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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,
> array_const_0D3,
> #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_tmp6,
> 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_const_0D3, 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_tmp6, 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,
> array_const_0D3,
> #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_tmp6,
> 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_const_0D3, 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_tmp6, 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,
> array_const_0D3,
> #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_tmp6,
> 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_const_0D3, 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_tmp6, 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,
> array_const_0D3,
> #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_tmp6,
> 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_const_0D3, 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_tmp6, 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,
> array_const_0D3,
> #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_tmp6,
> 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_const_0D3, 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_tmp6, 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,
> array_const_0D3,
> #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_tmp6,
> 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_const_0D3, 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_tmp6, 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,
> array_const_0D3,
> #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_tmp6,
> 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_const_0D3, 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_tmp6, 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,
> array_const_0D3,
> #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_tmp6,
> 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_const_0D3, 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_tmp6, 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,
> array_const_0D3,
> #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_tmp6,
> 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 mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D2[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp2[1] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[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 mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D2[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp2[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp6[2] := array_tmp5[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_tmp6[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 div LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp5[3] := - array_tmp5[2] * array_tmp4[2] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp6[3] := array_tmp5[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_tmp6[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 div LINEAR - LINEAR $eq_no = 1 i = 4
> array_tmp5[4] := - array_tmp5[3] * array_tmp4[2] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp6[4] := array_tmp5[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_tmp6[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 div LINEAR - LINEAR $eq_no = 1 i = 5
> array_tmp5[5] := - array_tmp5[4] * array_tmp4[2] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp6[5] := array_tmp5[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_tmp6[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 div LINEAR - LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp5[kkk] := - array_tmp5[kkk-1] * array_tmp4[2] / array_tmp4[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp6[kkk] := array_tmp5[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_tmp6[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_const_0D3, 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_tmp6, 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] := array_const_0D2[1]*array_x[1];
array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
array_tmp5[1] := array_tmp2[1]/array_tmp4[1];
array_tmp6[1] := array_const_0D0[1] + array_tmp5[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp6[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_const_0D2[1]*array_x[2];
array_tmp4[2] := array_tmp3[2];
array_tmp5[2] :=
(array_tmp2[2] - array_tmp5[1]*array_tmp4[2])/array_tmp4[1];
array_tmp6[2] := array_tmp5[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp6[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_tmp5[3] := -array_tmp5[2]*array_tmp4[2]/array_tmp4[1];
array_tmp6[3] := array_tmp5[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp6[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_tmp5[4] := -array_tmp5[3]*array_tmp4[2]/array_tmp4[1];
array_tmp6[4] := array_tmp5[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp6[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_tmp5[5] := -array_tmp5[4]*array_tmp4[2]/array_tmp4[1];
array_tmp6[5] := array_tmp5[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp6[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_tmp5[kkk] := -array_tmp5[kkk - 1]*array_tmp4[2]/array_tmp4[1]
;
array_tmp6[kkk] := array_tmp5[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_tmp6[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(0.5 * x + 0.25 * ln(2.0 * x + 3.0));
> end;
exact_soln_y := proc(x) return 0.5*x + 0.25*ln(2.0*x + 3.0) 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,
> array_const_0D3,
> #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_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_estimated_step_error := 0.0;
> glob_ratio_of_radius := 0.1;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_min_h := 0.000001;
> glob_type_given_pole := 0;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/div_lin_linpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"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(0.5 * x + 0.25 * ln(2.0 * x + 3.0));");
> 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_tmp6:= 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_tmp6[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_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp6[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_const_0D3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D3[1] := 0.3;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> 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 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3);");
> 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,"2013-05-26T00:40:59-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div_lin_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 7
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 7;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"div_lin_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"div_lin_lin 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_const_0D3, 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_tmp6, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_estimated_step_error := 0.;
glob_ratio_of_radius := 0.1;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_min_h := 0.1*10^(-5);
glob_type_given_pole := 0;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/div_lin_linpostode.ode#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3);");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "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(0.5 * x + 0.25 * ln(2.0 * x + 3.0));");
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_tmp6 := 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_tmp6[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_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[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_const_0D3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D3[term] := 0.; term := term + 1
end do;
array_const_0D3[1] := 0.3;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_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 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3);");
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, "2013-05-26T00:40:59-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"div_lin_lin");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3);");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 189 | ");
logitem_str(html_log_file, "div_lin_lin diffeq.mxt");
logitem_str(html_log_file, "div_lin_lin maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 13
> main();
##############ECHO OF PROBLEM#################
##############temp/div_lin_linpostode.ode#################
diff ( y , x , 1 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3);
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
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(0.5 * x + 0.25 * ln(2.0 * x + 3.0));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 4.9
estimated_steps = 4900000
step_error = 2.0408163265306122448979591836735e-17
est_needed_step_err = 2.0408163265306122448979591836735e-17
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.7407492057234676055014965036775e-164
estimated_step_error = 4.7407492057234676055014965036775e-164
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 = 3.1814619796659393518965782980853e-156
estimated_step_error = 3.1814619796659393518965782980853e-156
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 = 2.1350417081676936089437054185800e-148
estimated_step_error = 2.1350417081676936089437054185800e-148
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 = 1.4328005116123364579522323453140e-140
estimated_step_error = 1.4328005116123364579522323453140e-140
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 = 9.6153383193115333740333740333740e-133
estimated_step_error = 9.6153383193115333740333740333740e-133
best_h = 3.200000e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.4527132473775338640618640618641e-125
estimated_step_error = 6.4527132473775338640618640618641e-125
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 = 4.3303008587023443693323607000407e-117
estimated_step_error = 4.3303008587023443693323607000407e-117
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 = 2.9059597485076374855879028705766e-109
estimated_step_error = 2.9059597485076374855879028705766e-109
best_h = 0.000256
opt_iter = 9
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.9500814641776246482632346567236e-101
estimated_step_error = 1.9500814641776246482632346567236e-101
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 = 1.3085767166128052496726511189314e-93
estimated_step_error = 1.3085767166128052496726511189314e-93
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 = 8.7803570749745855131913529711279e-86
estimated_step_error = 8.7803570749745855131913529711279e-86
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 = 5.8905832785142122818834638418350e-78
estimated_step_error = 5.8905832785142122818834638418350e-78
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 = 3.9506702500394078436792474344815e-70
estimated_step_error = 3.9506702500394078436792474344815e-70
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 = 2.6479901017012872052715572005662e-62
estimated_step_error = 2.6479901017012872052715572005662e-62
best_h = 0.016384
opt_iter = 15
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.7726770762436426728249964978565e-54
estimated_step_error = 1.7726770762436426728249964978565e-54
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 = 1.1838165484769530903693972449166e-46
estimated_step_error = 1.1838165484769530903693972449166e-46
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 = 7.8676912272283018707615583109045e-39
estimated_step_error = 7.8676912272283018707615583109045e-39
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 = 5.1800284532005515817208636174860e-31
estimated_step_error = 5.1800284532005515817208636174860e-31
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 0.34078770245142021576704228815162
y[1] (numeric) = 0.34078770245142021576704228815162
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 = 1.673
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 0.3473453398890792343233386968357
y[1] (numeric) = 0.3473453398890792343233386968357
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 = 1.683
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 0.35389333245105950409486557030942
y[1] (numeric) = 0.35389333245105950409486557030943
absolute error = 1e-32
relative error = 2.8257102022070214012302967369336e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.694
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 0.36043179884465406886154539455255
y[1] (numeric) = 0.36043179884465406886154539455255
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 = 1.704
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 = 1.047
Order of pole (six term test) = -3.166e-27
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 0.3669608555990130910206192070108
y[1] (numeric) = 0.3669608555990130910206192070108
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 = 1.715
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 = 1.404
Order of pole (six term test) = -8.146e-27
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 0.37348061711810863785979934005082
y[1] (numeric) = 0.37348061711810863785979934005082
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 = 1.725
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.062
Order of pole (six term test) = -1.062e-26
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 0.37999119573209929356848838920975
y[1] (numeric) = 0.37999119573209929356848838920975
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 = 1.735
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 0.38649270174715226216024999720855
y[1] (numeric) = 0.38649270174715226216024999720856
absolute error = 1e-32
relative error = 2.5873709787519115921874269106848e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.746
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.162
Order of pole (six term test) = 3.455e-27
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 0.39298524349377821653338588920742
y[1] (numeric) = 0.39298524349377821653338588920742
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 = 1.756
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 0.39946892737373185337205602380502
y[1] (numeric) = 0.39946892737373185337205602380502
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 = 1.767
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=4003068, alloc=3079628, time=0.14
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 0.40594385790552892641219382116172
y[1] (numeric) = 0.40594385790552892641219382116173
absolute error = 1e-32
relative error = 2.4633948279437191387841917574601e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.777
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 0.4124101377686284460451917794556
y[1] (numeric) = 0.41241013776862844604519177945558
absolute error = 2e-32
relative error = 4.8495413105534420906762168276315e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.788
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 0.4188678678463267459221389920879
y[1] (numeric) = 0.4188678678463267459221389920879
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 = 1.798
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 0.4253171472674082220786874001326
y[1] (numeric) = 0.4253171472674082220786874001326
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 = 1.809
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.646
Order of pole (six term test) = -2.808e-27
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 0.43175807344659574234424965070802
y[1] (numeric) = 0.43175807344659574234424965070801
absolute error = 1e-32
relative error = 2.3161118725986955637178216314360e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.819
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 0.43819074212384199892203015549625
y[1] (numeric) = 0.43819074212384199892203015549625
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 = 1.83
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 = 1.396
Order of pole (six term test) = -7.980e-27
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 0.44461524740250143077803031897182
y[1] (numeric) = 0.44461524740250143077803031897182
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 = 1.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.983
Order of pole (six term test) = -1.179e-25
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 0.45103168178642077084813620568292
y[1] (numeric) = 0.45103168178642077084813620568292
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 = 1.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 0.45744013621598477227907421855438
y[1] (numeric) = 0.45744013621598477227907421855437
absolute error = 1e-32
relative error = 2.1860783976503547452147589299265e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.861
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 0.4638407001031522343897634105277
y[1] (numeric) = 0.46384070010315223438976341052771
absolute error = 1e-32
relative error = 2.1559125789901852086894597478469e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.871
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.796
Order of pole (six term test) = -3.901e-27
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 0.47023346136551607940174081551925
y[1] (numeric) = 0.47023346136551607940174081551926
absolute error = 1e-32
relative error = 2.1266032346913150087644878271472e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.882
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6294
Order of pole (six term test) = 2.867e-27
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 0.47661850645941992205508406268062
y[1] (numeric) = 0.47661850645941992205508406268061
absolute error = 1e-32
relative error = 2.0981140816972066798514009691799e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.892
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 0.48299592041216232298933037963902
y[1] (numeric) = 0.48299592041216232298933037963903
absolute error = 1e-32
relative error = 2.0704108621593628565434977312802e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.903
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 0.4893657868533187203819708881094
y[1] (numeric) = 0.4893657868533187203819708881094
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 = 1.913
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 0.49572818804520989010992460206855
y[1] (numeric) = 0.49572818804520989010992460206855
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 = 1.924
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 0.50208320491254469008752605408678
y[1] (numeric) = 0.50208320491254469008752605408678
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 = 1.934
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 0.50843091707126379703072272375312
y[1] (numeric) = 0.50843091707126379703072272375314
absolute error = 2e-32
relative error = 3.9336710905007211861212108129718e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.945
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 0.51477140285661014142318185198192
y[1] (numeric) = 0.51477140285661014142318185198194
absolute error = 2e-32
relative error = 3.8852197089843025033213154176709e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.955
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 0.5211047393504507867591660311945
y[1] (numeric) = 0.52110473935045078675916603119451
absolute error = 1e-32
relative error = 1.9190000099528646518817614099232e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.965
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 0.52743100240787408016808441657505
y[1] (numeric) = 0.52743100240787408016808441657507
absolute error = 2e-32
relative error = 3.7919651876158688280363539421421e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.976
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 0.53375026668308502135206702466542
y[1] (numeric) = 0.53375026668308502135206702466544
absolute error = 2e-32
relative error = 3.7470707273435478010699995302763e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.986
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 0.54006260565462095355779979107295
y[1] (numeric) = 0.54006260565462095355779979107298
absolute error = 3e-32
relative error = 5.5549115391235771847778622305831e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.997
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5393
Order of pole (six term test) = -2.529e-27
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 0.54636809164990887231997179444025
y[1] (numeric) = 0.54636809164990887231997179444028
absolute error = 3e-32
relative error = 5.4908038112926288861049250958147e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.007
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 9.613
Order of pole (six term test) = 1.581e-25
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 0.55266679586918487330904506636812
y[1] (numeric) = 0.55266679586918487330904506636815
absolute error = 3e-32
relative error = 5.4282255102405211400273579316052e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.018
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 = 6.261
Order of pole (six term test) = 6.686e-26
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 0.5589587884087955182288007388129
y[1] (numeric) = 0.55895878840879551822880073881292
absolute error = 2e-32
relative error = 3.5780813209744121459764458918722e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.028
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 0.56524413828390018585768530595088
y[1] (numeric) = 0.56524413828390018585768530595089
absolute error = 1e-32
relative error = 1.7691470503984931615200439965113e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.039
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 0.57152291345059279260660473547305
y[1] (numeric) = 0.57152291345059279260660473547306
absolute error = 1e-32
relative error = 1.7497111252503585587977925632239e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.049
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 0.57779518082746061204026163531308
y[1] (numeric) = 0.57779518082746061204026163531309
absolute error = 1e-32
relative error = 1.7307171004228518639002146698151e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.06
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 0.58406100631659729441272884633945
y[1] (numeric) = 0.58406100631659729441272884633947
absolute error = 2e-32
relative error = 3.4242998220563896728948177702420e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.07
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=8005576, alloc=4193536, time=0.30
x[1] = 0.49
y[1] (analytic) = 0.5903204548240865841978426259895
y[1] (numeric) = 0.59032045482408658419784262598952
absolute error = 2e-32
relative error = 3.3879903426283830091513267441893e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 0.5965735902799726547086160607291
y[1] (numeric) = 0.59657359027997265470861606072911
absolute error = 1e-32
relative error = 1.6762391367856208300264360231415e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.091
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.216
Order of pole (six term test) = -3.644e-27
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 0.60282047565773242311164161134392
y[1] (numeric) = 0.60282047565773242311164161134395
absolute error = 3e-32
relative error = 4.9766060065008987501166309917037e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.101
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 0.60906117299326467542066990011515
y[1] (numeric) = 0.60906117299326467542066990011518
absolute error = 3e-32
relative error = 4.9256136050445225251328557688846e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.112
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.475
Order of pole (six term test) = 8.417e-27
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 0.61529574340341031841746849697362
y[1] (numeric) = 0.61529574340341031841746849697366
absolute error = 4e-32
relative error = 6.5009388458867562653823423154804e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.122
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 0.62152424710401758296512332745038
y[1] (numeric) = 0.62152424710401758296512332745039
absolute error = 1e-32
relative error = 1.6089476873339764497493446905842e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.133
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 0.62774674342756552996219297958825
y[1] (numeric) = 0.62774674342756552996219297958829
absolute error = 4e-32
relative error = 6.3719964171531416053603039035536e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.143
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 0.63396329084035875539177091215028
y[1] (numeric) = 0.6339632908403587553917709121503
absolute error = 2e-32
relative error = 3.1547567956953351440991746565250e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.154
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = 0.64017394695930575374462312943618
y[1] (numeric) = 0.64017394695930575374462312943621
absolute error = 3e-32
relative error = 4.6862263205951779351288234318185e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.164
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 0.64637876856829297877591628487188
y[1] (numeric) = 0.6463787685682929787759162848719
absolute error = 2e-32
relative error = 3.0941610356879946406539382358060e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.175
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 0.6525778116341662363630550554856
y[1] (numeric) = 0.65257781163416623636305505548564
absolute error = 4e-32
relative error = 6.1295372424375220387568735460120e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.185
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 0.65877113132233065547495966178488
y[1] (numeric) = 0.65877113132233065547495966178491
absolute error = 3e-32
relative error = 4.5539336157281117903949325532478e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.195
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 = 2.067
Order of pole (six term test) = 6.361e-27
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 0.66495878201198010928080136938592
y[1] (numeric) = 0.66495878201198010928080136938596
absolute error = 4e-32
relative error = 6.0154104407751617987513698675692e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.206
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 0.67114081731096659859004564850872
y[1] (numeric) = 0.67114081731096659859004564850874
absolute error = 2e-32
relative error = 2.9800005429759450427737599831856e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.216
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 0.67731729007031976352648724538125
y[1] (numeric) = 0.67731729007031976352648724538128
absolute error = 3e-32
relative error = 4.4292387688619863478921018268307e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.227
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 0.68348825239842635602572003764272
y[1] (numeric) = 0.68348825239842635602572003764275
absolute error = 3e-32
relative error = 4.3892488122110511272701889128574e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.237
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 0.68965375567487918486371276466538
y[1] (numeric) = 0.6896537556748791848637127646654
absolute error = 2e-32
relative error = 2.9000059573993711429446236799289e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.248
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 0.6958138505640047359546703218079
y[1] (numeric) = 0.69581385056400473595467032180792
absolute error = 2e-32
relative error = 2.8743319759715377221164928910393e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.258
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 0.70196858702807837310394157001875
y[1] (numeric) = 0.70196858702807837310394157001878
absolute error = 3e-32
relative error = 4.2736955120756729572562748155751e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.269
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 0.7081180143402357377939494464392
y[1] (numeric) = 0.70811801434023573779394944643924
absolute error = 4e-32
relative error = 5.6487759370545889705660330568625e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.279
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 0.71426218109708869046715082661262
y[1] (numeric) = 0.71426218109708869046715082661266
absolute error = 4e-32
relative error = 5.6001845062776541152345779376886e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.29
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 = 2.292
Order of pole (six term test) = 5.752e-27
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 0.72040113523105386971960409154928
y[1] (numeric) = 0.72040113523105386971960409154931
absolute error = 3e-32
relative error = 4.1643465748257206855079960431021e-30 %
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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 0.72653492402240168942106781788198
y[1] (numeric) = 0.726534924022401689421067817882
absolute error = 2e-32
relative error = 2.7527926516280348747249361740974e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.31
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 0.7326635941110333466404555603754
y[1] (numeric) = 0.73266359411103334664045556037543
absolute error = 3e-32
relative error = 4.0946486547349279873566936148135e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.321
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 0.73878719150799317500433860545315
y[1] (numeric) = 0.73878719150799317500433860545318
absolute error = 3e-32
relative error = 4.0607092739067093587151380967360e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.331
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5657
Order of pole (six term test) = -1.361e-27
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 0.74490576160672344839319064070588
y[1] (numeric) = 0.74490576160672344839319064070591
absolute error = 3e-32
relative error = 4.0273550758006679458428823462824e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.342
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6084
Order of pole (six term test) = 1.586e-27
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 0.75101934919406851834331458809672
y[1] (numeric) = 0.75101934919406851834331458809675
absolute error = 3e-32
relative error = 3.9945708498980091573418283071803e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.352
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 0.7571279984610349548451532067909
y[1] (numeric) = 0.75712799846103495484515320679094
absolute error = 4e-32
relative error = 5.2831225474827782486520417271191e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.363
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 0.76323175301331415409865769723072
y[1] (numeric) = 0.76323175301331415409865769723076
absolute error = 4e-32
relative error = 5.2408720997359005597514238742346e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.373
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 = 2.089
Order of pole (six term test) = 1.520e-27
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 0.76933065588157367790499653095405
y[1] (numeric) = 0.76933065588157367790499653095407
absolute error = 2e-32
relative error = 2.5996624269550340912358694513258e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.384
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=12009424, alloc=4259060, time=0.46
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 0.77542474953152339745562120400552
y[1] (numeric) = 0.77542474953152339745562120400554
absolute error = 2e-32
relative error = 2.5792315775429010314959340222649e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.394
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6812
Order of pole (six term test) = 3.98e-28
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 0.781514075873762329051498374646
y[1] (numeric) = 0.78151407587376232905149837464603
absolute error = 3e-32
relative error = 3.8387024528584292026406808547207e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.405
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 0.78759867627341187048594769260508
y[1] (numeric) = 0.7875986762734118704859476926051
absolute error = 2e-32
relative error = 2.5393643491926180478265748927874e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.415
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 = 12.04
Order of pole (six term test) = -2.103e-25
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 0.79367859155954097420405440220648
y[1] (numeric) = 0.7936785915595409742040544022065
absolute error = 2e-32
relative error = 2.5199117391715132335675392416954e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.425
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 0.79975386203438862667086852168958
y[1] (numeric) = 0.79975386203438862667086852168961
absolute error = 3e-32
relative error = 3.7511541268068336769699175253971e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.436
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.902
Order of pole (six term test) = 2.986e-27
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = 0.8058245274823888424106148122395
y[1] (numeric) = 0.80582452748238884241061481223952
absolute error = 2e-32
relative error = 2.4819299137599279128880018845199e-30 %
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 = 0.6744
Order of pole (six term test) = 1.474e-27
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 0.81189062717900322570073980377195
y[1] (numeric) = 0.81189062717900322570073980377197
absolute error = 2e-32
relative error = 2.4633859944278503917885359842963e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 0.81795219989936600270794095718138
y[1] (numeric) = 0.81795219989936600270794095718139
absolute error = 1e-32
relative error = 1.2225653285400193751684531000922e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.467
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 0.82400928392674628173735999762335
y[1] (numeric) = 0.82400928392674628173735999762336
absolute error = 1e-32
relative error = 1.2135785597397457743992551498532e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.478
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 0.83006191706083215903834217371598
y[1] (numeric) = 0.830061917060832159038342173716
absolute error = 2e-32
relative error = 2.4094588113159122542827073684582e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.488
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.42
Order of pole (six term test) = -2.029e-27
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 0.83611013662584115208610320158785
y[1] (numeric) = 0.83611013662584115208610320158786
absolute error = 1e-32
relative error = 1.1960146829884679126609723883001e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.499
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 0.84215397947846131126154556701772
y[1] (numeric) = 0.84215397947846131126154556701774
absolute error = 2e-32
relative error = 2.3748626127000940290771849127565e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.509
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 = 0.9678
Order of pole (six term test) = -5.084e-27
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 0.84819348201562723421191513270008
y[1] (numeric) = 0.84819348201562723421191513270009
absolute error = 1e-32
relative error = 1.1789762845425589599981858058940e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 0.85422868018213508473059212236948
y[1] (numeric) = 0.85422868018213508473059212236949
absolute error = 1e-32
relative error = 1.1706467169737079783067037764185e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.53
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 0.86025960947810059958936884917552
y[1] (numeric) = 0.86025960947810059958936884917554
absolute error = 2e-32
relative error = 2.3248795804947221212525776444570e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.54
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 0.86628630496626395224177563960785
y[1] (numeric) = 0.86628630496626395224177563960787
absolute error = 2e-32
relative error = 2.3087055498099864347827446403781e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.551
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.568
Order of pole (six term test) = 8.743e-27
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 0.8723088012791452315481785080505
y[1] (numeric) = 0.87230880127914523154817850805051
absolute error = 1e-32
relative error = 1.1463830223122931047828947128783e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.561
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 0.8783271326260541865151224858769
y[1] (numeric) = 0.8783271326260541865151224858769
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 = 2.572
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 0.88434133279995778436094102138565
y[1] (numeric) = 0.88434133279995778436094102138567
absolute error = 2e-32
relative error = 2.2615701944719681133861804866640e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.582
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 0.89035143518420902889052747525158
y[1] (numeric) = 0.8903514351842090288905274752516
absolute error = 2e-32
relative error = 2.2463040109394674245141682726475e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.593
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 0.89635747275914038906299166807582
y[1] (numeric) = 0.89635747275914038906299166807585
absolute error = 3e-32
relative error = 3.3468789976899405771304854119383e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 0.90235947810852509365018983330655
y[1] (numeric) = 0.90235947810852509365018983330656
absolute error = 1e-32
relative error = 1.1082057918825692909187366939040e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 0.90835748342590945689995861277442
y[1] (numeric) = 0.90835748342590945689995861277444
absolute error = 2e-32
relative error = 2.2017763231904180195703648003241e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.624
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 0.9143515205208193120278891680735
y[1] (numeric) = 0.91435152052081931202788916807352
absolute error = 2e-32
relative error = 2.1873425647728892606266627244246e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.635
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 0.9203416208248435440624864054662
y[1] (numeric) = 0.92034162082484354406248640546621
absolute error = 1e-32
relative error = 1.0865530552706762594074716735526e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.645
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6713
Order of pole (six term test) = 1.943e-27
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 0.92632781539759763096148053531598
y[1] (numeric) = 0.926327815397597630961480535316
absolute error = 2e-32
relative error = 2.1590628789890776562906825758024e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.655
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 0.93231013493257002190669710002782
y[1] (numeric) = 0.93231013493257002190669710002784
absolute error = 2e-32
relative error = 2.1452089010537801235032318747228e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.666
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 0.93828860976285410417977654593872
y[1] (numeric) = 0.93828860976285410417977654593873
absolute error = 1e-32
relative error = 1.0657701581315614807351976226532e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.676
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 0.94426326986676843493326088171268
y[1] (numeric) = 0.94426326986676843493326088171269
absolute error = 1e-32
relative error = 1.0590266845189221249979317462959e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.687
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.627
Order of pole (six term test) = 3.263e-27
TOP MAIN SOLVE Loop
x[1] = 1.08
bytes used=16010516, alloc=4324584, time=0.62
y[1] (analytic) = 0.950234144873367841416642270954
y[1] (numeric) = 0.95023414487336784141664227095401
absolute error = 1e-32
relative error = 1.0523722025725187592000081834323e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.697
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 0.95620126406784792271367440664102
y[1] (numeric) = 0.95620126406784792271367440664103
absolute error = 1e-32
relative error = 1.0458049341472574205407006512569e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.708
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 0.96216465639684541771749005744932
y[1] (numeric) = 0.96216465639684541771749005744934
absolute error = 2e-32
relative error = 2.0786462968715603517565623256559e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.718
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 0.9681243504736368378387529295741
y[1] (numeric) = 0.96812435047363683783875292957412
absolute error = 2e-32
relative error = 2.0658503207997373339573982310033e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.729
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 = 1.224
Order of pole (six term test) = -2.443e-27
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 0.9740803745832376987369763361793
y[1] (numeric) = 0.9740803745832376987369763361793
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 = 2.739
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 0.98003275668740462311679386907362
y[1] (numeric) = 0.98003275668740462311679386907364
absolute error = 2e-32
relative error = 2.0407481141346466502462141990842e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.75
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 0.9859815244295425262725335978379
y[1] (numeric) = 0.98598152442954252627253359783792
absolute error = 2e-32
relative error = 2.0284355745480486903399145358290e-30 %
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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 0.99192670513951903753161942108618
y[1] (numeric) = 0.99192670513951903753161942108619
absolute error = 1e-32
relative error = 1.0081390034350828537705830541644e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.77
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 0.99786832583838825397821537721968
y[1] (numeric) = 0.99786832583838825397821537721968
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 = 2.781
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 1.0038064132430258677735774974204
y[1] (numeric) = 1.0038064132430258677735774974205
absolute error = 1e-31
relative error = 9.9620802059758875171807955765695e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.791
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 = 0.4492
Order of pole (six term test) = -7.49e-28
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 1.0097409937706776549714463628424
y[1] (numeric) = 1.0097409937706776549714463628424
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 = 2.802
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 1.0156720935434232619003005981462
y[1] (numeric) = 1.0156720935434232619003005981462
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 = 2.812
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 = 0.348
Order of pole (six term test) = 3.1e-29
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 1.0215997383925571748962440943854
y[1] (numeric) = 1.0215997383925571748962440943854
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 = 2.823
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 1.0275239538628887103695298213238
y[1] (numeric) = 1.0275239538628887103695298213239
absolute error = 1e-31
relative error = 9.7321332144188488046522967114178e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.833
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 1.0334447652169628148249280789488
y[1] (numeric) = 1.0334447652169628148249280789489
absolute error = 1e-31
relative error = 9.6763758805247673315731629999004e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.844
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.794
Order of pole (six term test) = 1.367e-27
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 1.0393621974392034184838336585051
y[1] (numeric) = 1.0393621974392034184838336585052
absolute error = 1e-31
relative error = 9.6212850771734376480289968134818e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.854
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 1.0452762752399810415284178653819
y[1] (numeric) = 1.045276275239981041528417865382
absolute error = 1e-31
relative error = 9.5668487239932214849813665290801e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.865
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 1.0511870230596063086611778641268
y[1] (numeric) = 1.0511870230596063086611778641269
absolute error = 1e-31
relative error = 9.5130550326751530925354596514975e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.875
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 1.0570944650722509856044278809346
y[1] (numeric) = 1.0570944650722509856044278809348
absolute error = 2e-31
relative error = 1.8919784996351321247897887802019e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.885
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.79
Order of pole (six term test) = 3.92e-28
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 1.0629986251897981103126616904035
y[1] (numeric) = 1.0629986251897981103126616904037
absolute error = 2e-31
relative error = 1.8814699780471499232246381032766e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.896
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 1.0688995270656227519968165631058
y[1] (numeric) = 1.068899527065622751996816563106
absolute error = 2e-31
relative error = 1.8710832490406877764319613021822e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.906
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = 1.0747971940983048925252260026192
y[1] (numeric) = 1.0747971940983048925252260026194
absolute error = 2e-31
relative error = 1.8608161716293731468736714708383e-29 %
Correct digits = 31
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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 1.0806916494352758873347644132833
y[1] (numeric) = 1.0806916494352758873347644132835
absolute error = 2e-31
relative error = 1.8506666550492141626261358662071e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.927
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 12.94
Order of pole (six term test) = 1.988e-26
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 1.0865829159763999266219718841956
y[1] (numeric) = 1.0865829159763999266219718841958
absolute error = 2e-31
relative error = 1.8406326572904069713664157057734e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.938
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = 1.0924710163774918822536693100606
y[1] (numeric) = 1.0924710163774918822536693100607
absolute error = 1e-31
relative error = 9.1535609184020723343279761657729e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.948
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 1.0983559730537728915068090897212
y[1] (numeric) = 1.0983559730537728915068090897213
absolute error = 1e-31
relative error = 9.1045164275811916815767300452804e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.959
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = 1.1042378081832649953862919968797
y[1] (numeric) = 1.1042378081832649953862919968799
absolute error = 2e-31
relative error = 1.8112040587439021074803349256298e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.969
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 = 2.103
Order of pole (six term test) = 7.4e-29
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 1.1101165437101261168465703035315
y[1] (numeric) = 1.1101165437101261168465703035317
absolute error = 2e-31
relative error = 1.8016126426832536716729691056677e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.98
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 = 3.985
Order of pole (six term test) = -1.196e-27
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 1.1159922013479266327284780882695
y[1] (numeric) = 1.1159922013479266327284780882697
absolute error = 2e-31
relative error = 1.7921272187962819028187430255575e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.99
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.36
Order of pole (six term test) = -3.051e-27
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 1.1218648025828687625883413321425
y[1] (numeric) = 1.1218648025828687625883413321427
absolute error = 2e-31
relative error = 1.7827460094972237478532192950933e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=20013416, alloc=4324584, time=0.78
x[1] = 1.38
y[1] (analytic) = 1.1277343686769499678144750733064
y[1] (numeric) = 1.1277343686769499678144750733065
absolute error = 1e-31
relative error = 8.8673363850140788824169235159778e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.011
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 1.1336009206710715254700796119589
y[1] (numeric) = 1.1336009206710715254700796119591
absolute error = 2e-31
relative error = 1.7642893222211178808557261902332e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.021
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 = 2.18
Order of pole (six term test) = 6.85e-28
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 1.1394644793880934131456281747839
y[1] (numeric) = 1.1394644793880934131456281747841
absolute error = 2e-31
relative error = 1.7552104836774068255976290902569e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.032
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 = 3.278
Order of pole (six term test) = -5.025e-27
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 1.145325065435836613723304017679
y[1] (numeric) = 1.1453250654358366137233040176792
absolute error = 2e-31
relative error = 1.7462291364757038704758110904521e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.042
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 1.1511826992100339223269555781111
y[1] (numeric) = 1.1511826992100339223269555781113
absolute error = 2e-31
relative error = 1.7373436912945639136011817990168e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.053
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.032
Order of pole (six term test) = -3.666e-27
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 1.1570374008972303118302723687255
y[1] (numeric) = 1.1570374008972303118302723687257
absolute error = 2e-31
relative error = 1.7285525934158137131906915485998e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.063
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 1.1628891904776338881011080143391
y[1] (numeric) = 1.1628891904776338881011080143393
absolute error = 2e-31
relative error = 1.7198543217849839100476494923805e-29 %
Correct digits = 31
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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 1.1687380877279184416495147297588
y[1] (numeric) = 1.168738087727918441649514729759
absolute error = 2e-31
relative error = 1.7112473881022339507070582265968e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.084
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 1.1745841122239785785002603118738
y[1] (numeric) = 1.174584112223978578500260311874
absolute error = 2e-31
relative error = 1.7027303359426207527199219474176e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.095
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 17.4
Order of pole (six term test) = 6.752e-26
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 1.1804272833436383899072321252056
y[1] (numeric) = 1.1804272833436383899072321252057
absolute error = 1e-31
relative error = 8.4715086995230560004014979434351e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.105
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 1.1862676202693145979477274021629
y[1] (numeric) = 1.1862676202693145979477274021631
absolute error = 2e-31
relative error = 1.6859602047857854413089754886117e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.115
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 1.1921051419906350920603723713662
y[1] (numeric) = 1.1921051419906350920603723713664
absolute error = 2e-31
relative error = 1.6777043647847226104206506107820e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.126
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 1.1979398673070137502031193395952
y[1] (numeric) = 1.1979398673070137502031193395953
absolute error = 1e-31
relative error = 8.3476644136405155993786640302541e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.136
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 1.2037718148301824174898611172196
y[1] (numeric) = 1.2037718148301824174898611172197
absolute error = 1e-31
relative error = 8.3072222466105109790212539127577e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.147
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = 1.209601002986680894898679408258
y[1] (numeric) = 1.2096010029866808948986794082581
absolute error = 1e-31
relative error = 8.2671889121359397202923870492432e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.157
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 1.2154274500203057709151731789812
y[1] (numeric) = 1.2154274500203057709151731789813
absolute error = 1e-31
relative error = 8.2275581317773702489481034000085e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.168
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 1.2212511739945189097648012824525
y[1] (numeric) = 1.2212511739945189097648012824526
absolute error = 1e-31
relative error = 8.1883237559490615821355829363650e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.178
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 1.2270721927948163911833494121853
y[1] (numeric) = 1.2270721927948163911833494121854
absolute error = 1e-31
relative error = 8.1494797606192186503749621141635e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.189
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = 1.2328905241310586784596266063164
y[1] (numeric) = 1.2328905241310586784596266063165
absolute error = 1e-31
relative error = 8.1110202441112933769677476218318e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.199
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 1.238706185539762773744927944843
y[1] (numeric) = 1.238706185539762773744927944843
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 = 3.21
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.308
Order of pole (six term test) = 4.468e-27
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 1.2445191943863571023457524441035
y[1] (numeric) = 1.2445191943863571023457524441035
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 = 3.22
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 1.2503295678673998508862741910164
y[1] (numeric) = 1.2503295678673998508862741910163
absolute error = 1e-31
relative error = 7.9978913216107527754162168215920e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.23
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 1.256137323012761467832101247829
y[1] (numeric) = 1.256137323012761467832101247829
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 = 3.241
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = 1.2619424766877720188943111943805
y[1] (numeric) = 1.2619424766877720188943111943805
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 = 3.251
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 1.267745045595334074270419563738
y[1] (numeric) = 1.2677450455953340742704195637379
absolute error = 1e-31
relative error = 7.8880213610331974164442555069228e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.262
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 = 5.074
Order of pole (six term test) = 1.462e-26
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 1.2735450462780017895150036303367
y[1] (numeric) = 1.2735450462780017895150036303366
absolute error = 1e-31
relative error = 7.8520975989231737124223358371772e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.272
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 1.2793424951200268270557316424878
y[1] (numeric) = 1.2793424951200268270557316424877
absolute error = 1e-31
relative error = 7.8165151537953161537535763373133e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.283
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 = 6.199
Order of pole (six term test) = -6.907e-27
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 1.285137408349371750969462940651
y[1] (numeric) = 1.2851374083493717509694629406509
absolute error = 1e-31
relative error = 7.7812690962314937073911964270714e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.293
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 1.2909298020396915135971647491218
y[1] (numeric) = 1.2909298020396915135971647491217
absolute error = 1e-31
relative error = 7.7463545920156357668335491724963e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.304
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = 1.296719692112283638895252845347
y[1] (numeric) = 1.2967196921122836388952528453469
absolute error = 1e-31
relative error = 7.7117668998382842096718884234597e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.314
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 = 0.8465
Order of pole (six term test) = 1.478e-27
TOP MAIN SOLVE Loop
bytes used=24014788, alloc=4324584, time=0.94
x[1] = 1.68
y[1] (analytic) = 1.3025070943380076940845489273748
y[1] (numeric) = 1.3025070943380076940845489273747
absolute error = 1e-31
relative error = 7.6775013690673576215551690607465e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.325
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 1.3082920243391746281566162056041
y[1] (numeric) = 1.308292024339174628156616205604
absolute error = 1e-31
relative error = 7.6435534375829081757152037514961e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.335
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 = 5.501
Order of pole (six term test) = -6.763e-27
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 1.3140744975914065431213503185162
y[1] (numeric) = 1.3140744975914065431213503185161
absolute error = 1e-31
relative error = 7.6099186296737363207421659101440e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.345
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 = 12.19
Order of pole (six term test) = -1.344e-26
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 1.3198545294254674515202233165088
y[1] (numeric) = 1.3198545294254674515202233165087
absolute error = 1e-31
relative error = 7.5765925539938094759874509671796e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.356
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 1.3256321350290655616776467272002
y[1] (numeric) = 1.3256321350290655616776467272001
absolute error = 1e-31
relative error = 7.5435709015765085346927915731025e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.366
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 13.97
Order of pole (six term test) = -1.014e-25
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 1.3314073294486276204099528154626
y[1] (numeric) = 1.3314073294486276204099528154625
absolute error = 1e-31
relative error = 7.5108494439048002917547196876594e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.377
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 1.337180127591045831449173600674
y[1] (numeric) = 1.3371801275910458314491736006739
absolute error = 1e-31
relative error = 7.4784240310355050996410294755231e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.387
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 1.3429505442253978566590638300268
y[1] (numeric) = 1.3429505442253978566590638300267
absolute error = 1e-31
relative error = 7.4462905897758972582120317022877e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.398
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.077
Order of pole (six term test) = -7.416e-27
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 1.3487185939846403962158534249171
y[1] (numeric) = 1.348718593984640396215853424917
absolute error = 1e-31
relative error = 7.4144451219109410004559115640175e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.408
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 1.3544842913672768332884527253053
y[1] (numeric) = 1.3544842913672768332884527253052
absolute error = 1e-31
relative error = 7.3828837024795275777889342382201e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.419
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 1.3602476507389994183749272373754
y[1] (numeric) = 1.3602476507389994183749272373753
absolute error = 1e-31
relative error = 7.3516024780981390003223321315668e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.429
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = 1.3660086863343064583268881563262
y[1] (numeric) = 1.3660086863343064583268881563262
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 = 3.44
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 = 4.028
Order of pole (six term test) = 6.829e-27
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 1.3717674122580949652141073704154
y[1] (numeric) = 1.3717674122580949652141073704154
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 = 3.45
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 1.3775238424872292105414665129165
y[1] (numeric) = 1.3775238424872292105414665129166
absolute error = 1e-31
relative error = 7.2594024811535763314249625655753e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.46
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 1.3832779908720856209227964195743
y[1] (numeric) = 1.3832779908720856209227964195744
absolute error = 1e-31
relative error = 7.2292048785475972004106778404511e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.471
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 = 2.176
Order of pole (six term test) = -5.030e-27
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 1.3890298711380744421349588392415
y[1] (numeric) = 1.3890298711380744421349588392416
absolute error = 1e-31
relative error = 7.1992692221994446355325591494237e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.481
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = 1.3947794968871385895145580275731
y[1] (numeric) = 1.3947794968871385895145580275732
absolute error = 1e-31
relative error = 7.1695920554596238605193608290231e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.492
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = 1.4005268815992300939130201354198
y[1] (numeric) = 1.4005268815992300939130201354199
absolute error = 1e-31
relative error = 7.1401699827290892752913326446964e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.502
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 = 5.057
Order of pole (six term test) = -4.855e-27
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 1.406272038633764543887693919572
y[1] (numeric) = 1.406272038633764543887693919572
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 = 3.513
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 = 1.615
Order of pole (six term test) = 1.61e-28
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 1.4120149812310539164715289416845
y[1] (numeric) = 1.4120149812310539164715289416845
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 = 3.523
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 1.4177557225137181807263640541696
y[1] (numeric) = 1.4177557225137181807263640541696
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 = 3.534
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 1.423494275488076050339656485657
y[1] (numeric) = 1.423494275488076050339656485657
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 = 3.544
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = 1.4292306530455152537665018515263
y[1] (numeric) = 1.4292306530455152537665018515263
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 = 3.555
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.662
Order of pole (six term test) = -2.522e-26
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 1.4349648679638426828430892786492
y[1] (numeric) = 1.4349648679638426828430892786493
absolute error = 1e-31
relative error = 6.9688117272094591348751481868423e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.565
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 1.4406969329086147733994998098201
y[1] (numeric) = 1.4406969329086147733994998098202
absolute error = 1e-31
relative error = 6.9410850898467989129737412584237e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.575
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.974
Order of pole (six term test) = 2.985e-27
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = 1.4464268604344484641743268606048
y[1] (numeric) = 1.4464268604344484641743268606048
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 = 3.586
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 1.4521546629863130732764470224524
y[1] (numeric) = 1.4521546629863130732764470224525
absolute error = 1e-31
relative error = 6.8863188301412027633472301191541e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.596
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 1.4578803529008034245460016535121
y[1] (numeric) = 1.4578803529008034245460016535121
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 = 3.607
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.832
Order of pole (six term test) = 8.481e-27
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 1.4636039424073945494329954304972
y[1] (numeric) = 1.4636039424073945494329954304972
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 = 3.617
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 1.4693254436296782834337315146188
y[1] (numeric) = 1.4693254436296782834337315146189
absolute error = 1e-31
relative error = 6.8058441670328495955849863842779e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.628
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=28018140, alloc=4390108, time=1.10
x[1] = 1.98
y[1] (analytic) = 1.4750448685865820696985576810726
y[1] (numeric) = 1.4750448685865820696985576810726
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 = 3.638
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 1.480762229193570276145182683647
y[1] (numeric) = 1.4807622291935702761451826836471
absolute error = 1e-31
relative error = 6.7532786850229456926907690681143e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.649
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 1.4864775372638283262763381858608
y[1] (numeric) = 1.4864775372638283262763381858609
absolute error = 1e-31
relative error = 6.7273132282961260857869012582847e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.659
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 1.4921908045094299379051180911056
y[1] (numeric) = 1.4921908045094299379051180911057
absolute error = 1e-31
relative error = 6.7015558397624509316317520328385e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.67
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 1.4979020425424877581323383493364
y[1] (numeric) = 1.4979020425424877581323383493365
absolute error = 1e-31
relative error = 6.6760039815596630094994781532304e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.68
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 1.5036112628762876771942423323194
y[1] (numeric) = 1.5036112628762876771942423323195
absolute error = 1e-31
relative error = 6.6506551572850036556874470593172e-30 %
Correct digits = 32
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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 1.5093184769264070982024442360474
y[1] (numeric) = 1.5093184769264070982024442360476
absolute error = 2e-31
relative error = 1.3251013822296949564834853243578e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.701
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 1.5150236960118174343278657694572
y[1] (numeric) = 1.5150236960118174343278657694573
absolute error = 1e-31
relative error = 6.6005568271468133876421207351880e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.711
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 1.5207269313559710996333822489189
y[1] (numeric) = 1.520726931355971099633382248919
absolute error = 1e-31
relative error = 6.5758025282575891615114501035241e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.722
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 = 0.7387
Order of pole (six term test) = 3.101e-27
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 1.5264281940878732545328454525821
y[1] (numeric) = 1.5264281940878732545328454525822
absolute error = 1e-31
relative error = 6.5512416756528548978892692872356e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.732
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.276
Order of pole (six term test) = -1.124e-26
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 1.5321274952431385617440714408922
y[1] (numeric) = 1.5321274952431385617440714408924
absolute error = 2e-31
relative error = 1.3053743935863595655959904955905e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.743
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 = 8.124
Order of pole (six term test) = -2.544e-26
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 1.5378248457650332036073355244235
y[1] (numeric) = 1.5378248457650332036073355244237
absolute error = 2e-31
relative error = 1.3005382280743715471461614643730e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.753
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.19
Order of pole (six term test) = -3.289e-27
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 1.5435202565055024067560488458838
y[1] (numeric) = 1.543520256505502406756048845884
absolute error = 2e-31
relative error = 1.2957393928395589635792777697174e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.764
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 1.5492137382261837153498260189663
y[1] (numeric) = 1.5492137382261837153498260189665
absolute error = 2e-31
relative error = 1.2909774491736413481979234928314e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.774
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 1.5549053015994062494093920930452
y[1] (numeric) = 1.5549053015994062494093920930454
absolute error = 2e-31
relative error = 1.2862519652758020494384897970271e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.785
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 1.5605949572091761802250954012356
y[1] (numeric) = 1.5605949572091761802250954012358
absolute error = 2e-31
relative error = 1.2815625161166835989968214806421e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.795
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.192
Order of pole (six term test) = -2.536e-27
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 1.5662827155521486503436384100036
y[1] (numeric) = 1.5662827155521486503436384100038
absolute error = 2e-31
relative error = 1.2769086833055912220168664758971e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.805
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 1.5719685870385863612685293506886
y[1] (numeric) = 1.5719685870385863612685293506888
absolute error = 2e-31
relative error = 1.2722900549608164379311002566014e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.816
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 1.577652581993305047736278918474
y[1] (numeric) = 1.5776525819933050477362789184742
absolute error = 2e-31
relative error = 1.2677062255829954535989851937162e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.826
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 1.583334710656606053250170287812
y[1] (numeric) = 1.5833347106566060532501702878122
absolute error = 2e-31
relative error = 1.2631567959314197069470799060201e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.837
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 13.06
Order of pole (six term test) = 2.758e-26
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 1.5890149831851962174642326324331
y[1] (numeric) = 1.5890149831851962174642326324333
absolute error = 2e-31
relative error = 1.2586413729032184831163012589229e-29 %
Correct digits = 31
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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 1.594693409653095282009625764743
y[1] (numeric) = 1.5946934096530952820096257647432
absolute error = 2e-31
relative error = 1.2541595694153359997536807497715e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.858
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 1.6003700000525310174418340844513
y[1] (numeric) = 1.6003700000525310174418340844515
absolute error = 2e-31
relative error = 1.2497110042892277469812796958813e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.868
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 1.6060447642948222701577677736404
y[1] (numeric) = 1.6060447642948222701577677736406
absolute error = 2e-31
relative error = 1.2452953021382031740223721554814e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.879
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 1.6117177122112501243850307541177
y[1] (numeric) = 1.6117177122112501243850307541178
absolute error = 1e-31
relative error = 6.2045604662867202080748033258492e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.889
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.315
Order of pole (six term test) = 3.480e-27
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 1.6173888535539173706792459542978
y[1] (numeric) = 1.6173888535539173706792459542979
absolute error = 1e-31
relative error = 6.1828050675796495510680775829393e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 1.6230581979965964687774898823465
y[1] (numeric) = 1.6230581979965964687774898823466
absolute error = 1e-31
relative error = 6.1612085212615215573252715739532e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.91
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 1.6287257551355661891446931121726
y[1] (numeric) = 1.6287257551355661891446931121728
absolute error = 2e-31
relative error = 1.2279538121711171573131189126578e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.92
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 1.634391534490437114113474061559
y[1] (numeric) = 1.6343915344904371141134740615592
absolute error = 2e-31
relative error = 1.2236969892428808800023890656539e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.931
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 1.6400555455049661761545021715042
y[1] (numeric) = 1.6400555455049661761545021715043
absolute error = 1e-31
relative error = 6.0973544630288983487725163103295e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.941
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=32018904, alloc=4390108, time=1.26
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 1.6457177975478604075223924469396
y[1] (numeric) = 1.6457177975478604075223924469397
absolute error = 1e-31
relative error = 6.0763759223483649371526918616330e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.952
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 1.6513782999135700722996214489358
y[1] (numeric) = 1.6513782999135700722996214489359
absolute error = 1e-31
relative error = 6.0555476601111813970485175420553e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.962
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 1.65703706182307134870637505503
y[1] (numeric) = 1.6570370618230713487063750550301
absolute error = 1e-31
relative error = 6.0348680366859175672836252476348e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.973
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 1.6626940924246387264559838141821
y[1] (numeric) = 1.6626940924246387264559838141822
absolute error = 1e-31
relative error = 6.0143354364225889483694744608933e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.983
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 1.6683494007946072809121078214375
y[1] (numeric) = 1.6683494007946072809121078214376
absolute error = 1e-31
relative error = 5.9939482672137893090388683586508e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.994
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 1.6740029959381249828435759373105
y[1] (numeric) = 1.6740029959381249828435759373106
absolute error = 1e-31
relative error = 5.9737049600654496659523691905957e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 1.6796548867898951996742798248048
y[1] (numeric) = 1.6796548867898951996742798248049
absolute error = 1e-31
relative error = 5.9536039686769778517349032211422e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.015
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2033
Order of pole (six term test) = -5.50e-28
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 1.685305082214909541287326216681
y[1] (numeric) = 1.6853050822149095412873262166811
absolute error = 1e-31
relative error = 5.9336437690305400381123666546558e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.025
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 1.6909535910091712006633530967327
y[1] (numeric) = 1.6909535910091712006633530967328
absolute error = 1e-31
relative error = 5.9138228589892524991673086434461e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.035
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 1.6966004219004089369111455498201
y[1] (numeric) = 1.6966004219004089369111455498202
absolute error = 1e-31
relative error = 5.8941397579040585930515278362747e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.046
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 1.7022455835487818455831087691774
y[1] (numeric) = 1.7022455835487818455831087691776
absolute error = 2e-31
relative error = 1.1749186012458144833960760465772e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.056
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 1.7078890845475750585574673614304
y[1] (numeric) = 1.7078890845475750585574673614306
absolute error = 2e-31
relative error = 1.1710362330290353715535604194841e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.067
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 1.7135309334238865132119933363154
y[1] (numeric) = 1.7135309334238865132119933363156
absolute error = 2e-31
relative error = 1.1671805632383339652031202204607e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.077
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 1.7191711386393049281093841654432
y[1] (numeric) = 1.7191711386393049281093841654434
absolute error = 2e-31
relative error = 1.1633513121811516667051393334640e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.088
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 1.7248097085905791199609127658376
y[1] (numeric) = 1.7248097085905791199609127658378
absolute error = 2e-31
relative error = 1.1595482040939411514919090248976e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.098
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 1.7304466516102787942314796150454
y[1] (numeric) = 1.7304466516102787942314796150456
absolute error = 2e-31
relative error = 1.1557709670730886275712664799003e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.109
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 1.7360819759674469393945696656776
y[1] (numeric) = 1.7360819759674469393945696656778
absolute error = 2e-31
relative error = 1.1520193330072921367429793599178e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.119
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 1.7417156898682439525387385216992
y[1] (numeric) = 1.7417156898682439525387385216994
absolute error = 2e-31
relative error = 1.1482930375113601646143423539394e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.13
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = 1.747347801456583621767036876704
y[1] (numeric) = 1.7473478014565836217670368767041
absolute error = 1e-31
relative error = 5.7229590993069791302606276064996e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.14
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.292
Order of pole (six term test) = 3.399e-27
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 1.7529783188147610886161703105666
y[1] (numeric) = 1.7529783188147610886161703105667
absolute error = 1e-31
relative error = 5.7045771146566643044853931801098e-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 = 5.148
Order of pole (six term test) = 9.56e-28
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 1.758607249964072911552150656354
y[1] (numeric) = 1.7586072499640729115521506563542
absolute error = 2e-31
relative error = 1.1372635931307906126845143300686e-29 %
Correct digits = 31
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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 1.7642346028654293494727186560858
y[1] (numeric) = 1.7642346028654293494727186560859
absolute error = 1e-31
relative error = 5.6681804017210803590420183377313e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.171
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 1.7698603854199589820629240910936
y[1] (numeric) = 1.7698603854199589820629240910938
absolute error = 2e-31
relative error = 1.1300326378712819450454536902240e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.182
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 1.7754846054696057818079820748597
y[1] (numeric) = 1.7754846054696057818079820748599
absolute error = 2e-31
relative error = 1.1264530223685105665901683643854e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.192
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 1.7811072707977187504659496417085
y[1] (numeric) = 1.7811072707977187504659496417087
absolute error = 2e-31
relative error = 1.1228969937920942926757012950891e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.203
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 1.7867283891296342308409752445493
y[1] (numeric) = 1.7867283891296342308409752445495
absolute error = 2e-31
relative error = 1.1193643153418838233670781088003e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.213
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 1.7923479681332510027749779304797
y[1] (numeric) = 1.7923479681332510027749779304799
absolute error = 2e-31
relative error = 1.1158547534065166720781284879416e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.224
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 1.7979660154195982703907473732514
y[1] (numeric) = 1.7979660154195982703907473732516
absolute error = 2e-31
relative error = 1.1123680775096587566139654608871e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.234
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 1.8035825385433966457717765273382
y[1] (numeric) = 1.8035825385433966457717765273383
absolute error = 1e-31
relative error = 5.5445203012866640793942455724374e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.245
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 1.8091975450036122324528221152715
y[1] (numeric) = 1.8091975450036122324528221152716
absolute error = 1e-31
relative error = 5.5273123864315403229340808870299e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.255
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=36021888, alloc=4390108, time=1.43
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 1.8148110422440039103194313578149
y[1] (numeric) = 1.814811042244003910319431357815
absolute error = 1e-31
relative error = 5.5102155360676309255653164574399e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.265
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.923
Order of pole (six term test) = -1.025e-27
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 1.8204230376536639217736928553044
y[1] (numeric) = 1.8204230376536639217736928553046
absolute error = 2e-31
relative error = 1.0986457315865394217438782816956e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.276
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 1.8260335385675518573165010099528
y[1] (numeric) = 1.8260335385675518573165010099529
absolute error = 1e-31
relative error = 5.4763506741746859435588770281991e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.286
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 1.831642552267022137022921144248
y[1] (numeric) = 1.8316425522670221370229211442481
absolute error = 1e-31
relative error = 5.4595805211136911510251421240389e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.297
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 1.8372500859803450827460789425148
y[1] (numeric) = 1.837250085980345082746078942515
absolute error = 2e-31
relative error = 1.0885834298017259786574001043336e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 1.8428561468832216742756630823131
y[1] (numeric) = 1.8428561468832216742756630823133
absolute error = 2e-31
relative error = 1.0852719043657053476716594548197e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 1.8484607420992920810989311598007
y[1] (numeric) = 1.8484607420992920810989311598009
absolute error = 2e-31
relative error = 1.0819813234056597685042295408403e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.328
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 = 7.984
Order of pole (six term test) = 1.360e-26
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 1.8540638787006380598643701921518
y[1] (numeric) = 1.8540638787006380598643701921519
absolute error = 1e-31
relative error = 5.3935574253289391735565997326425e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.339
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 1.8596655637082793061302243152364
y[1] (numeric) = 1.8596655637082793061302243152366
absolute error = 2e-31
relative error = 1.0754621901003994588818428712668e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.349
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 1.8652658040926638474913198419719
y[1] (numeric) = 1.8652658040926638474913198419721
absolute error = 2e-31
relative error = 1.0722332418316519688921441971943e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.36
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.867
Order of pole (six term test) = 4.492e-27
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 1.8708646067741525637173630858502
y[1] (numeric) = 1.8708646067741525637173630858504
absolute error = 2e-31
relative error = 1.0690244461081070793259075926695e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.37
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 1.8764619786234979181035457834437
y[1] (numeric) = 1.876461978623497918103545783444
absolute error = 3e-31
relative error = 1.5987534168961352506575166394780e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.38
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 1.8820579264623169828292676921494
y[1] (numeric) = 1.8820579264623169828292676921497
absolute error = 3e-31
relative error = 1.5939998221197506391773020742440e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.391
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 1.8876524570635588397424913601216
y[1] (numeric) = 1.8876524570635588397424913601219
absolute error = 3e-31
relative error = 1.5892756046135814112627800937355e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.401
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 1.8932455771519664366351093997505
y[1] (numeric) = 1.8932455771519664366351093997507
absolute error = 2e-31
relative error = 1.0563869918072781707321878134050e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.412
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 1.8988372934045329777481725889267
y[1] (numeric) = 1.8988372934045329777481725889269
absolute error = 2e-31
relative error = 1.0532761321609007759602038927543e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.422
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 1.9044276124509529259443536788732
y[1] (numeric) = 1.9044276124509529259443536788735
absolute error = 3e-31
relative error = 1.5752764664754422119099251788796e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.433
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 1.9100165408740676927080756241038
y[1] (numeric) = 1.910016540874067692708075624104
absolute error = 2e-31
relative error = 1.0471113507136193688004974774634e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.443
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 1.9156040852103060908807952757458
y[1] (numeric) = 1.9156040852103060908807952757461
absolute error = 3e-31
relative error = 1.5660856140169708692866150640918e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.454
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 1.9211902519501196238094977647396
y[1] (numeric) = 1.9211902519501196238094977647399
absolute error = 3e-31
relative error = 1.5615319705868931309393144374909e-29 %
Correct digits = 31
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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 1.9267750475384126833800280680073
y[1] (numeric) = 1.9267750475384126833800280680076
absolute error = 3e-31
relative error = 1.5570058392819160834990047736092e-29 %
Correct digits = 31
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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 1.9323584783749677282229813671356
y[1] (numeric) = 1.9323584783749677282229813671359
absolute error = 3e-31
relative error = 1.5525069667833444253995700618783e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.485
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 1.9379405508148655122180207950299
y[1] (numeric) = 1.9379405508148655122180207950302
absolute error = 3e-31
relative error = 1.5480351029026971869398765234126e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.495
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 9.839
Order of pole (six term test) = 3.707e-26
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 1.9435212711689004322822290046036
y[1] (numeric) = 1.9435212711689004322822290046039
absolute error = 3e-31
relative error = 1.5435900005332573391955465434554e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.506
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 1.9491006457039910633089783521724
y[1] (numeric) = 1.9491006457039910633089783521727
absolute error = 3e-31
relative error = 1.5391714156025211712529065873178e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.516
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = 1.9546786806435859470253834465155
y[1] (numeric) = 1.9546786806435859470253834465158
absolute error = 3e-31
relative error = 1.5347791070255279680700273694694e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.527
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 1.9602553821680647004582496003833
y[1] (numeric) = 1.9602553821680647004582496003836
absolute error = 3e-31
relative error = 1.5304128366590510016665963783589e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.537
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 1.96583075641513450864013145365
y[1] (numeric) = 1.9658307564151345086401314536503
absolute error = 3e-31
relative error = 1.5260723692566313154372924609087e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.548
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 = 10.33
Order of pole (six term test) = 5.699e-26
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 1.9714048094802220651482574768038
y[1] (numeric) = 1.971404809480222065148257476804
absolute error = 2e-31
relative error = 1.0145049816162908237204314510796e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.558
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 1.9769775474168610230492573689469
y[1] (numeric) = 1.9769775474168610230492573689471
absolute error = 2e-31
relative error = 1.0116452777186166568877412595000e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.569
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=40024128, alloc=4390108, time=1.60
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = 1.9825489762370750178214588569772
y[1] (numeric) = 1.9825489762370750178214588569774
absolute error = 2e-31
relative error = 1.0088023165995361381749975945816e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.579
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 1.988119101911756322843615335458
y[1] (numeric) = 1.9881191019117563228436153354583
absolute error = 3e-31
relative error = 1.5089639232957566167421404008566e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.59
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = 1.9936879303710401970739121219138
y[1] (numeric) = 1.9936879303710401970739121219141
absolute error = 3e-31
relative error = 1.5047490403584264160733667668086e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 1.9992554675046749835956112932052
y[1] (numeric) = 1.9992554675046749835956112932055
absolute error = 3e-31
relative error = 1.5005586073221454942083411567080e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = 2.0048217191623880167753758482465
y[1] (numeric) = 2.0048217191623880167753758482468
absolute error = 3e-31
relative error = 1.4963924080258848216034054021003e-29 %
Correct digits = 31
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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 2.0103866911542473948668141174837
y[1] (numeric) = 2.010386691154247394866814117484
absolute error = 3e-31
relative error = 1.4922502288739158240412323563080e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.631
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = 2.01595038925101967399476359074
y[1] (numeric) = 2.0159503892510196739947635907403
absolute error = 3e-31
relative error = 1.4881318587976668834301299338206e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.642
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 2.0215128191845235385749560214964
y[1] (numeric) = 2.0215128191845235385749560214967
absolute error = 3e-31
relative error = 1.4840370892182604679891316898303e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.652
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 2.0270739866479795023586466358177
y[1] (numeric) = 2.027073986647979502358646635818
absolute error = 3e-31
relative error = 1.4799657140097167391344168726161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.663
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = 2.032633897296355693442230681029
y[1] (numeric) = 2.0326338972963556934422306810293
absolute error = 3e-31
relative error = 1.4759175294628098180793572903989e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.673
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 2.0381925567467097757474986710704
y[1] (numeric) = 2.0381925567467097757474986710707
absolute error = 3e-31
relative error = 1.4718923342495632219196694430974e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.684
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 = 3.515
Order of pole (six term test) = -5.193e-27
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 2.0437499705785270586586927507289
y[1] (numeric) = 2.0437499705785270586586927507292
absolute error = 3e-31
relative error = 1.4678899293883712970604860039430e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.694
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = 2.0493061443340548456976226184613
y[1] (numeric) = 2.0493061443340548456976226184616
absolute error = 3e-31
relative error = 1.4639101182097337875088412813859e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.705
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = 2.054861083518633072327489040773
y[1] (numeric) = 2.0548610835186330723274890407733
absolute error = 3e-31
relative error = 1.4599527063225909770500443640966e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.715
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = 2.0604147936010212821994612371554
y[1] (numeric) = 2.0604147936010212821994612371558
absolute error = 4e-31
relative error = 1.9413566687749961838515964397479e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.725
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = 2.0659672800137219903931826871241
y[1] (numeric) = 2.0659672800137219903931826871245
absolute error = 4e-31
relative error = 1.9361390854038270722613879783748e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.736
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 8.832
Order of pole (six term test) = 1.005e-26
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = 2.0715185481533004814529657275953
y[1] (numeric) = 2.0715185481533004814529657275957
absolute error = 4e-31
relative error = 1.9309506079807422231850831254802e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.746
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.124
Order of pole (six term test) = -1.103e-27
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = 2.077068603380701089285212182581
y[1] (numeric) = 2.0770686033807010892852121825815
absolute error = 5e-31
relative error = 2.4072387362949136018127797739653e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.757
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = 2.0826174510215600052593045613186
y[1] (numeric) = 2.0826174510215600052593045613191
absolute error = 5e-31
relative error = 2.4008249799056534462922659644767e-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 = 5.053
Order of pole (six term test) = 6.401e-27
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = 2.0881650963665146601435951483107
y[1] (numeric) = 2.0881650963665146601435951483112
absolute error = 5e-31
relative error = 2.3944466884827195606658101122635e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = 2.09371154467150972480992923437
y[1] (numeric) = 2.0937115446715097248099292343705
absolute error = 5e-31
relative error = 2.3881035631316962512309781600939e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.788
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = 2.0992568011580997739541298851826
y[1] (numeric) = 2.099256801158099773954129885183
absolute error = 4e-31
relative error = 1.9054362466723055099522827870689e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.799
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = 2.1048008710137486564058064050106
y[1] (numeric) = 2.104800871013748656405806405011
absolute error = 4e-31
relative error = 1.9004173055446592008933172249845e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.809
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = 2.110343759392125614938493601341
y[1] (numeric) = 2.1103437593921256149384936013414
absolute error = 4e-31
relative error = 1.8954257960097367218405853359354e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.82
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = 2.1158854714133981978402557229696
y[1] (numeric) = 2.11588547141339819784025572297
absolute error = 4e-31
relative error = 1.8904614895474588884941944307717e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.83
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = 2.121426012164522003865274098337
y[1] (numeric) = 2.1214260121645220038652740983374
absolute error = 4e-31
relative error = 1.8855241601938978142540621612861e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = 2.126965386699527301558362432571
y[1] (numeric) = 2.1269653866995273015583624325714
absolute error = 4e-31
relative error = 1.8806135845054412436765951635596e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.851
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = 2.1325036000398025633266045266951
y[1] (numeric) = 2.1325036000398025633266045266955
absolute error = 4e-31
relative error = 1.8757295415235599865528600413775e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.861
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 = 1.519
Order of pole (six term test) = -7.157e-27
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = 2.1380406571743749540251765520541
y[1] (numeric) = 2.1380406571743749540251765520545
absolute error = 4e-31
relative error = 1.8708718127401666214743243443607e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.872
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = 2.1435765630601878132276951252059
y[1] (numeric) = 2.1435765630601878132276951252063
absolute error = 4e-31
relative error = 1.8660401820635539025748270465216e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.882
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
bytes used=44025624, alloc=4390108, time=1.77
Radius of convergence (six term test) for eq 1 = 10.39
Order of pole (six term test) = -2.553e-26
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = 2.149111322622375169764922842604
y[1] (numeric) = 2.1491113226223751697649228426044
absolute error = 4e-31
relative error = 1.8612344357849015613049994940008e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.893
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = 2.1546449407545333265391684879741
y[1] (numeric) = 2.1546449407545333265391684879744
absolute error = 3e-31
relative error = 1.3923407719090053350949714092681e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.903
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.846
Order of pole (six term test) = 1.324e-27
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = 2.1601774223189895530550478341365
y[1] (numeric) = 2.1601774223189895530550478341368
absolute error = 3e-31
relative error = 1.3887748149776723953168720471746e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.914
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = 2.1657087721470679225502349213538
y[1] (numeric) = 2.1657087721470679225502349213542
absolute error = 4e-31
relative error = 1.8469704013039708462096266116962e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = 2.1712389950393523300622489875459
y[1] (numeric) = 2.1712389950393523300622489875463
absolute error = 4e-31
relative error = 1.8422661020453450985895814316258e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = 2.1767680957659467272290088258501
y[1] (numeric) = 2.1767680957659467272290088258505
absolute error = 4e-31
relative error = 1.8375866532500360434322827659978e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.945
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = 2.1822960790667326090916680279879
y[1] (numeric) = 2.1822960790667326090916680279883
absolute error = 4e-31
relative error = 1.8329318548336555367287170277952e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.955
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = 2.1878229496516237876479488276074
y[1] (numeric) = 2.1878229496516237876479488276078
absolute error = 4e-31
relative error = 1.8283015088752665085168365275692e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.966
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.872
Order of pole (six term test) = 4.504e-27
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = 2.1933487122008184863926502040805
y[1] (numeric) = 2.1933487122008184863926502040809
absolute error = 4e-31
relative error = 1.8236954195880587574335133436690e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.976
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 2.1988733713650487895790522062409
y[1] (numeric) = 2.1988733713650487895790522062413
absolute error = 4e-31
relative error = 1.8191133932905019739184698623701e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.987
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = 2.2043969317658274794404112319524
y[1] (numeric) = 2.2043969317658274794404112319528
absolute error = 4e-31
relative error = 1.8145552383779669377010246903557e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.997
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 15.75
Order of pole (six term test) = -1.746e-26
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = 2.2099193979956922941244817608723
y[1] (numeric) = 2.2099193979956922941244817608727
absolute error = 4e-31
relative error = 1.8100207652948060312403622132604e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.008
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.488
Order of pole (six term test) = -9.6e-29
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = 2.2154407746184476386158535973822
y[1] (numeric) = 2.2154407746184476386158535973827
absolute error = 5e-31
relative error = 2.2568872331336055025798916785190e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.018
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = 2.2209610661694037804507080811716
y[1] (numeric) = 2.220961066169403780450708081172
absolute error = 4e-31
relative error = 1.8010221164745532935847850544857e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.029
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = 2.2264802771556135615662231630646
y[1] (numeric) = 2.2264802771556135615662231630651
absolute error = 5e-31
relative error = 2.2456969645325715576283230650365e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.039
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 11.18
Order of pole (six term test) = -2.508e-26
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = 2.2319984120561066571721500060664
y[1] (numeric) = 2.2319984120561066571721500060668
absolute error = 4e-31
relative error = 1.7921159703313670474241730946020e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.05
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = 2.237515475322121412084900152734
y[1] (numeric) = 2.2375154753221214120849001527345
absolute error = 5e-31
relative error = 2.2346214160955381074949419236462e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.06
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = 2.2430314713773342845246825417549
y[1] (numeric) = 2.2430314713773342845246825417554
absolute error = 5e-31
relative error = 2.2291261017972914109251142037748e-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 = 19.32
Order of pole (six term test) = -7.199e-26
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = 2.2485464046180869269436768795401
y[1] (numeric) = 2.2485464046180869269436768795406
absolute error = 5e-31
relative error = 2.2236588000723268887858947197556e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = 2.254060279413610933027790010835
y[1] (numeric) = 2.2540602794136109330277900108355
absolute error = 5e-31
relative error = 2.2182192932749516094233530926357e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.091
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 11.26
Order of pole (six term test) = -2.943e-26
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = 2.2595731001062502795960836699724
y[1] (numeric) = 2.2595731001062502795960836699729
absolute error = 5e-31
relative error = 2.2128073660307288127420890279616e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.102
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = 2.2650848710116814917103567037832
y[1] (numeric) = 2.2650848710116814917103567037837
absolute error = 5e-31
relative error = 2.2074228052067608414129595245216e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.112
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.92
Order of pole (six term test) = 2.303e-27
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = 2.270595596419131558902486538415
y[1] (numeric) = 2.2705955964191315589024865384156
absolute error = 6e-31
relative error = 2.6424784798589267920743624737066e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.123
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.331
Order of pole (six term test) = 3.947e-27
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = 2.2761052805915936300288598842761
y[1] (numeric) = 2.2761052805915936300288598842767
absolute error = 6e-31
relative error = 2.6360819295847820897913199126322e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.133
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = 2.2816139277660405138694305162414
y[1] (numeric) = 2.281613927766040513869430516242
absolute error = 6e-31
relative error = 2.6297174675273315334404274502138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.144
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = 2.2871215421536360122035139655811
y[1] (numeric) = 2.2871215421536360122035139655817
absolute error = 6e-31
relative error = 2.6233848483409342193261448439705e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.154
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = 2.2926281279399441117152490517502
y[1] (numeric) = 2.2926281279399441117152490517508
absolute error = 6e-31
relative error = 2.6170838291996962248202187232895e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.165
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = 2.2981336892851360607086106492814
y[1] (numeric) = 2.2981336892851360607086106492821
absolute error = 7e-31
relative error = 3.0459498647258592337080277694253e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.175
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = 2.3036382303241953562448355056161
y[1] (numeric) = 2.3036382303241953562448355056168
absolute error = 7e-31
relative error = 3.0386715708459469296003758036051e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.185
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = 2.3091417551671206669540141220114
y[1] (numeric) = 2.3091417551671206669540141220121
bytes used=48026452, alloc=4455632, time=1.93
absolute error = 7e-31
relative error = 3.0314293110573393584111729466372e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.196
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = 2.3146442678991267164172996984404
y[1] (numeric) = 2.3146442678991267164172996984411
absolute error = 7e-31
relative error = 3.0242228134492169340460979256173e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.206
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = 2.3201457725808431516665850875184
y[1] (numeric) = 2.3201457725808431516665850875192
absolute error = 8e-31
relative error = 3.4480592101336374226976726606957e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.217
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = 2.3256462732485114210044978636711
y[1] (numeric) = 2.3256462732485114210044978636718
absolute error = 7e-31
relative error = 3.0099160308769800135734328969769e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = 2.3311457739141796850090613064392
y[1] (numeric) = 2.3311457739141796850090613064399
absolute error = 7e-31
relative error = 3.0028152157324943625227558133297e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = 2.336644278565895784254266643139
y[1] (numeric) = 2.3366442785658957842542666431397
absolute error = 7e-31
relative error = 2.9957491023392813633495209624510e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.248
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 16.58
Order of pole (six term test) = 3.477e-26
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = 2.3421417911678982869500025819313
y[1] (numeric) = 2.342141791167898286950002581932
absolute error = 7e-31
relative error = 2.9887174322223600436803167483880e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.259
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = 2.347638315660805639382197198438
y[1] (numeric) = 2.3476383156608056393821971984388
absolute error = 8e-31
relative error = 3.4076799422777293856414488578238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.269
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = 2.3531338559618034417165517030572
y[1] (numeric) = 2.3531338559618034417165517030579
absolute error = 7e-31
relative error = 2.9747564008163356501564193412547e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.28
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = 2.3586284159648298714167944358308
y[1] (numeric) = 2.3586284159648298714167944358315
absolute error = 7e-31
relative error = 2.9678265353792713912855438320558e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.29
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = 2.3641219995407592762208673330356
y[1] (numeric) = 2.3641219995407592762208673330364
absolute error = 8e-31
relative error = 3.3839201198390074306848949097529e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = 2.3696146105375839583157885656805
y[1] (numeric) = 2.3696146105375839583157885656813
absolute error = 8e-31
relative error = 3.3760764153058102039146882375804e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.311
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = 2.3751062527805941710540282670373
y[1] (numeric) = 2.3751062527805941710540282670381
absolute error = 8e-31
relative error = 3.3682703629086939004779467547975e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.321
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.123
Order of pole (six term test) = -1.098e-26
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = 2.3805969300725563492610051303924
y[1] (numeric) = 2.3805969300725563492610051303932
absolute error = 8e-31
relative error = 3.3605016871781710085179785635019e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.332
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = 2.3860866461938895938946777032428
y[1] (numeric) = 2.3860866461938895938946777032436
absolute error = 8e-31
relative error = 3.3527701153522707255083210884794e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.342
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = 2.3915754049028404315340845763032
y[1] (numeric) = 2.3915754049028404315340845763041
absolute error = 9e-31
relative error = 3.7632097995110598823737270694974e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.353
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = 2.3970632099356558688940030886862
y[1] (numeric) = 2.3970632099356558688940030886871
absolute error = 9e-31
relative error = 3.7545943564173203891102863986646e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.363
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 = 12.17
Order of pole (six term test) = -2.275e-26
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = 2.4025500650067547622875689120772
y[1] (numeric) = 2.4025500650067547622875689120781
absolute error = 9e-31
relative error = 3.7460197525476733518337744807806e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.374
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = 2.4080359738088975216876527150923
y[1] (numeric) = 2.4080359738088975216876527150931
absolute error = 8e-31
relative error = 3.3222095047633546980528261016329e-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 = 1.839
Order of pole (six term test) = 5.669e-27
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = 2.4135209400133541687709503013186
y[1] (numeric) = 2.4135209400133541687709503013194
absolute error = 8e-31
relative error = 3.3146594534853032923095050378434e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = 2.4190049672700707680660358649567
y[1] (numeric) = 2.4190049672700707680660358649575
absolute error = 8e-31
relative error = 3.3071449245630411432377878364230e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.405
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.137
Order of pole (six term test) = -2.179e-27
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = 2.4244880592078342500679824370056
y[1] (numeric) = 2.4244880592078342500679824370064
absolute error = 8e-31
relative error = 3.2996656632798109654031373535299e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.415
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = 2.4299702194344356449274987093632
y[1] (numeric) = 2.4299702194344356449274987093641
absolute error = 9e-31
relative error = 3.7037490945443390940018720674485e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.426
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 = 4.144
Order of pole (six term test) = -4.932e-27
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = 2.4354514515368317450717980878139
y[1] (numeric) = 2.4354514515368317450717980878147
absolute error = 8e-31
relative error = 3.2848119370032183308859105715384e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.436
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = 2.4409317590813052148675362296518
y[1] (numeric) = 2.4409317590813052148675362296527
absolute error = 9e-31
relative error = 3.6871165965685721543657187283297e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.447
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = 2.4464111456136231651930609599386
y[1] (numeric) = 2.4464111456136231651930609599395
absolute error = 9e-31
relative error = 3.6788583211521329595143737819761e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.457
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 = 2.453
Order of pole (six term test) = -3.839e-27
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = 2.4518896146591942105478480972506
y[1] (numeric) = 2.4518896146591942105478480972515
absolute error = 9e-31
relative error = 3.6706383297973121819270405015210e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.468
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = 2.4573671697232240260912843665438
y[1] (numeric) = 2.4573671697232240260912843665447
absolute error = 9e-31
relative error = 3.6624563520207197704723533742680e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.478
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = 2.4628438142908694217708414647269
y[1] (numeric) = 2.4628438142908694217708414647278
absolute error = 9e-31
relative error = 3.6543121199065497649590718174062e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.489
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = 2.4683195518273909504711018994382
y[1] (numeric) = 2.4683195518273909504711018994391
absolute error = 9e-31
relative error = 3.6462053680760083542743682221503e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.499
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=52027780, alloc=4455632, time=2.09
x[1] = 3.77
y[1] (analytic) = 2.4737943857783040668899870386262
y[1] (numeric) = 2.4737943857783040668899870386272
absolute error = 1.0e-30
relative error = 4.0423731485079769629396098693332e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = 2.4792683195695288536268416282024
y[1] (numeric) = 2.4792683195695288536268416282034
absolute error = 1.0e-30
relative error = 4.0334480625059102160041772784768e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = 2.4847413566075383307486887189274
y[1] (numeric) = 2.4847413566075383307486887189284
absolute error = 1.0e-30
relative error = 4.0245637532484178829596373666118e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = 2.4902135002795053648859274514507
y[1] (numeric) = 2.4902135002795053648859274514517
absolute error = 1.0e-30
relative error = 4.0157199368156926037790078274436e-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 = 1.176
Order of pole (six term test) = 7.310e-27
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = 2.4956847539534481936969475149136
y[1] (numeric) = 2.4956847539534481936969475149145
absolute error = 9e-31
relative error = 3.6062246987497028535605983697621e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.551
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.244
Order of pole (six term test) = -1.235e-26
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = 2.5011551209783745813325234075842
y[1] (numeric) = 2.5011551209783745813325234075852
absolute error = 1.0e-30
relative error = 3.9981526599950782201680480088486e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.562
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.469
Order of pole (six term test) = -6.220e-27
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = 2.506624604684424620325375006673
y[1] (numeric) = 2.506624604684424620325375006674
absolute error = 1.0e-30
relative error = 3.9894286449242627853749959211586e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.572
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 = 7.867
Order of pole (six term test) = -1.538e-27
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = 2.512093208383012195127885527785
y[1] (numeric) = 2.512093208383012195127885527786
absolute error = 1.0e-30
relative error = 3.9807440132513293659772594328663e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.583
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = 2.5175609353669651223216018405847
y[1] (numeric) = 2.5175609353669651223216018405857
absolute error = 1.0e-30
relative error = 3.9720984940300475349824305833517e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.593
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = 2.5230277889106639823257543932069
y[1] (numeric) = 2.5230277889106639823257543932079
absolute error = 1.0e-30
relative error = 3.9634918188188384536170987129827e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.604
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = 2.5284937722701796572385747197584
y[1] (numeric) = 2.5284937722701796572385747197593
absolute error = 9e-31
relative error = 3.5594313494865567175427017991643e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.614
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = 2.5339588886834095892546086285107
y[1] (numeric) = 2.5339588886834095892546086285117
absolute error = 1.0e-30
relative error = 3.9463939390097147223741752538650e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.625
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 = 4.317
Order of pole (six term test) = -8.372e-27
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = 2.5394231413702127739134745692352
y[1] (numeric) = 2.5394231413702127739134745692362
absolute error = 1.0e-30
relative error = 3.9379022097925106288982633795189e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.635
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 11.52
Order of pole (six term test) = -4.393e-27
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = 2.5448865335325435022505521247499
y[1] (numeric) = 2.5448865335325435022505521247509
absolute error = 1.0e-30
relative error = 3.9294482752907073729893068725914e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.645
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.633
Order of pole (six term test) = 4.779e-27
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = 2.5503490683545838657378587061685
y[1] (numeric) = 2.5503490683545838657378587061695
absolute error = 1.0e-30
relative error = 3.9210318791583024816768606555339e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.656
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = 2.5558107490028750377238378516884
y[1] (numeric) = 2.5558107490028750377238378516893
absolute error = 9e-31
relative error = 3.5213874906470533347475717230929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.666
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = 2.5612715786264473449038953719112
y[1] (numeric) = 2.5612715786264473449038953719122
absolute error = 1.0e-30
relative error = 3.9043106882725713577772529997742e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.677
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = 2.5667315603569491421792361093134
y[1] (numeric) = 2.5667315603569491421792361093143
absolute error = 9e-31
relative error = 3.5064048531621249070279360121248e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.687
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = 2.5721906973087745040898312493812
y[1] (numeric) = 2.5721906973087745040898312493821
absolute error = 9e-31
relative error = 3.4989629693539045733937139341934e-29 %
Correct digits = 31
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 = 4.548
Order of pole (six term test) = 5.236e-27
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = 2.5776489925791897458381416888696
y[1] (numeric) = 2.5776489925791897458381416888706
absolute error = 1.0e-30
relative error = 3.8795041639839498244934521112177e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.708
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 10.23
Order of pole (six term test) = -5.434e-27
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = 2.5831064492484587867534954584218
y[1] (numeric) = 2.5831064492484587867534954584227
absolute error = 9e-31
relative error = 3.4841769694077077569738552686618e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.719
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = 2.5885630703799673688827258957464
y[1] (numeric) = 2.5885630703799673688827258957473
absolute error = 9e-31
relative error = 3.4768324183342834810508817738426e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.729
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = 2.59401885902034614323078219734
y[1] (numeric) = 2.5940188590203461432307821973409
absolute error = 9e-31
relative error = 3.4695198798203527831727027804093e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.74
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 = 4.285
Order of pole (six term test) = -1.508e-27
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = 2.5994738181995926360154858944913
y[1] (numeric) = 2.5994738181995926360154858944922
absolute error = 9e-31
relative error = 3.4622391412402994871340752414874e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.75
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = 2.6049279509311921071433871690848
y[1] (numeric) = 2.6049279509311921071433871690857
absolute error = 9e-31
relative error = 3.4549899918662781399826150133755e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.76
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = 2.6103812602122373129587359112992
y[1] (numeric) = 2.6103812602122373129587359113001
absolute error = 9e-31
relative error = 3.4477722228469622432583632254938e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.771
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 = 5.884
Order of pole (six term test) = -1.020e-26
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = 2.6158337490235471851648868742535
y[1] (numeric) = 2.6158337490235471851648868742544
absolute error = 9e-31
relative error = 3.4405856271865784743956177153360e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.781
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.685
Order of pole (six term test) = -8.050e-27
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = 2.621285420329784437666969720768
y[1] (numeric) = 2.6212854203297844376669697207689
absolute error = 9e-31
relative error = 3.4334299997242224077498753683240e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.792
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = 2.6267362770795721129363373633174
y[1] (numeric) = 2.6267362770795721129363373633182
absolute error = 8e-31
relative error = 3.0456045663230678446556194068747e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.802
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = 2.6321863222056090793511245934703
y[1] (numeric) = 2.6321863222056090793511245934711
absolute error = 8e-31
relative error = 3.0392985224907998093143473933336e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.813
Order 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) = -9.556e-26
bytes used=56029704, alloc=4455632, time=2.26
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = 2.6376355586247844908231690372336
y[1] (numeric) = 2.6376355586247844908231690372343
absolute error = 7e-31
relative error = 2.6538920348987384315040113499030e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.823
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = 2.6430839892382912198795340329838
y[1] (numeric) = 2.6430839892382912198795340329845
absolute error = 7e-31
relative error = 2.6484213246728212282280001222567e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.834
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = 2.6485316169317382752268947917502
y[1] (numeric) = 2.6485316169317382752268947917509
absolute error = 7e-31
relative error = 2.6429739238338169170405028765197e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.844
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = 2.6539784445752622146890724436479
y[1] (numeric) = 2.6539784445752622146890724436486
absolute error = 7e-31
relative error = 2.6375496810488477837566728849453e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = 2.6594244750236375642719931612126
y[1] (numeric) = 2.6594244750236375642719931612133
absolute error = 7e-31
relative error = 2.6321484463053918543511296216849e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.865
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 11.02
Order of pole (six term test) = 5.628e-27
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = 2.6648697111163862539762799145602
y[1] (numeric) = 2.6648697111163862539762799145609
absolute error = 7e-31
relative error = 2.6267700708968281982140443023110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.875
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = 2.6703141556778860808455215501768
y[1] (numeric) = 2.6703141556778860808455215501775
absolute error = 7e-31
relative error = 2.6214144074081724144888445414283e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.886
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 = 7.874
Order of pole (six term test) = -1.348e-27
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = 2.6757578115174782096079773404251
y[1] (numeric) = 2.6757578115174782096079773404258
absolute error = 7e-31
relative error = 2.6160813097019993816123879678271e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.896
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = 2.6812006814295737211410350097329
y[1] (numeric) = 2.6812006814295737211410350097336
absolute error = 7e-31
relative error = 2.6107706329045504013794695827266e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.907
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = 2.6866427681937592188611171200857
y[1] (numeric) = 2.6866427681937592188611171200864
absolute error = 7e-31
relative error = 2.6054822333920219190456373276471e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.917
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = 2.6920840745749015030168957258057
y[1] (numeric) = 2.6920840745749015030168957258064
absolute error = 7e-31
relative error = 2.6002159687770330501875514945461e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.928
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = 2.6975246033232513227406000272442
y[1] (numeric) = 2.697524603323251322740600027245
absolute error = 8e-31
relative error = 2.9656819404517362208915011195193e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.938
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = 2.7029643571745462155908585053684
y[1] (numeric) = 2.7029643571745462155908585053691
absolute error = 7e-31
relative error = 2.5897492807922990542448194812084e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.949
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = 2.708403338850112444200878333896
y[1] (numeric) = 2.7084033388501124442008783338968
absolute error = 8e-31
relative error = 2.9537698042406428063965992729606e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.959
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = 2.7138415510569660395278038520073
y[1] (numeric) = 2.713841551056966039527803852008
absolute error = 7e-31
relative error = 2.5793694540765263482850501751521e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.97
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.816
Order of pole (six term test) = -1.471e-27
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = 2.719278996487912960082786118634
y[1] (numeric) = 2.7192789964879129600827861186348
absolute error = 8e-31
relative error = 2.9419563091291502730301558670876e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.98
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = 2.7247156778216483764066111003036
y[1] (numeric) = 2.7247156778216483764066111003043
absolute error = 7e-31
relative error = 2.5690753927016522886620843457329e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.99
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = 2.730151597722855089942649362507
y[1] (numeric) = 2.7301515977228550899426493625078
absolute error = 8e-31
relative error = 2.9302402132806770096273991517784e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.001
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = 2.735586758842301095347380177588
y[1] (numeric) = 2.7355867588423010953473801775888
absolute error = 8e-31
relative error = 2.9244183077511297326316753166668e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.011
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = 2.7410211638169362951687831036709
y[1] (numeric) = 2.7410211638169362951687831036717
absolute error = 8e-31
relative error = 2.9186202958242804156433631279618e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.022
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = 2.74645481526998837571445612984
y[1] (numeric) = 2.7464548152699883757144561298408
absolute error = 8e-31
relative error = 2.9128460280944274090190995904774e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.032
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = 2.7518877158110578528243876423235
y[1] (numeric) = 2.7518877158110578528243876423242
absolute error = 7e-31
relative error = 2.5437084368600065853301153434507e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.043
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = 2.7573198680362122961578563755988
y[1] (numeric) = 2.7573198680362122961578563755995
absolute error = 7e-31
relative error = 2.5386971171340603955417642562828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.053
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = 2.7627512745280797404999362051485
y[1] (numeric) = 2.7627512745280797404999362051492
absolute error = 7e-31
relative error = 2.5337061879360483805071078497805e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.064
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = 2.768181937855941292490518544706
y[1] (numeric) = 2.7681819378559412924905185447067
absolute error = 7e-31
relative error = 2.5287355228615346781649095060360e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.074
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = 2.7736118605758229410776120480435
y[1] (numeric) = 2.7736118605758229410776120480442
absolute error = 7e-31
relative error = 2.5237849965592325887421434979165e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.085
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = 2.7790410452305865798969154822709
y[1] (numeric) = 2.7790410452305865798969154822716
absolute error = 7e-31
relative error = 2.5188544847199930287860895734469e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.095
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = 2.7844694943500202496812636084756
y[1] (numeric) = 2.7844694943500202496812636084763
absolute error = 7e-31
relative error = 2.5139438640659313831272170067891e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.105
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = 2.7898972104509276087064966151815
y[1] (numeric) = 2.7898972104509276087064966151822
absolute error = 7e-31
relative error = 2.5090530123396907246729105541256e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.116
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = 2.79532419603721663918458039909
y[1] (numeric) = 2.7953241960372166391845803990907
absolute error = 7e-31
relative error = 2.5041818082938394059492261109223e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.126
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 = 3.056
Order of pole (six term test) = -3.730e-27
bytes used=60031880, alloc=4455632, time=2.42
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = 2.8007504535999875974203874274148
y[1] (numeric) = 2.8007504535999875974203874274154
absolute error = 6e-31
relative error = 2.1422829700117723368723221366310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.137
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 = 22.06
Order of pole (six term test) = -2.155e-26
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = 2.8061759856176202154554160447037
y[1] (numeric) = 2.8061759856176202154554160447043
absolute error = 6e-31
relative error = 2.1381410256347272101230727124565e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.147
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = 2.8116007945558601618298602421299
y[1] (numeric) = 2.8116007945558601618298602421305
absolute error = 6e-31
relative error = 2.1340156154521934363372124418764e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.158
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = 2.8170248828679047690038227601234
y[1] (numeric) = 2.817024882867904769003822760124
absolute error = 6e-31
relative error = 2.1299066389117694241777635190806e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.168
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = 2.8224482529944880348890729445437
y[1] (numeric) = 2.8224482529944880348890729445443
absolute error = 6e-31
relative error = 2.1258139962829346556596841008496e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.179
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = 2.8278709073639649058545683422384
y[1] (numeric) = 2.827870907363964905854568342239
absolute error = 6e-31
relative error = 2.1217375886486185977440046841199e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.189
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 = 10.27
Order of pole (six term test) = -5.361e-27
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = 2.8332928483923948484819672389349
y[1] (numeric) = 2.8332928483923948484819672389355
absolute error = 6e-31
relative error = 2.1176773178968735849186591107044e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = 2.8387140784836247172615401555701
y[1] (numeric) = 2.8387140784836247172615401555707
absolute error = 6e-31
relative error = 2.1136330867126501762619427048434e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.21
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = 2.844134600029370925334223976658
y[1] (numeric) = 2.8441346000293709253342239766586
absolute error = 6e-31
relative error = 2.1096047985696735150918980792818e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.22
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.084
Order of pole (six term test) = 6.072e-27
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = 2.8495544154093009253020354325275
y[1] (numeric) = 2.8495544154093009253020354325281
absolute error = 6e-31
relative error = 2.1055923577224192434575141853972e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.231
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 = 26.47
Order of pole (six term test) = -3.269e-26
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = 2.8549735269911140070466539352201
y[1] (numeric) = 2.8549735269911140070466539352207
absolute error = 6e-31
relative error = 2.1015956691981875474347533948078e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.241
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.914
Order of pole (six term test) = 5.289e-27
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = 2.8603919371306214194146804017308
y[1] (numeric) = 2.8603919371306214194146804017314
absolute error = 6e-31
relative error = 2.0976146387892739324612118412193e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.252
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = 2.8658096481718258225478620962427
y[1] (numeric) = 2.8658096481718258225478620962433
absolute error = 6e-31
relative error = 2.0936491730452353507865820290958e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.262
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = 2.8712266624470000775574273699597
y[1] (numeric) = 2.8712266624470000775574273699603
absolute error = 6e-31
relative error = 2.0896991792652503255407360046151e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.273
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = 2.8766429822767653801635824296672
y[1] (numeric) = 2.8766429822767653801635824296677
absolute error = 5e-31
relative error = 1.7381371379088097816130827594407e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.283
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = 2.8820586099701687448441691475842
y[1] (numeric) = 2.8820586099701687448441691475847
absolute error = 5e-31
relative error = 1.7348710337475591381086394611166e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.294
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = 2.8874735478247598459604529205746
y[1] (numeric) = 2.8874735478247598459604529205751
absolute error = 5e-31
relative error = 1.7316175948232267352547231973534e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.304
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = 2.8928877981266672222529874386226
y[1] (numeric) = 2.8928877981266672222529874386231
absolute error = 5e-31
relative error = 1.7283767463217290387757963983070e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.315
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = 2.8983013631506738510264739253115
y[1] (numeric) = 2.898301363150673851026473925312
absolute error = 5e-31
relative error = 1.7251484140229710283812695092840e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.325
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = 2.9037142451602920982694812093458
y[1] (numeric) = 2.9037142451602920982694812093463
absolute error = 5e-31
relative error = 1.7219325242949269006331928978370e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.335
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = 2.909126446407838050882805361734
y[1] (numeric) = 2.9091264464078380508828053617346
absolute error = 6e-31
relative error = 2.0624748049053500287668512685504e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.346
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = 2.914537969134505237119109312817
y[1] (numeric) = 2.9145379691345052371191093128176
absolute error = 6e-31
relative error = 2.0586453371138433848920476246150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.356
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = 2.9199488155704377412662798062043
y[1] (numeric) = 2.9199488155704377412662798062048
absolute error = 5e-31
relative error = 1.7123587829135306002401037434618e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.367
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = 2.9253589879348027185376574425498
y[1] (numeric) = 2.9253589879348027185376574425504
absolute error = 6e-31
relative error = 2.0510303264474840588286790313286e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.377
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = 2.9307684884358623160639218308567
y[1] (numeric) = 2.9307684884358623160639218308573
absolute error = 6e-31
relative error = 2.0472446130339597200601642697501e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.388
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 = 1.724
Order of pole (six term test) = 2.035e-27
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = 2.936177319271045005813934636681
y[1] (numeric) = 2.9361773192710450058139346366816
absolute error = 6e-31
relative error = 2.0434733149868483005807080199824e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.398
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = 2.9415854826270163352052454514164
y[1] (numeric) = 2.941585482627016335205245451417
absolute error = 6e-31
relative error = 2.0397163486956128953938902629524e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.409
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = 2.9469929806797491010992359752075
y[1] (numeric) = 2.9469929806797491010992359752082
absolute error = 7e-31
relative error = 2.3753025697351305578555669746656e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.419
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = 2.9523998155945929528110042888189
y[1] (numeric) = 2.9523998155945929528110042888196
absolute error = 7e-31
relative error = 2.3709525935565906057416135865447e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.43
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = 2.9578059895263434297000604744681
y[1] (numeric) = 2.9578059895263434297000604744688
absolute error = 7e-31
relative error = 2.3666190496561150930208974758869e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.44
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=64033380, alloc=4455632, time=2.58
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = 2.9632115046193104388447052226749
y[1] (numeric) = 2.9632115046193104388447052226756
absolute error = 7e-31
relative error = 2.3623018434856217433972487191949e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.45
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = 2.9686163630073861782405822213809
y[1] (numeric) = 2.9686163630073861782405822213816
absolute error = 7e-31
relative error = 2.3580008812282435651318271212994e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.461
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.095
Order of pole (six term test) = 3.431e-27
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = 2.9740205668141125109023211505598
y[1] (numeric) = 2.9740205668141125109023211505605
absolute error = 7e-31
relative error = 2.3537160697912303207896237915151e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = 2.9794241181527477951864092781936
y[1] (numeric) = 2.9794241181527477951864092781943
absolute error = 7e-31
relative error = 2.3494473167989328541953951416897e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.482
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = 2.9848270191263331765934344386668
y[1] (numeric) = 2.9848270191263331765934344386675
absolute error = 7e-31
relative error = 2.3451945305858691455451270860733e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.492
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = 2.9902292718277583462486192247451
y[1] (numeric) = 2.9902292718277583462486192247458
absolute error = 7e-31
relative error = 2.3409576201898709831984415486318e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.503
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = 2.9956308783398267712011043740506
y[1] (numeric) = 2.9956308783398267712011043740513
absolute error = 7e-31
relative error = 2.3367364953453101579489790493517e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.513
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = 3.0010318407353204016247275941025
y[1] (numeric) = 3.0010318407353204016247275941032
absolute error = 7e-31
relative error = 2.3325310664764031025396975102649e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.524
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 = 39.74
Order of pole (six term test) = 1.626e-25
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = 3.0064321610770638599460716362486
y[1] (numeric) = 3.0064321610770638599460716362492
absolute error = 6e-31
relative error = 1.9957210668776510707406299703952e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.534
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = 3.0118318414179881168693116607012
y[1] (numeric) = 3.0118318414179881168693116607019
absolute error = 7e-31
relative error = 2.3241669417720077276780511214709e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.545
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = 3.0172308838011936592118663647162
y[1] (numeric) = 3.0172308838011936592118663647169
absolute error = 7e-31
relative error = 2.3200080701749943757470932030927e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.555
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = 3.0226292902600131544100396728523
y[1] (numeric) = 3.022629290260013154410039672853
absolute error = 7e-31
relative error = 2.3158645430177263831727098580498e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.565
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = 3.0280270628180736164997198752485
y[1] (numeric) = 3.0280270628180736164997198752492
absolute error = 7e-31
relative error = 2.3117362740758852391898315674585e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.576
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = 3.0334242034893580783237709710155
y[1] (numeric) = 3.0334242034893580783237709710162
absolute error = 7e-31
relative error = 2.3076231777764140020043020449390e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.586
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = 3.0388207142782667746649968114388
y[1] (numeric) = 3.0388207142782667746649968114394
absolute error = 6e-31
relative error = 1.9744501450211505062184228733944e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.597
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = 3.0442165971796778409514727794864
y[1] (numeric) = 3.044216597179677840951472779487
absolute error = 6e-31
relative error = 1.9709504263128698403774318238913e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.607
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = 3.0496118541790075321296126786166
y[1] (numeric) = 3.0496118541790075321296126786172
absolute error = 6e-31
relative error = 1.9674634959783341709917875538220e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.618
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = 3.0550064872522699662495608757116
y[1] (numeric) = 3.0550064872522699662495608757122
absolute error = 6e-31
relative error = 1.9639892828497763153525466345441e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = 3.060400498366136397257362338258
y[1] (numeric) = 3.0604004983661363972573623382586
absolute error = 6e-31
relative error = 1.9605277162917843196723077683964e-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
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = 3.0657938894779940214388569577394
y[1] (numeric) = 3.06579388947799402143885695774
absolute error = 6e-31
relative error = 1.9570787261963023859993719790956e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.649
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.785
Order of pole (six term test) = -1.905e-27
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = 3.0711866625360043219113605351353
y[1] (numeric) = 3.0711866625360043219113605351359
absolute error = 6e-31
relative error = 1.9536422429776882491212625459940e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.66
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = 3.0765788194791609555109242359687
y[1] (numeric) = 3.0765788194791609555109242359693
absolute error = 6e-31
relative error = 1.9502181975678262592233649352807e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.67
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 = 10.15
Order of pole (six term test) = -9.898e-27
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = 3.0819703622373471863752985546119
y[1] (numeric) = 3.0819703622373471863752985546125
absolute error = 6e-31
relative error = 1.9468065214112954372810242507296e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.68
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = 3.0873612927313928704756583488807
y[1] (numeric) = 3.0873612927313928704756583488813
absolute error = 6e-31
relative error = 1.9434071464605917811860937203107e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.691
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = 3.0927516128731309953036639375228
y[1] (numeric) = 3.0927516128731309953036639375233
absolute error = 5e-31
relative error = 1.6166833376428367595376943441025e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.701
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = 3.0981413245654537788745313468734
y[1] (numeric) = 3.0981413245654537788745313468739
absolute error = 5e-31
relative error = 1.6138708587482856299505906218436e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.712
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = 3.1035304297023683321614544289094
y[1] (numeric) = 3.1035304297023683321614544289099
absolute error = 5e-31
relative error = 1.6110684632402669864320560920908e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.722
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 = 9.051
Order of pole (six term test) = 3.211e-27
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = 3.1089189301690518890319547575648
y[1] (numeric) = 3.1089189301690518890319547575653
absolute error = 5e-31
relative error = 1.6082760960666535900551754393755e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.733
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 = 3.809
Order of pole (six term test) = -8.439e-27
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = 3.114306827841906607712524073896
y[1] (numeric) = 3.1143068278419066077125240738965
absolute error = 5e-31
relative error = 1.6054937025793329910577926815170e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.743
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = 3.1196941245886139477642608458272
y[1] (numeric) = 3.1196941245886139477642608458276
absolute error = 4e-31
relative error = 1.2821769828243881849255513734517e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.754
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 = 39.18
Order of pole (six term test) = -7.088e-26
bytes used=68036476, alloc=4455632, time=2.75
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = 3.1250808222681886265090796069368
y[1] (numeric) = 3.1250808222681886265090796069372
absolute error = 4e-31
relative error = 1.2799668960551214301266116563354e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.764
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = 3.1304669227310321588034816310385
y[1] (numeric) = 3.130466922731032158803481631039
absolute error = 5e-31
relative error = 1.5972058237363452258258764588766e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.775
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = 3.1358524278189859840148107909436
y[1] (numeric) = 3.135852427818985984014810790944
absolute error = 4e-31
relative error = 1.2755702291711592270927551693684e-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
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3);
Iterations = 490
Total Elapsed Time = 2 Seconds
Elapsed Time(since restart) = 2 Seconds
Time to Timeout = 2 Minutes 57 Seconds
Percent Done = 100.2 %
> quit
bytes used=68488676, alloc=4455632, time=2.77