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = -10.361937681579415828275952647974
y[1] (numeric) = -10.361937681579415828275952647967
absolute error = 7e-30
relative error = 6.7554932437434102617591114109942e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.426
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.95
Order of pole (six term test) = -2.485
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = -10.340612621408680110456315876177
y[1] (numeric) = -10.340612621408680110456315876171
absolute error = 6e-30
relative error = 5.8023641535298442524286159002821e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.438
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 44.99
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = -10.319273483019482456371742606759
y[1] (numeric) = -10.319273483019482456371742606752
absolute error = 7e-30
relative error = 6.7834232821899756847304470999657e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.449
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.03
Order of pole (six term test) = -2.484
bytes used=196056584, alloc=4652204, time=6.65
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = -10.297920269377160116350164284402
y[1] (numeric) = -10.297920269377160116350164284395
absolute error = 7e-30
relative error = 6.7974890238913985369932907835183e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.46
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.07
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = -10.276552983433213028957905902826
y[1] (numeric) = -10.276552983433213028957905902819
absolute error = 7e-30
relative error = 6.8116225462805183461202082983474e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.471
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.11
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = -10.255171628125365080183961704956
y[1] (numeric) = -10.255171628125365080183961704949
absolute error = 7e-30
relative error = 6.8258243292604873395143360522705e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.483
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.15
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = -10.233776206377624985554975840958
y[1] (numeric) = -10.233776206377624985554975840951
absolute error = 7e-30
relative error = 6.8400948572997365463707427149214e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.494
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.19
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = -10.212366721100346798139093567903
y[1] (numeric) = -10.212366721100346798139093567897
absolute error = 6e-30
relative error = 5.8752296738453992611863848068254e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.505
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.23
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = -10.190943175190290045368623468168
y[1] (numeric) = -10.190943175190290045368623468161
absolute error = 7e-30
relative error = 6.8688441095829118233462689914297e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.516
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.27
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = -10.169505571530679497583543227111
y[1] (numeric) = -10.169505571530679497583543227104
absolute error = 7e-30
relative error = 6.8833238260829073270458499718013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.527
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.31
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = -10.148053912991264571170286643158
y[1] (numeric) = -10.148053912991264571170286643151
absolute error = 7e-30
relative error = 6.8978742722669112301730928355731e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.539
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.35
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
bytes used=200058288, alloc=4652204, time=6.79
x[1] = 3.84
y[1] (analytic) = -10.126588202428378369142963703968
y[1] (numeric) = -10.126588202428378369142963703961
absolute error = 7e-30
relative error = 6.9124959562603567056305443148416e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.55
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.38
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = -10.105108442684996361987184768953
y[1] (numeric) = -10.105108442684996361987184768946
absolute error = 7e-30
relative error = 6.9271893910918309438866558309095e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.561
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.42
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = -10.083614636590794711559980226801
y[1] (numeric) = -10.083614636590794711559980226794
absolute error = 7e-30
relative error = 6.9419550947522673299167815418909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.572
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.46
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = -10.062106786962208240812924579982
y[1] (numeric) = -10.062106786962208240812924579975
absolute error = 7e-30
relative error = 6.9567935902549977049927632322084e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.583
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.5
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = -10.04058489660248805207948493552
y[1] (numeric) = -10.040584896602488052079484935513
absolute error = 7e-30
relative error = 6.9717054056966793252489214763596e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.595
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.54
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = -10.019048968301758796641814597053
y[1] (numeric) = -10.019048968301758796641814597047
absolute error = 6e-30
relative error = 5.9885923494163812114688663848533e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.606
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.58
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = -9.997499004837075598266699156056
y[1] (numeric) = -9.9974990048370755982666991560501
absolute error = 5.9e-30
relative error = 5.9014759562820776134221497710926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.617
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.62
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = -9.975935008972480633375131522282
y[1] (numeric) = -9.9759350089724806333751315222763
absolute error = 5.7e-30
relative error = 5.7137501345721967488367168736440e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.628
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.66
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
bytes used=204059144, alloc=4652204, time=6.93
x[1] = 3.92
y[1] (analytic) = -9.954356983459059370485040119814
y[1] (numeric) = -9.9543569834590593704850401198083
absolute error = 5.7e-30
relative error = 5.7261358111544193651930242085819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.639
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.7
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = -9.932764931034996471542017462104
y[1] (numeric) = -9.9327649310349964715420174620981
absolute error = 5.9e-30
relative error = 5.9399372087880656154542874307329e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.651
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.74
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = -9.911158854425631357728491014579
y[1] (numeric) = -9.9111588544256313577284910145729
absolute error = 6.1e-30
relative error = 6.1546788721645461455397379549249e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.662
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.77
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = -9.889538756343513442317641214359
y[1] (numeric) = -9.8895387563435134423176412143528
absolute error = 6.2e-30
relative error = 6.2692509254014422544685048466519e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.673
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.81
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = -9.867904639488457033114499350304
y[1] (numeric) = -9.8679046394884570331144993502977
absolute error = 6.3e-30
relative error = 6.3843340913421981753842156060150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.684
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.85
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = -9.846256506547595907003047368411
y[1] (numeric) = -9.8462565065475959070030473684051
absolute error = 5.9e-30
relative error = 5.9921250234305785881502685132237e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.696
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.89
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = -9.824594360195437559094789260715
y[1] (numeric) = -9.8245943601954375590947892607084
absolute error = 6.6e-30
relative error = 6.7178346077473149539641007326555e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.707
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.93
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = -9.802918203093917128951166270454
y[1] (numeric) = -9.8029182030939171289511662704485
absolute error = 5.5e-30
relative error = 5.6105742045915825723367290256012e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.718
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 45.97
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
bytes used=208060184, alloc=4652204, time=7.07
x[1] = 4
y[1] (analytic) = -9.781228037892451006329342498834
y[1] (numeric) = -9.7812280378924510063293424988281
absolute error = 5.9e-30
relative error = 6.0319624255189797558141527732114e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.729
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.01
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = -9.759523867227990118878290471042
y[1] (numeric) = -9.7595238672279901188782904710357
absolute error = 6.3e-30
relative error = 6.4552329454873262695174151093585e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.74
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.05
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = -9.737805693725072904189754698159
y[1] (numeric) = -9.7378056937250729041897546981536
absolute error = 5.4e-30
relative error = 5.5453971560345430666613351134596e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.752
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.08
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = -9.716073519995877968586562187844
y[1] (numeric) = -9.716073519995877968586562187838
absolute error = 6.0e-30
relative error = 6.1753340870176386768525769675775e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.763
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.12
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = -9.694327348640276435008879184451
y[1] (numeric) = -9.6943273486402764350088791844455
absolute error = 5.5e-30
relative error = 5.6734209627978246657031666232622e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.774
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.16
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = -9.672567182245883982337380175471
y[1] (numeric) = -9.6725671822458839823373801754653
absolute error = 5.7e-30
relative error = 5.8929546754272434513934054520222e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.785
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.2
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = -9.650793023388112578470895444591
y[1] (numeric) = -9.6507930233881125784708954445853
absolute error = 5.7e-30
relative error = 5.9062503839698925366107428053592e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.796
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.24
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = -9.62900487463022190945493428276
y[1] (numeric) = -9.6290048746302219094549342827537
absolute error = 6.3e-30
relative error = 6.5427321743275531377660257586032e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.808
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.28
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
bytes used=212061248, alloc=4652204, time=7.21
x[1] = 4.08
y[1] (analytic) = -9.607202738523370506936539528177
y[1] (numeric) = -9.6072027385233705069365395281709
absolute error = 6.1e-30
relative error = 6.3494028033154336704166798542564e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.819
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.32
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = -9.585386617606666576200212575337
y[1] (numeric) = -9.5853866176066665762002125753305
absolute error = 6.5e-30
relative error = 6.7811557940298882606620742193854e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.83
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.35
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = -9.563556514407218527019153592543
y[1] (numeric) = -9.5635565144072185270191535925371
absolute error = 5.9e-30
relative error = 6.1692530295730697522899380795964e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.841
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.39
Order of pole (six term test) = -2.484
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = -9.541712431440185209535786676128
y[1] (numeric) = -9.541712431440185209535786676122
absolute error = 6.0e-30
relative error = 6.2881794469406218486935885729137e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.853
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.43
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = -9.519854371208825857365481345447
y[1] (numeric) = -9.5198543712088258573654813454415
absolute error = 5.5e-30
relative error = 5.7773993020668582281407626785961e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.864
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.47
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = -9.49798233620454974009753748091
y[1] (numeric) = -9.4979823362045497400975374809047
absolute error = 5.3e-30
relative error = 5.5801325085617200020937036549559e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.875
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.51
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = -9.476096328906965527347867900021
y[1] (numeric) = -9.4760963289069655273478679000151
absolute error = 5.9e-30
relative error = 6.2261925113635313844776936247330e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.886
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.54
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = -9.454196351783930366498388662489
y[1] (numeric) = -9.4541963517839303664983886624827
absolute error = 6.3e-30
relative error = 6.6637075914033041712984741238624e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.897
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.58
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
bytes used=216062148, alloc=4652204, time=7.34
x[1] = 4.16
y[1] (analytic) = -9.432282407291598676238909339546
y[1] (numeric) = -9.4322824072915986762389093395398
absolute error = 6.2e-30
relative error = 6.5731704504596977550985276317131e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.909
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.62
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = -9.410354497874470658008301354712
y[1] (numeric) = -9.4103544978744706580083013547056
absolute error = 6.4e-30
relative error = 6.8010190279713442781987600283434e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.92
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.66
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = -9.388412625965440527412909618238
y[1] (numeric) = -9.3884126259654405274129096182321
absolute error = 5.9e-30
relative error = 6.2843424496303325942691569016173e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.931
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.7
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = -9.366456793985844467681558584452
y[1] (numeric) = -9.3664567939858444676815585844458
absolute error = 6.2e-30
relative error = 6.6193653975759428075586294182692e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.942
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.74
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = -9.344487004345508307198086143055
y[1] (numeric) = -9.3444870043455083071980861430491
absolute error = 5.9e-30
relative error = 6.3138832525063139234454434464438e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.953
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.77
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = -9.322503259442794923134115028255
y[1] (numeric) = -9.3225032594427949231341150282491
absolute error = 5.9e-30
relative error = 6.3287722576271240727115392862917e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.965
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.81
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = -9.300505561664651373186739342182
y[1] (numeric) = -9.3005055616646513731867393421757
absolute error = 6.3e-30
relative error = 6.7738253132901672487688323320434e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.976
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.85
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = -9.278493913386655757407961022466
y[1] (numeric) = -9.2784939133866557574079610224599
absolute error = 6.1e-30
relative error = 6.5743428372563283795949665911494e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.987
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.89
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
bytes used=220063196, alloc=4652204, time=7.48
x[1] = 4.24
y[1] (analytic) = -9.256468316973063812095055350855
y[1] (numeric) = -9.256468316973063812095055350849
absolute error = 6.0e-30
relative error = 6.4819538019680124105372639563051e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.998
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.93
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = -9.234428774776855237693573644345
y[1] (numeric) = -9.2344287747768552376935736443396
absolute error = 5.4e-30
relative error = 5.8476816830833025228693982487095e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.009
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 46.96
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = -9.212375289139779762647402867305
y[1] (numeric) = -9.2123752891397797626474028672994
absolute error = 5.6e-30
relative error = 6.0787797112452514215822336564263e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.021
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = -9.190307862392402945113193857507
y[1] (numeric) = -9.1903078623924029451131938575014
absolute error = 5.6e-30
relative error = 6.0933758518751285516013525539265e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.032
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.04
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = -9.168226496854151714439540005833
y[1] (numeric) = -9.1682264968541517144395400058274
absolute error = 5.6e-30
relative error = 6.1080515429254505737207682535233e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.043
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.08
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = -9.146131194833359654294534432928
y[1] (numeric) = -9.146131194833359654294534432922
absolute error = 6.0e-30
relative error = 6.5601508137007634296760255972416e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.054
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.11
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = -9.124021958627312029308753859547
y[1] (numeric) = -9.1240219586273120293087538595411
absolute error = 5.9e-30
relative error = 6.4664465153124657039610795346026e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.066
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.15
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = -9.101898790522290557084309392497
y[1] (numeric) = -9.1018987905222905570843093924908
absolute error = 6.2e-30
relative error = 6.8117654817871556679647189640011e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.077
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.19
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
bytes used=224064204, alloc=4652204, time=7.62
x[1] = 4.32
y[1] (analytic) = -9.079761692793617927404366294736
y[1] (numeric) = -9.0797616927936179274043662947299
absolute error = 6.1e-30
relative error = 6.7182379960934646395487183992140e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.088
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.23
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = -9.05761066770570207046146445389
y[1] (numeric) = -9.057610667705702070461464453884
absolute error = 6.0e-30
relative error = 6.6242635283415238798061070137557e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.099
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.27
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = -9.03544571751208017590706671282
y[1] (numeric) = -9.0354457175120801759070667128141
absolute error = 5.9e-30
relative error = 6.5298383549191100991225523376972e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.11
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.3
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = -9.013266844455462464509021510543
y[1] (numeric) = -9.0132668444554624645090215105366
absolute error = 6.4e-30
relative error = 7.1006440954724188281975933356893e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.122
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.34
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = -8.991074050767775714188047459682
y[1] (numeric) = -8.9910740507677757141880474596759
absolute error = 6.1e-30
relative error = 6.7845064622497487611652776781605e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.133
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.38
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = -8.968867338670206542188928641742
y[1] (numeric) = -8.968867338670206542188928641736
absolute error = 6.0e-30
relative error = 6.6898079472425403096948519381430e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.144
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.42
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = -8.946646710373244445126848643454
y[1] (numeric) = -8.9466467103732444451268486434483
absolute error = 5.7e-30
relative error = 6.3711021397448275362830845190338e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.155
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.45
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = -8.924412168076724598634186821178
y[1] (numeric) = -8.9244121680767245986341868211719
absolute error = 6.1e-30
relative error = 6.8351840828465390578599749999161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.166
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.49
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
bytes used=228065188, alloc=4652204, time=7.76
x[1] = 4.4
y[1] (analytic) = -8.90216371396987041831815012558
y[1] (numeric) = -8.9021637139698704183181501255743
absolute error = 5.7e-30
relative error = 6.4029377386704076778789589864720e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.178
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.53
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = -8.879901350231335883724816229886
y[1] (numeric) = -8.8799013502313358837248162298796
absolute error = 6.4e-30
relative error = 7.2072872744619731422020490467775e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.189
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.57
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = -8.857625079029247626990516890282
y[1] (numeric) = -8.8576250790292476269905168902761
absolute error = 5.9e-30
relative error = 6.6609276723265996876394749579689e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.6
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = -8.835334902521246787846992658846
y[1] (numeric) = -8.83533490252124678784699265884
absolute error = 6.0e-30
relative error = 6.7909140583769416305625439421383e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.211
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.64
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = -8.81303082285453063663239952322
y[1] (numeric) = -8.8130308228545306366323995232142
absolute error = 5.8e-30
relative error = 6.5811638658508476792358064398616e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.222
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.68
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = -8.790712842165893966946043042029
y[1] (numeric) = -8.790712842165893966946043042023
absolute error = 6.0e-30
relative error = 6.8253850486619853801320714574879e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.234
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.72
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = -8.768380962581770259570654382106
y[1] (numeric) = -8.7683809625817702595706543821
absolute error = 6.0e-30
relative error = 6.8427683806217224510031312878209e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.245
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.75
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = -8.746035186218272619272103666969
y[1] (numeric) = -8.7460351862182726192721036669628
absolute error = 6.2e-30
relative error = 7.0889264312242479308988955571082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.256
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.79
Order of pole (six term test) = -2.483
TOP MAIN SOLVE Loop
bytes used=232066124, alloc=4652204, time=7.89
x[1] = 4.48
y[1] (analytic) = -8.72367551518123448607266756158
y[1] (numeric) = -8.723675515181234486072667561574
absolute error = 6.0e-30
relative error = 6.8778349097907155622616515678205e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.267
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.83
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = -8.701301951566250122580328414036
y[1] (numeric) = -8.7013019515662501225803284140299
absolute error = 6.1e-30
relative error = 7.0104451425248941551991212797913e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.279
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.86
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = -8.678914497458714878943079939614
y[1] (numeric) = -8.6789144974587148789430799396086
absolute error = 5.4e-30
relative error = 6.2219762639454295468786844400991e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.29
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.9
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = -8.656513154933865236983847776902
y[1] (numeric) = -8.6565131549338652369838477768959
absolute error = 6.1e-30
relative error = 7.0467171837233848656916173384722e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.301
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.94
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = -8.63409792605681863505840070063
y[1] (numeric) = -8.6340979260568186350584007006243
absolute error = 5.7e-30
relative error = 6.6017319340309852541377005920046e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.312
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 47.98
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = -8.611668812882613075165528293054
y[1] (numeric) = -8.6116688128826130751655282930479
absolute error = 6.1e-30
relative error = 7.0834122079505822696140734961645e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.323
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.01
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = -8.589225817456246513825791926996
y[1] (numeric) = -8.5892258174562465138257919269906
absolute error = 5.4e-30
relative error = 6.2869461285152753303440533358734e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.335
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.05
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = -8.566768941812716038232316490927
y[1] (numeric) = -8.5667689418127160382323164909209
absolute error = 6.1e-30
relative error = 7.1205375578966516830049075245343e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.346
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.09
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
bytes used=236067396, alloc=4652204, time=8.03
x[1] = 4.56
y[1] (analytic) = -8.544298187977056829164378900933
y[1] (numeric) = -8.5442981879770568291643789009274
absolute error = 5.6e-30
relative error = 6.5540783769460798855575151619887e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.357
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.12
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = -8.521813557964380912141964627051
y[1] (numeric) = -8.5218135579643809121419646270449
absolute error = 6.1e-30
relative error = 7.1581007475797401174996125686465e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.368
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.16
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = -8.499315053779915698287003761827
y[1] (numeric) = -8.4993150537799156982870037618214
absolute error = 5.6e-30
relative error = 6.5887662294733996355235973692491e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.379
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.2
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = -8.476802677419042316344662145933
y[1] (numeric) = -8.4768026774190423163446621459271
absolute error = 5.9e-30
relative error = 6.9601714520461042498534273605624e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.391
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.23
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = -8.454276430867333737305849326105
y[1] (numeric) = -8.4542764308673337373058493260984
absolute error = 6.6e-30
relative error = 7.8067000221364876395193412797702e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.402
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.27
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = -8.431736316100592693060012260162
y[1] (numeric) = -8.4317363161005926930600122601564
absolute error = 5.6e-30
relative error = 6.6415739179446021700563833880988e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.413
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.31
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = -8.409182335084889390495310325596
y[1] (numeric) = -8.4091823350848893904953103255899
absolute error = 6.1e-30
relative error = 7.2539751868020607579945248267554e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.424
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.35
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = -8.386614489776599022451411973336
y[1] (numeric) = -8.3866144897765990224514119733302
absolute error = 5.8e-30
relative error = 6.9157822945960870707824776900912e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.435
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.38
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
bytes used=240068288, alloc=4652204, time=8.17
x[1] = 4.64
y[1] (analytic) = -8.364032782122439076918414955431
y[1] (numeric) = -8.3640327821224390769184149554254
absolute error = 5.6e-30
relative error = 6.6953348293536410225698499512486e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.447
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.42
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = -8.341437214059506445863769120124
y[1] (numeric) = -8.3414372140595064458637691201179
absolute error = 6.1e-30
relative error = 7.3128884668920599752100592956086e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.458
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.46
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = -8.318827787515314335057572003108
y[1] (numeric) = -8.3188277875153143350575720031024
absolute error = 5.6e-30
relative error = 6.7317176686892568059558133075283e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.469
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.49
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = -8.296204504407828976255211558975
y[1] (numeric) = -8.2962045044078289762552115589686
absolute error = 6.4e-30
relative error = 7.7143710676365766627964203246915e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.48
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.53
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = -8.27356736664550614308504609801
y[1] (numeric) = -8.2735673666455061430850460980048
absolute error = 5.2e-30
relative error = 6.2850760374098759478325018903494e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.492
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.57
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = -8.250916376127327471977637562894
y[1] (numeric) = -8.2509163761273274719776375628878
absolute error = 6.2e-30
relative error = 7.5143168556873059055139289360603e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.503
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.6
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = -8.22825153474283658946198945559
y[1] (numeric) = -8.2282515347428365894619894555847
absolute error = 5.3e-30
relative error = 6.4412226311037836764246739533538e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.514
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.64
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = -8.205572844372175047143283781113
y[1] (numeric) = -8.2055728443721750471432837811071
absolute error = 5.9e-30
relative error = 7.1902353582133374107897500012609e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.525
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.68
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = -8.182880306886118065665761101242
y[1] (numeric) = -8.1828803068861180656657611012363
absolute error = 5.7e-30
relative error = 6.9657624042273889387230082067863e-29 %
Correct digits = 31
h = 0.01
bytes used=244069028, alloc=4652204, time=8.31
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.536
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.71
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = -8.160173924146110088953642992979
y[1] (numeric) = -8.1601739241461100889536429929732
absolute error = 5.8e-30
relative error = 7.1076916422549395825714591629657e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.548
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.75
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = -8.137453698004300150012355703407
y[1] (numeric) = -8.1374536980043001500123557034007
absolute error = 6.3e-30
relative error = 7.7419795353736596249208305301305e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.559
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.79
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = -8.11471963030357704956177641994
y[1] (numeric) = -8.1147196303035770495617764199346
absolute error = 5.4e-30
relative error = 6.6545737203713868970576276805878e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.57
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.82
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = -8.091971722877604348762788182366
y[1] (numeric) = -8.0919717228776043487627881823604
absolute error = 5.6e-30
relative error = 6.9204394080712028815623358230384e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.581
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.86
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = -8.06920997755085517728809491489
y[1] (numeric) = -8.0692099775508551772880949148841
absolute error = 5.9e-30
relative error = 7.3117442927055320822712156281067e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.592
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.89
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = -8.046434396138646857978013231254
y[1] (numeric) = -8.0464343961386468579780132312479
absolute error = 6.1e-30
relative error = 7.5809976191781180713378620614771e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.604
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.93
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = -8.023644980447175349311821456469
y[1] (numeric) = -8.0236449804471753493118214564625
absolute error = 6.5e-30
relative error = 8.1010563351691823363209144292600e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.615
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 48.97
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = -8.000841732273549506915207621472
y[1] (numeric) = -8.0008417322735495069152076214661
absolute error = 5.9e-30
relative error = 7.3742241096968101644371087107145e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.626
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49
Order of pole (six term test) = -2.482
bytes used=248072684, alloc=4652204, time=8.45
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = -7.978024653405825165314415942346
y[1] (numeric) = -7.9780246534058251653144159423405
absolute error = 5.5e-30
relative error = 6.8939370820971900102739285924719e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.637
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.04
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = -7.955193745623039041137844427405
y[1] (numeric) = -7.9551937456230390411378444273996
absolute error = 5.4e-30
relative error = 6.7880182088224929390389103310044e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.648
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.08
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = -7.932349010695242458956093710668
y[1] (numeric) = -7.9323490106952424589560937106621
absolute error = 5.9e-30
relative error = 7.4378976417262883083988868509714e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.66
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.11
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = -7.909490450383534900941807949211
y[1] (numeric) = -7.9094904503835349009418079492049
absolute error = 6.1e-30
relative error = 7.7122540804183007004235921270276e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.671
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.15
Order of pole (six term test) = -2.482
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = -7.886618066440097381521081617922
y[1] (numeric) = -7.8866180664400973815210816179165
absolute error = 5.5e-30
relative error = 6.9738384104133732468268778853112e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.682
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.19
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = -7.863731860608225648178730274245
y[1] (numeric) = -7.8637318606082256481787302742392
absolute error = 5.8e-30
relative error = 7.3756329727542300576889384392705e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.693
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.22
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = -7.840831834622363209570337846248
y[1] (numeric) = -7.8408318346223632095703378462422
absolute error = 5.8e-30
relative error = 7.3971743334543081899338248481015e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.704
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.26
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = -7.817917990208134192084696730848
y[1] (numeric) = -7.8179179902081341920846967308424
absolute error = 5.6e-30
relative error = 7.1630324173442919468306616991165e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.716
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.29
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
bytes used=252073860, alloc=4652204, time=8.59
x[1] = 4.89
y[1] (analytic) = -7.794990329082376025991048998504
y[1] (numeric) = -7.7949903290823760259910489984984
absolute error = 5.6e-30
relative error = 7.1841012799040000305104034359715e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.727
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.33
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = -7.772048852953171962296416321637
y[1] (numeric) = -7.7720488529531719622964163216314
absolute error = 5.6e-30
relative error = 7.2053072567501282019907293146601e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.738
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.37
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = -7.749093563519883421429271923696
y[1] (numeric) = -7.7490935635198834214292719236901
absolute error = 5.9e-30
relative error = 7.6137937316632854888044855109159e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.749
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.4
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = -7.726124462473182174856858943236
y[1] (numeric) = -7.7261244624731821748568589432304
absolute error = 5.6e-30
relative error = 7.2481358890863686032532955035631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.761
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.44
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = -7.703141551495082360734595193296
y[1] (numeric) = -7.7031415514950823607345951932904
absolute error = 5.6e-30
relative error = 7.2697612559295509998135697275929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.772
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.47
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = -7.680144832258972334677223452798
y[1] (numeric) = -7.6801448322589723346772234527926
absolute error = 5.4e-30
relative error = 7.0311174046071863336364770518209e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.783
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.51
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = -7.65713430642964635673266824707
y[1] (numeric) = -7.6571343064296463567326682470648
absolute error = 5.2e-30
relative error = 6.7910523596714158372875726335768e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.794
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.55
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = -7.634109975663336115630943663337
y[1] (numeric) = -7.6341099756633361156309436633318
absolute error = 5.2e-30
relative error = 6.8115340446718759072264251921323e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.805
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.58
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
bytes used=256074636, alloc=4652204, time=8.73
x[1] = 4.97
y[1] (analytic) = -7.611071841607742091371921219651
y[1] (numeric) = -7.6110718416077420913719212196453
absolute error = 5.7e-30
relative error = 7.4890897348249803416992184373010e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.817
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.62
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = -7.588019905902064757207311288482
y[1] (numeric) = -7.5880199059020647572073112884759
absolute error = 6.1e-30
relative error = 8.0389878725217066172919042717118e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.828
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.65
Order of pole (six term test) = -2.481
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = -7.564954170177035622063835206036
y[1] (numeric) = -7.5649541701770356220638352060309
absolute error = 5.1e-30
relative error = 6.7416138753430801278554811172665e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.839
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 49.69
Order of pole (six term test) = -2.481
Finished!
diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));
Iterations = 500
Total Elapsed Time = 8 Seconds
Elapsed Time(since restart) = 8 Seconds
Time to Timeout = 2 Minutes 51 Seconds
Percent Done = 100.2 %
> quit
bytes used=257522792, alloc=4652204, time=8.77