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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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_0D2[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D3[1];
> #emit pre exp 1 $eq_no = 1
> array_tmp3[1] := exp(array_x[1]);
> #emit pre div LINEAR - FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp2[1] / array_tmp3[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D2[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre exp ID_LINEAR iii = 2 $eq_no = 1
> array_tmp3[2] := array_tmp3[1] * array_x[2] / 1;
> #emit pre div LINEAR - FULL $eq_no = 1 i = 2
> array_tmp4[2] := (array_tmp2[2] - array_tmp4[1] * array_tmp3[2]) / array_tmp3[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre exp ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := array_tmp3[2] * array_x[2] / 2;
> #emit pre div LINEAR FULL $eq_no = 1 i = 3
> array_tmp4[3] := - ats(3,array_tmp3,array_tmp4,2) / array_tmp3[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre exp ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := array_tmp3[3] * array_x[2] / 3;
> #emit pre div LINEAR FULL $eq_no = 1 i = 4
> array_tmp4[4] := - ats(4,array_tmp3,array_tmp4,2) / array_tmp3[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre exp ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := array_tmp3[4] * array_x[2] / 4;
> #emit pre div LINEAR FULL $eq_no = 1 i = 5
> array_tmp4[5] := - ats(5,array_tmp3,array_tmp4,2) / array_tmp3[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit exp LINEAR $eq_no = 1
> array_tmp3[kkk] := array_tmp3[kkk - 1] * array_x[2] / (kkk - 1);
> #emit div LINEAR FULL $eq_no = 1 i = 1
> array_tmp4[kkk] := -ats(kkk,array_tmp3,array_tmp4,2) / array_tmp3[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_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_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_0D2[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D3[1];
array_tmp3[1] := exp(array_x[1]);
array_tmp4[1] := array_tmp2[1]/array_tmp3[1];
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D2[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp3[1]*array_x[2];
array_tmp4[2] :=
(array_tmp2[2] - array_tmp4[1]*array_tmp3[2])/array_tmp3[1];
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp3[3] := 1/2*array_tmp3[2]*array_x[2];
array_tmp4[3] := -ats(3, array_tmp3, array_tmp4, 2)/array_tmp3[1];
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp3[4] := 1/3*array_tmp3[3]*array_x[2];
array_tmp4[4] := -ats(4, array_tmp3, array_tmp4, 2)/array_tmp3[1];
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp3[5] := 1/4*array_tmp3[4]*array_x[2];
array_tmp4[5] := -ats(5, array_tmp3, array_tmp4, 2)/array_tmp3[1];
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp3[kkk] := array_tmp3[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp4[kkk] :=
-ats(kkk, array_tmp3, array_tmp4, 2)/array_tmp3[1];
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 13
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s
", str)
end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-42.4g %s
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then printf("%-30s = %-32d %s
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " |
")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,m,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_int(ALWAYS,"m",4, m ,4," ");
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, m, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_int(ALWAYS, "m", 4, m, 4, " ");
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file)
fprintf(file, "
")
end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(-(0.1 * (5.0 + 2.0*x))/exp(x));
> end;
exact_soln_y := proc(x) return -0.1*(5.0 + 2.0*x)/exp(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_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_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_exppostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 1.0;");
> omniout_str(ALWAYS,"## did poorly with x_start := -5.0;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(-(0.1 * (5.0 + 2.0*x))/exp(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(2 + 1),[]);
> array_last_rel_error:= Array(0..(2 + 1),[]);
> array_type_pole:= Array(0..(2 + 1),[]);
> array_type_real_pole:= Array(0..(2 + 1),[]);
> array_type_complex_pole:= Array(0..(2 + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_const_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 := 1.0;
> ## did poorly with x_start := -5.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> found_h := false;
> glob_h := glob_min_h;
> if (glob_max_h < glob_h) then # if number 4
> glob_h := glob_max_h;
> fi;# end if 4;
> if (glob_display_interval < glob_h) then # if number 4
> glob_h := glob_display_interval;
> fi;# end if 4;
> best_h := glob_h;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := 0.0;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4
> found_h := true;
> glob_h := glob_max_h;
> best_h := glob_h;
> elif
> ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5
> glob_h := glob_h/2.0;
> best_h := glob_h;
> found_h := true;
> else
> glob_h := glob_h*2.0;
> best_h := glob_h;
> fi;# end if 5;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 5
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 5;
> if (opt_iter > 100) then # if number 5
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 5;
> if (glob_display_interval < glob_h) then # if number 5
> glob_h := glob_display_interval;
> fi;# end if 5;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 5
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 5;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 5
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 6
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 6;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 6
> #left paren 0004C
> check_for_pole();
> fi;# end if 6;#was right paren 0004C
> if (reached_interval()) then # if number 6
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 6;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 6
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 6;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 6;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 6
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T00:38:12-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div_lin_exp")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 7
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 7;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"div_lin_exp diffeq.mxt")
> ;
> logitem_str(html_log_file,"div_lin_exp maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_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_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_exppostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 1.0;");
omniout_str(ALWAYS, "## did poorly with x_start := -5.0;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(-(0.1 * (5.0 + 2.0*x))/exp(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_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 := 1.0;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
found_h := false;
glob_h := glob_min_h;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
best_h := glob_h;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err,
16, "");
estimated_step_error := 0.;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if est_needed_step_err < estimated_step_error and opt_iter = 1 or
glob_max_h <= glob_h then
found_h := true; glob_h := glob_max_h; best_h := glob_h
elif est_needed_step_err < estimated_step_error and not found_h
then glob_h := glob_h/2.0; best_h := glob_h; found_h := true
else glob_h := glob_h*2.0; best_h := glob_h
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,
"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T00:38:12-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"div_lin_exp");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 189 | ");
logitem_str(html_log_file, "div_lin_exp diffeq.mxt");
logitem_str(html_log_file, "div_lin_exp maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 13
> main();
##############ECHO OF PROBLEM#################
##############temp/div_lin_exppostode.ode#################
diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 1.0;
## did poorly with x_start := -5.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(-(0.1 * (5.0 + 2.0*x))/exp(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 4
estimated_steps = 4000000
step_error = 2.5000000000000000000000000000000e-17
est_needed_step_err = 2.5000000000000000000000000000000e-17
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.1048661150121780371637913489201e-183
estimated_step_error = 4.1048661150121780371637913489201e-183
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.7547289652248410630600428198733e-175
estimated_step_error = 2.7547289652248410630600428198733e-175
best_h = 4.00e-06
opt_iter = 3
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.8486672433291175267476193880828e-167
estimated_step_error = 1.8486672433291175267476193880828e-167
best_h = 8.000e-06
opt_iter = 4
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.2406194901562091326028780353513e-159
estimated_step_error = 1.2406194901562091326028780353513e-159
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 = 8.3256551758148895297327195118363e-152
estimated_step_error = 8.3256551758148895297327195118363e-152
best_h = 3.200000e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.5872508799883415175070451286084e-144
estimated_step_error = 5.5872508799883415175070451286084e-144
best_h = 6.4000000e-05
opt_iter = 7
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.7495382736895762263439532229913e-136
estimated_step_error = 3.7495382736895762263439532229913e-136
best_h = 0.000128
opt_iter = 8
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.5162694259322292023918421138892e-128
estimated_step_error = 2.5162694259322292023918421138892e-128
best_h = 0.000256
opt_iter = 9
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.6886356463423070720953376633391e-120
estimated_step_error = 1.6886356463423070720953376633391e-120
best_h = 0.000512
opt_iter = 10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.1332185883198211555385793129102e-112
estimated_step_error = 1.1332185883198211555385793129102e-112
best_h = 0.001024
opt_iter = 11
bytes used=4000380, alloc=2883056, time=0.13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.6048259035613479009330536153264e-105
estimated_step_error = 7.6048259035613479009330536153264e-105
best_h = 0.002048
opt_iter = 12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.1034111978908212028075737625071e-97
estimated_step_error = 5.1034111978908212028075737625071e-97
best_h = 0.004096
opt_iter = 13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.4247056271197763495299671765467e-89
estimated_step_error = 3.4247056271197763495299671765467e-89
best_h = 0.008192
opt_iter = 14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.2980989921127089988834200403461e-81
estimated_step_error = 2.2980989921127089988834200403461e-81
best_h = 0.016384
opt_iter = 15
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.5419838402869234539780683746088e-73
estimated_step_error = 1.5419838402869234539780683746088e-73
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 = 1.0344801120150850060074101048472e-65
estimated_step_error = 1.0344801120150850060074101048472e-65
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 = 6.9378838760705646127052428579083e-58
estimated_step_error = 6.9378838760705646127052428579083e-58
best_h = 0.131072
opt_iter = 18
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.6500474852119528547967616703486e-50
estimated_step_error = 4.6500474852119528547967616703486e-50
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = -0.25751560882000962511686663911302
y[1] (numeric) = -0.25751560882000962511686663911302
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 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 275.1
Order of pole (three term test) = -7220
Radius of convergence (six term test) for eq 1 = 2.986e+10
Order of pole (six term test) = 1.274e+20
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = -0.25568172365920937046944649953742
y[1] (numeric) = -0.25568172365920937046944649953741
absolute error = 1e-32
relative error = 3.9111125570041545498429862060689e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 275
Order of pole (three term test) = -7217
Radius of convergence (six term test) for eq 1 = 3.338e+10
Order of pole (six term test) = 1.588e+20
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = -0.25385883788184712199006451079643
y[1] (numeric) = -0.25385883788184712199006451079642
absolute error = 1e-32
relative error = 3.9391971079038322681806815016270e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 274.8
Order of pole (three term test) = -7213
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = -0.25204691416181804305580601464985
y[1] (numeric) = -0.25204691416181804305580601464984
absolute error = 1e-32
relative error = 3.9675153465992621945747348720731e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 274.7
Order of pole (three term test) = -7209
Radius of convergence (six term test) for eq 1 = 2.073e+10
Order of pole (six term test) = 6.085e+19
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = -0.25024591482681634489201125183874
y[1] (numeric) = -0.25024591482681634489201125183873
absolute error = 1e-32
relative error = 3.9960692293101123157054887107081e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 274.5
Order of pole (three term test) = -7205
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = -0.24845580186892030181697720023953
y[1] (numeric) = -0.24845580186892030181697720023953
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 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 274.4
Order of pole (three term test) = -7201
Radius of convergence (six term test) for eq 1 = 3.380e+10
Order of pole (six term test) = 1.609e+20
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = -0.24667653695500089706889794384017
y[1] (numeric) = -0.24667653695500089706889794384016
absolute error = 1e-32
relative error = 4.0538918388594919188783360743280e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 274.2
Order of pole (three term test) = -7198
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = -0.24490808143695656104710871943071
y[1] (numeric) = -0.2449080814369565610471087194307
absolute error = 1e-32
relative error = 4.0831645657941129886244688697136e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 274.1
Order of pole (three term test) = -7194
Radius of convergence (six term test) for eq 1 = 3.904e+10
Order of pole (six term test) = 2.134e+20
TOP MAIN SOLVE Loop
bytes used=8001332, alloc=3931440, time=0.27
x[1] = 1.08
y[1] (analytic) = -0.24315039636177643227001891411732
y[1] (numeric) = -0.24315039636177643227001891411731
absolute error = 1e-32
relative error = 4.1126809372423516984917616274223e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 273.9
Order of pole (three term test) = -7190
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = -0.24140344248143454020615485234121
y[1] (numeric) = -0.24140344248143454020615485234121
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 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 273.8
Order of pole (three term test) = -7186
Radius of convergence (six term test) for eq 1 = 2.675e+11
Order of pole (six term test) = 9.965e+21
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = -0.23966718026261727836796977263054
y[1] (numeric) = -0.23966718026261727836796977263054
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 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 273.6
Order of pole (three term test) = -7182
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = -0.23794156989628650566605335731524
y[1] (numeric) = -0.23794156989628650566605335731524
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 = 17.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 273.5
Order of pole (three term test) = -7179
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = -0.23622657130708058399967521238963
y[1] (numeric) = -0.23622657130708058399967521238962
absolute error = 1e-32
relative error = 4.2332240376975166366969932208546e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 273.3
Order of pole (three term test) = -7175
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = -0.23452214416255563040386515477689
y[1] (numeric) = -0.23452214416255563040386515477688
absolute error = 1e-32
relative error = 4.2639896695932665156928544449359e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 273.2
Order of pole (three term test) = -7171
Radius of convergence (six term test) for eq 1 = 2.020e+10
Order of pole (six term test) = 5.618e+19
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = -0.23282824788226923277915751934655
y[1] (numeric) = -0.23282824788226923277915751934654
absolute error = 1e-32
relative error = 4.2950114906403238408400497818399e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 273
Order of pole (three term test) = -7167
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = -0.23114484164670884929344596527355
y[1] (numeric) = -0.23114484164670884929344596527355
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 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 272.9
Order of pole (three term test) = -7163
Radius of convergence (six term test) for eq 1 = 2.054e+10
Order of pole (six term test) = 5.777e+19
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = -0.22947188440606708296189744676165
y[1] (numeric) = -0.22947188440606708296189744676164
absolute error = 1e-32
relative error = 4.3578323444210173123603705410133e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 272.7
Order of pole (three term test) = -7160
Radius of convergence (six term test) for eq 1 = 4.267e+10
Order of pole (six term test) = 2.488e+20
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = -0.22780933488886599467639555874577
y[1] (numeric) = -0.22780933488886599467639555874577
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 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 272.6
Order of pole (three term test) = -7156
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = -0.22615715161043259006640870493178
y[1] (numeric) = -0.22615715161043259006640870493178
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 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 272.4
Order of pole (three term test) = -7152
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = -0.22451529288122758802443914265516
y[1] (numeric) = -0.22451529288122758802443914265515
absolute error = 1e-32
relative error = 4.4540395763998892651095273761623e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 272.3
Order of pole (three term test) = -7148
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = -0.22288371681502955151728342924159
y[1] (numeric) = -0.22288371681502955151728342924158
absolute error = 1e-32
relative error = 4.4866444901845236345010370670291e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 272.1
Order of pole (three term test) = -7144
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = -0.22126238133697643442524790517897
y[1] (numeric) = -0.22126238133697643442524790517896
absolute error = 1e-32
relative error = 4.5195210950795467398970207916114e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 272
Order of pole (three term test) = -7141
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = -0.2196512441914665716012851395343
y[1] (numeric) = -0.21965124419146657160128513953429
absolute error = 1e-32
relative error = 4.5526716849749121423214317043861e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 271.8
Order of pole (three term test) = -7137
Radius of convergence (six term test) for eq 1 = 5.174e+10
Order of pole (six term test) = 3.598e+20
TOP MAIN SOLVE Loop
bytes used=12002460, alloc=4193536, time=0.41
x[1] = 1.23
y[1] (analytic) = -0.21805026294992111311686451636277
y[1] (numeric) = -0.21805026294992111311686451636275
absolute error = 2e-32
relative error = 9.1721971482296878653891483953140e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 271.7
Order of pole (three term test) = -7133
Radius of convergence (six term test) for eq 1 = 4.477e+10
Order of pole (six term test) = 2.687e+20
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = -0.21645939501840987775742287432843
y[1] (numeric) = -0.21645939501840987775742287432842
absolute error = 1e-32
relative error = 4.6198040972763042754780955803771e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 271.5
Order of pole (three term test) = -7129
Radius of convergence (six term test) for eq 1 = 6.869e+10
Order of pole (six term test) = 6.308e+20
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = -0.21487859764514257524366406998588
y[1] (numeric) = -0.21487859764514257524366406998586
absolute error = 2e-32
relative error = 9.3075812198982436696814560791260e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 271.4
Order of pole (three term test) = -7125
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = -0.21330782792782732138203799037388
y[1] (numeric) = -0.21330782792782732138203799037387
absolute error = 1e-32
relative error = 4.6880604885177954321458883718389e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 271.2
Order of pole (three term test) = -7122
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = -0.21174704282089834538472159813669
y[1] (numeric) = -0.21174704282089834538472159813667
absolute error = 2e-32
relative error = 9.4452322608899748656749904232145e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 271.1
Order of pole (three term test) = -7118
Radius of convergence (six term test) for eq 1 = 2.751e+10
Order of pole (six term test) = 1.003e+20
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = -0.21019619914261476394268150194665
y[1] (numeric) = -0.21019619914261476394268150194664
absolute error = 1e-32
relative error = 4.7574599544567215110697333429111e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 270.9
Order of pole (three term test) = -7114
Radius of convergence (six term test) for eq 1 = 3.696e+10
Order of pole (six term test) = 1.806e+20
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = -0.20865525358203227228129601694921
y[1] (numeric) = -0.2086552535820322722812960169492
absolute error = 1e-32
relative error = 4.7925944007292995917093426154505e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 270.8
Order of pole (three term test) = -7110
Radius of convergence (six term test) for eq 1 = 5.424e+10
Order of pole (six term test) = 3.882e+20
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = -0.20712416270584957837297320734814
y[1] (numeric) = -0.20712416270584957837297320734814
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 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 270.6
Order of pole (three term test) = -7106
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = -0.20560288296513138272167978906589
y[1] (numeric) = -0.20560288296513138272167978906589
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 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 270.5
Order of pole (three term test) = -7102
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = -0.2040913707019096826667946600333
y[1] (numeric) = -0.2040913707019096826667946600333
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 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 270.3
Order of pole (three term test) = -7099
Radius of convergence (six term test) for eq 1 = 5.229e+10
Order of pole (six term test) = 3.578e+20
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = -0.20258958215566515697476124460871
y[1] (numeric) = -0.20258958215566515697476124460871
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 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 270.2
Order of pole (three term test) = -7095
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = -0.20109747346969036359321573543502
y[1] (numeric) = -0.20109747346969036359321573543502
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 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 270
Order of pole (three term test) = -7091
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = -0.19961500069733646083023411024789
y[1] (numeric) = -0.19961500069733646083023411024789
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 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 269.9
Order of pole (three term test) = -7087
Radius of convergence (six term test) for eq 1 = 2.973e+10
Order of pole (six term test) = 1.148e+20
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = -0.19814211980814513988772893629301
y[1] (numeric) = -0.19814211980814513988772893629301
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 = 17.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 269.7
Order of pole (three term test) = -7083
Radius of convergence (six term test) for eq 1 = 4.183e+11
Order of pole (six term test) = 2.267e+22
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = -0.19667878669386743461953547666174
y[1] (numeric) = -0.19667878669386743461953547666174
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 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 269.6
Order of pole (three term test) = -7080
NO COMPLEX POLE (six term test) for Equation 1
bytes used=16003232, alloc=4259060, time=0.55
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = -0.19522495717437105259809165153842
y[1] (numeric) = -0.19522495717437105259809165153842
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 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 269.4
Order of pole (three term test) = -7076
Radius of convergence (six term test) for eq 1 = 3.799e+10
Order of pole (six term test) = 1.860e+20
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = -0.19378058700343785005561186637287
y[1] (numeric) = -0.19378058700343785005561186637287
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 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 269.3
Order of pole (three term test) = -7072
Radius of convergence (six term test) for eq 1 = 2.229e+10
Order of pole (six term test) = 6.389e+19
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = -0.19234563187445305201309176707034
y[1] (numeric) = -0.19234563187445305201309176707034
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 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 269.1
Order of pole (three term test) = -7068
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = -0.19092004742598779792020765098168
y[1] (numeric) = -0.19092004742598779792020765098168
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 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 269
Order of pole (three term test) = -7064
Radius of convergence (six term test) for eq 1 = 2.075e+10
Order of pole (six term test) = 5.505e+19
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = -0.18950378924727657239807502829262
y[1] (numeric) = -0.18950378924727657239807502829262
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 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 268.8
Order of pole (three term test) = -7060
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = -0.18809681288359106020182619962463
y[1] (numeric) = -0.18809681288359106020182619962463
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 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 268.7
Order of pole (three term test) = -7057
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = -0.1866990738415119442980128237105
y[1] (numeric) = -0.18669907384151194429801282371051
absolute error = 1e-32
relative error = 5.3562129657316660224280823975774e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 268.5
Order of pole (three term test) = -7053
Radius of convergence (six term test) for eq 1 = 2.791e+10
Order of pole (six term test) = 9.883e+19
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = -0.18531052759410014597992764447817
y[1] (numeric) = -0.18531052759410014597992764447818
absolute error = 1e-32
relative error = 5.3963474875554650485931780703556e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 268.4
Order of pole (three term test) = -7049
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = -0.1839311295859689862190959999805
y[1] (numeric) = -0.18393112958596898621909599998051
absolute error = 1e-32
relative error = 5.4368175862944521517121084460640e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 268.2
Order of pole (three term test) = -7045
Radius of convergence (six term test) for eq 1 = 1.641e+10
Order of pole (six term test) = 3.401e+19
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = -0.18256083523825872797047304114329
y[1] (numeric) = -0.1825608352382587279704730411433
absolute error = 1e-32
relative error = 5.4776261222452656278440452391212e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 268
Order of pole (three term test) = -7041
Radius of convergence (six term test) for eq 1 = 2.353e+10
Order of pole (six term test) = 6.970e+19
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = -0.18119959995351493990939137501262
y[1] (numeric) = -0.18119959995351493990939137501263
absolute error = 1e-32
relative error = 5.5187759810537144293138035720066e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 267.9
Order of pole (three term test) = -7037
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = -0.17984737912047210307716439149093
y[1] (numeric) = -0.17984737912047210307716439149094
absolute error = 1e-32
relative error = 5.5602700739394293342217491904936e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 267.7
Order of pole (three term test) = -7034
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = -0.17850412811874386314662437661121
y[1] (numeric) = -0.17850412811874386314662437661122
absolute error = 1e-32
relative error = 5.6021113379225810282525693251491e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 267.6
Order of pole (three term test) = -7030
Radius of convergence (six term test) for eq 1 = 1.841e+10
Order of pole (six term test) = 4.237e+19
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = -0.17716980232342131248595608940911
y[1] (numeric) = -0.17716980232342131248595608940912
absolute error = 1e-32
relative error = 5.6443027360526835213021692566229e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 267.4
Order of pole (three term test) = -7026
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = -0.17584435710958066789620272820068
y[1] (numeric) = -0.1758443571095806678962027282007
absolute error = 2e-32
relative error = 1.1373694515279003002458299560795e-29 %
Correct digits = 31
h = 0.01
bytes used=20004024, alloc=4259060, time=0.70
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 267.3
Order of pole (three term test) = -7022
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = -0.17452774785670169182203122564831
y[1] (numeric) = -0.17452774785670169182203122564833
absolute error = 2e-32
relative error = 1.1459495836972160816574490589962e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 267.1
Order of pole (three term test) = -7018
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = -0.17321992995299818698403846064011
y[1] (numeric) = -0.17321992995299818698403846064013
absolute error = 2e-32
relative error = 1.1546015522247836393052937540208e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 267
Order of pole (three term test) = -7014
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = -0.17192085879966187675138154803958
y[1] (numeric) = -0.17192085879966187675138154803959
absolute error = 1e-32
relative error = 5.8166298550502979326822713735610e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 266.8
Order of pole (three term test) = -7011
Radius of convergence (six term test) for eq 1 = 3.807e+10
Order of pole (six term test) = 1.789e+20
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = -0.17063048981502096616317721615346
y[1] (numeric) = -0.17063048981502096616317721615348
absolute error = 2e-32
relative error = 1.1721234593935601137645161340924e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 266.7
Order of pole (three term test) = -7007
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = -0.16934877843861466131332146670224
y[1] (numeric) = -0.16934877843861466131332146670226
absolute error = 2e-32
relative error = 1.1809946422052034824621965010022e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 266.5
Order of pole (three term test) = -7003
Radius of convergence (six term test) for eq 1 = 3.392e+10
Order of pole (six term test) = 1.414e+20
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = -0.16807568013518490783354565347136
y[1] (numeric) = -0.16807568013518490783354565347138
absolute error = 2e-32
relative error = 1.1899401498130964010978926628039e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 266.4
Order of pole (three term test) = -6999
Radius of convergence (six term test) for eq 1 = 2.553e+10
Order of pole (six term test) = 7.987e+19
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = -0.16681115039858659244109324873472
y[1] (numeric) = -0.16681115039858659244109324873474
absolute error = 2e-32
relative error = 1.1989606181727682635809992104166e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 266.2
Order of pole (three term test) = -6995
Radius of convergence (six term test) for eq 1 = 5.003e+10
Order of pole (six term test) = 3.060e+20
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = -0.16555514475561743495784699946755
y[1] (numeric) = -0.16555514475561743495784699946757
absolute error = 2e-32
relative error = 1.2080566888768572691839722820546e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 266.1
Order of pole (three term test) = -6991
Radius of convergence (six term test) for eq 1 = 2.349e+10
Order of pole (six term test) = 6.730e+19
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = -0.16430761876976878185456235273505
y[1] (numeric) = -0.16430761876976878185456235273507
absolute error = 2e-32
relative error = 1.2172290092052524816350081375460e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 265.9
Order of pole (three term test) = -6987
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = -0.16306852804489849622460239810636
y[1] (numeric) = -0.16306852804489849622460239810638
absolute error = 2e-32
relative error = 1.2264782321756959241276924575012e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 265.8
Order of pole (three term test) = -6984
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = -0.16183782822882712314378325339081
y[1] (numeric) = -0.16183782822882712314378325339083
absolute error = 2e-32
relative error = 1.2358050165948488463769139068093e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 265.6
Order of pole (three term test) = -6980
Radius of convergence (six term test) for eq 1 = 3.055e+10
Order of pole (six term test) = 1.130e+20
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = -0.16061547501685849362421627326992
y[1] (numeric) = -0.16061547501685849362421627326994
absolute error = 2e-32
relative error = 1.2452100271098263395675841313694e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 265.5
Order of pole (three term test) = -6976
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = -0.15940142415522591481799217667387
y[1] (numeric) = -0.15940142415522591481799217667389
absolute error = 2e-32
relative error = 1.2546939342602045150981462874005e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 265.3
Order of pole (three term test) = -6972
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = -0.15819563144446507876883736050089
y[1] (numeric) = -0.15819563144446507876883736050091
absolute error = 2e-32
relative error = 1.2642574145305045034183823251572e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 265.2
Order of pole (three term test) = -6968
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=24004972, alloc=4324584, time=0.85
x[1] = 1.67
y[1] (analytic) = -0.15699805274271480684415687584571
y[1] (numeric) = -0.15699805274271480684415687584573
absolute error = 2e-32
relative error = 1.2739011504031575700045602371299e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 265
Order of pole (three term test) = -6964
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = -0.15580864396894673200386144658671
y[1] (numeric) = -0.15580864396894673200386144658673
absolute error = 2e-32
relative error = 1.2836258304119556866084294896945e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 264.9
Order of pole (three term test) = -6960
Radius of convergence (six term test) for eq 1 = 2.019e+10
Order of pole (six term test) = 4.877e+19
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = -0.15462736110612500627378393582625
y[1] (numeric) = -0.15462736110612500627378393582628
absolute error = 3e-32
relative error = 1.9401482237939879060458923172745e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 264.7
Order of pole (three term test) = -6957
Radius of convergence (six term test) for eq 1 = 1.855e+10
Order of pole (six term test) = 4.105e+19
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = -0.15345416020429710618807670371751
y[1] (numeric) = -0.15345416020429710618807670371753
absolute error = 2e-32
relative error = 1.3033208075540951811406815864307e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 264.5
Order of pole (three term test) = -6953
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = -0.15228899738361679454452440312886
y[1] (numeric) = -0.15228899738361679454452440312888
absolute error = 2e-32
relative error = 1.3132925124997634337004399884705e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 264.4
Order of pole (three term test) = -6949
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = -0.15113182883730028257701184377505
y[1] (numeric) = -0.15113182883730028257701184377507
absolute error = 2e-32
relative error = 1.3233479773166004757455415812842e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 264.2
Order of pole (three term test) = -6945
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = -0.14998261083451662258828410634347
y[1] (numeric) = -0.1499826108345166225882841063435
absolute error = 3e-32
relative error = 2.0002318824213903537769846517050e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 264.1
Order of pole (three term test) = -6941
Radius of convergence (six term test) for eq 1 = 2.142e+10
Order of pole (six term test) = 5.421e+19
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = -0.14884129972321334720148186880219
y[1] (numeric) = -0.14884129972321334720148186880222
absolute error = 3e-32
relative error = 2.0155696070773553108268038336180e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 263.9
Order of pole (three term test) = -6937
Radius of convergence (six term test) for eq 1 = 2.617e+10
Order of pole (six term test) = 8.075e+19
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = -0.14770785193287835767860966986642
y[1] (numeric) = -0.14770785193287835767860966986644
absolute error = 2e-32
relative error = 1.3540241590601718674979999305512e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 263.8
Order of pole (three term test) = -6933
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = -0.14658222397723905021600403622931
y[1] (numeric) = -0.14658222397723905021600403622933
absolute error = 2e-32
relative error = 1.3644219235686827816620517897769e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 263.6
Order of pole (three term test) = -6930
Radius of convergence (six term test) for eq 1 = 2.070e+10
Order of pole (six term test) = 5.029e+19
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = -0.14546437245689965575894191986325
y[1] (numeric) = -0.14546437245689965575894191986327
absolute error = 2e-32
relative error = 1.3749071103940517789499423690465e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 263.5
Order of pole (three term test) = -6926
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = -0.14435425406191775567772175258403
y[1] (numeric) = -0.14435425406191775567772175258405
absolute error = 2e-32
relative error = 1.3854804716334453064413718649642e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 263.3
Order of pole (three term test) = -6922
Radius of convergence (six term test) for eq 1 = 5.171e+10
Order of pole (six term test) = 3.124e+20
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = -0.14325182557432092261383751862116
y[1] (numeric) = -0.14325182557432092261383751862118
absolute error = 2e-32
relative error = 1.3961427660566697736499922440129e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 263.2
Order of pole (three term test) = -6918
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = -0.1421570438705644229352520595717
y[1] (numeric) = -0.14215704387056442293525205957173
absolute error = 3e-32
relative error = 2.1103421387487021222317525417539e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 263
Order of pole (three term test) = -6914
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = -0.14106986592393090453228417382358
y[1] (numeric) = -0.1410698659239309045322841738236
absolute error = 2e-32
relative error = 1.4177372232553619082898006788851e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 262.9
Order of pole (three term test) = -6910
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=28006292, alloc=4324584, time=1.01
x[1] = 1.82
y[1] (analytic) = -0.13999024880687298113830282854031
y[1] (numeric) = -0.13999024880687298113830282854034
absolute error = 3e-32
relative error = 2.1430064062095670580082540437152e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 262.7
Order of pole (three term test) = -6906
Radius of convergence (six term test) for eq 1 = 2.787e+10
Order of pole (six term test) = 8.991e+19
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = -0.13891814969329961197034163770439
y[1] (numeric) = -0.13891814969329961197034163770442
absolute error = 3e-32
relative error = 2.1595450318214956017422749780507e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 262.6
Order of pole (three term test) = -6902
Radius of convergence (six term test) for eq 1 = 2.736e+10
Order of pole (six term test) = 8.647e+19
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = -0.13785352586080716325200088210822
y[1] (numeric) = -0.13785352586080716325200088210824
absolute error = 2e-32
relative error = 1.4508152675176628611087591191301e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 262.4
Order of pole (three term test) = -6899
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = -0.13679633469285602610270824316572
y[1] (numeric) = -0.13679633469285602610270824316574
absolute error = 2e-32
relative error = 1.4620274764601911964016602001463e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 262.3
Order of pole (three term test) = -6895
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = -0.13574653368089365335170060303866
y[1] (numeric) = -0.13574653368089365335170060303868
absolute error = 2e-32
relative error = 1.4733341218874160649123725442453e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 262.1
Order of pole (three term test) = -6891
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = -0.13470408042642486606012701260046
y[1] (numeric) = -0.13470408042642486606012701260048
absolute error = 2e-32
relative error = 1.4847360181434121544688858865787e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 261.9
Order of pole (three term test) = -6887
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = -0.13366893264303026890863805380436
y[1] (numeric) = -0.13366893264303026890863805380439
absolute error = 3e-32
relative error = 2.2443509802024481326375404593561e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 261.8
Order of pole (three term test) = -6883
Radius of convergence (six term test) for eq 1 = 2.541e+10
Order of pole (six term test) = 7.371e+19
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = -0.13264104815833360212892140943797
y[1] (numeric) = -0.132641048158333602128921409438
absolute error = 3e-32
relative error = 2.2617432850944455639410839966150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 261.6
Order of pole (three term test) = -6879
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = -0.13162038491591884632409062081129
y[1] (numeric) = -0.13162038491591884632409062081132
absolute error = 3e-32
relative error = 2.2792821962315691191156354753498e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 261.5
Order of pole (three term test) = -6875
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = -0.1306069009771978853328776762566
y[1] (numeric) = -0.13060690097719788533287767625663
absolute error = 3e-32
relative error = 2.2969689790922743817961421492693e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 261.3
Order of pole (three term test) = -6871
Radius of convergence (six term test) for eq 1 = 3.170e+10
Order of pole (six term test) = 1.139e+20
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = -0.12960055452322952124448469998359
y[1] (numeric) = -0.12960055452322952124448469998362
absolute error = 3e-32
relative error = 2.3148049103927884055248638573331e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 261.2
Order of pole (three term test) = -6868
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = -0.12860130385649062476300039214676
y[1] (numeric) = -0.12860130385649062476300039214679
absolute error = 3e-32
relative error = 2.3327912781877967496430087699753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 261
Order of pole (three term test) = -6864
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = -0.12760910740260019335078788544181
y[1] (numeric) = -0.12760910740260019335078788544184
absolute error = 3e-32
relative error = 2.3509293819720513855175230154987e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 260.9
Order of pole (three term test) = -6860
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = -0.12662392371199707894752706788881
y[1] (numeric) = -0.12662392371199707894752706788884
absolute error = 3e-32
relative error = 2.3692205327829078654913085169318e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 260.7
Order of pole (three term test) = -6856
Radius of convergence (six term test) for eq 1 = 2.239e+10
Order of pole (six term test) = 5.631e+19
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = -0.1256457114615721365639905432976
y[1] (numeric) = -0.12564571146157213656399054329763
absolute error = 3e-32
relative error = 2.3876660533038002258211105847809e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 260.6
Order of pole (three term test) = -6852
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=32007780, alloc=4390108, time=1.15
x[1] = 1.97
y[1] (analytic) = -0.12467442945625553468551203393797
y[1] (numeric) = -0.12467442945625553468551203393801
absolute error = 4e-32
relative error = 3.2083563706248828992741987042048e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 260.4
Order of pole (three term test) = -6848
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = -0.12371003663055995818785213165665
y[1] (numeric) = -0.12371003663055995818785213165668
absolute error = 3e-32
relative error = 2.4250255530673031948144312789547e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 260.3
Order of pole (three term test) = -6844
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = -0.12275249205008042436618079563696
y[1] (numeric) = -0.12275249205008042436618079563699
absolute error = 3e-32
relative error = 2.4439422368517482777623065145370e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 260.1
Order of pole (three term test) = -6840
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = -0.12180175491295142270459954547524
y[1] (numeric) = -0.12180175491295142270459954547527
absolute error = 3e-32
relative error = 2.4630186996435500757434758201916e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 260
Order of pole (three term test) = -6837
Radius of convergence (six term test) for eq 1 = 4.829e+10
Order of pole (six term test) = 2.591e+20
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = -0.12085778455126207916745810743713
y[1] (numeric) = -0.12085778455126207916745810743716
absolute error = 3e-32
relative error = 2.4822563239420823555487022574385e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 259.8
Order of pole (three term test) = -6833
Radius of convergence (six term test) for eq 1 = 3.338e+10
Order of pole (six term test) = 1.235e+20
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = -0.11992054043243003607313785931741
y[1] (numeric) = -0.11992054043243003607313785931744
absolute error = 3e-32
relative error = 2.5016565045338237094482617291129e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 259.6
Order of pole (three term test) = -6829
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = -0.11898998216053472901445341435182
y[1] (numeric) = -0.11898998216053472901445341435185
absolute error = 3e-32
relative error = 2.5212206486026405684381952503762e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 259.5
Order of pole (three term test) = -6825
Radius of convergence (six term test) for eq 1 = 2.834e+10
Order of pole (six term test) = 8.868e+19
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = -0.11806606947761073281585761798056
y[1] (numeric) = -0.11806606947761073281585761798059
absolute error = 3e-32
relative error = 2.5409501758410786461261800313274e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 259.3
Order of pole (three term test) = -6821
Radius of convergence (six term test) for eq 1 = 4.090e+10
Order of pole (six term test) = 1.842e+20
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = -0.11714876226490183916473533023783
y[1] (numeric) = -0.11714876226490183916473533023786
absolute error = 3e-32
relative error = 2.5608465185626720273334057621685e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 259.2
Order of pole (three term test) = -6817
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = -0.11623802054407651932076635185884
y[1] (numeric) = -0.11623802054407651932076635185887
absolute error = 3e-32
relative error = 2.5809111218152792018178603338671e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 259
Order of pole (three term test) = -6813
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = -0.11533380447840541619217373726719
y[1] (numeric) = -0.11533380447840541619217373726721
absolute error = 2e-32
relative error = 1.7340969623303036204267299900101e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 258.9
Order of pole (three term test) = -6809
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = -0.11443607437390150106921363007176
y[1] (numeric) = -0.11443607437390150106921363007178
absolute error = 2e-32
relative error = 1.7477006363092472804017432156920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 258.7
Order of pole (three term test) = -6805
Radius of convergence (six term test) for eq 1 = 5.407e+10
Order of pole (six term test) = 3.192e+20
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = -0.11354479068042352142208666220373
y[1] (numeric) = -0.11354479068042352142208666220375
absolute error = 2e-32
relative error = 1.7614194257745229139375687835386e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 258.6
Order of pole (three term test) = -6801
Radius of convergence (six term test) for eq 1 = 1.064e+11
Order of pole (six term test) = 1.234e+21
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = -0.11265991399274335740115558598682
y[1] (numeric) = -0.11265991399274335740115558598684
absolute error = 2e-32
relative error = 1.7752543288190543637934190022779e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 258.4
Order of pole (three term test) = -6798
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = -0.11178140505157789602055238104201
y[1] (numeric) = -0.11178140505157789602055238104204
absolute error = 3e-32
relative error = 2.6838095286203886164595077006259e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 258.3
Order of pole (three term test) = -6794
Radius of convergence (six term test) for eq 1 = 2.773e+10
Order of pole (six term test) = 8.341e+19
bytes used=36011760, alloc=4390108, time=1.30
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = -0.11090922474458602346058013925996
y[1] (numeric) = -0.11090922474458602346058013925999
absolute error = 3e-32
relative error = 2.7049147687297701095781329381320e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 258.1
Order of pole (three term test) = -6790
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = -0.11004333410733132748840626037928
y[1] (numeric) = -0.11004333410733132748840626037931
absolute error = 3e-32
relative error = 2.7261987510065213859954019291843e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 257.9
Order of pole (three term test) = -6786
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = -0.10918369432421109366906551679945
y[1] (numeric) = -0.10918369432421109366906551679948
absolute error = 3e-32
relative error = 2.7476630265795656732275826713502e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 257.8
Order of pole (three term test) = -6782
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = -0.10833026672935217081842176419004
y[1] (numeric) = -0.10833026672935217081842176419007
absolute error = 3e-32
relative error = 2.7693091603799657633032218104521e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 257.6
Order of pole (three term test) = -6778
Radius of convergence (six term test) for eq 1 = 6.266e+10
Order of pole (six term test) = 4.222e+20
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = -0.10748301280747427303516846429221
y[1] (numeric) = -0.10748301280747427303516846429225
absolute error = 4e-32
relative error = 3.7215183083534141132484920323651e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 257.5
Order of pole (three term test) = -6774
Radius of convergence (six term test) for eq 1 = 2.625e+10
Order of pole (six term test) = 7.392e+19
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = -0.10664189419472127763888913389901
y[1] (numeric) = -0.10664189419472127763888913389905
absolute error = 4e-32
relative error = 3.7508711095249826048147431557850e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 257.3
Order of pole (three term test) = -6770
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = -0.10580687267946107043437295382424
y[1] (numeric) = -0.10580687267946107043437295382427
absolute error = 3e-32
relative error = 2.8353545701028468995560921206215e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 257.2
Order of pole (three term test) = -6766
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = -0.1049779102030544819175267316456
y[1] (numeric) = -0.10497791020305448191752673164563
absolute error = 3e-32
relative error = 2.8577440665347810707690216730273e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 257
Order of pole (three term test) = -6762
Radius of convergence (six term test) for eq 1 = 3.477e+10
Order of pole (six term test) = 1.289e+20
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = -0.10415496886059385033409576029894
y[1] (numeric) = -0.10415496886059385033409576029897
absolute error = 3e-32
relative error = 2.8803234572662088063207799468794e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 256.9
Order of pole (three term test) = -6759
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = -0.10333801090161173989777110837224
y[1] (numeric) = -0.10333801090161173989777110837226
absolute error = 2e-32
relative error = 1.9353962617919970494310412682721e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 256.7
Order of pole (three term test) = -6755
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = -0.10252699873076033496790231405919
y[1] (numeric) = -0.10252699873076033496790231405922
absolute error = 3e-32
relative error = 2.9260585378863085674127576363602e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 256.6
Order of pole (three term test) = -6751
Radius of convergence (six term test) for eq 1 = 5.835e+10
Order of pole (six term test) = 3.606e+20
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = -0.10172189490846202357774950233917
y[1] (numeric) = -0.1017218949084620235777495023392
absolute error = 3e-32
relative error = 2.9492175727749213543530386663651e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 256.4
Order of pole (three term test) = -6747
Radius of convergence (six term test) for eq 1 = 2.912e+10
Order of pole (six term test) = 8.962e+19
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = -0.10092266215153167639080898000512
y[1] (numeric) = -0.10092266215153167639080898000515
absolute error = 3e-32
relative error = 2.9725731922287285781978510034853e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 256.2
Order of pole (three term test) = -6743
Radius of convergence (six term test) for eq 1 = 3.125e+10
Order of pole (six term test) = 1.030e+20
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = -0.10012926333377111994405680477866
y[1] (numeric) = -0.10012926333377111994405680477869
absolute error = 3e-32
relative error = 2.9961271062184818064895902245827e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 256.1
Order of pole (three term test) = -6739
Radius of convergence (six term test) for eq 1 = 6.081e+10
Order of pole (six term test) = 3.893e+20
TOP MAIN SOLVE Loop
bytes used=40012452, alloc=4390108, time=1.46
x[1] = 2.26
y[1] (analytic) = -0.099341661486536295911814973424912
y[1] (numeric) = -0.099341661486536295911814973424939
absolute error = 2.7e-32
relative error = 2.7178929359520819594206933057040e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 255.9
Order of pole (three term test) = -6735
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = -0.098559819799277591091207751429108
y[1] (numeric) = -0.098559819799277591091207751429135
absolute error = 2.7e-32
relative error = 2.7394530605866530337973080347474e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 255.8
Order of pole (three term test) = -6731
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = -0.097783701620053815868707858622811
y[1] (numeric) = -0.097783701620053815868707858622838
absolute error = 2.7e-32
relative error = 2.7611963499715526909478568834632e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 255.6
Order of pole (three term test) = -6727
Radius of convergence (six term test) for eq 1 = 3.025e+10
Order of pole (six term test) = 9.569e+19
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = -0.097013270456020302075953723274113
y[1] (numeric) = -0.09701327045602030207595372327414
absolute error = 2.7e-32
relative error = 2.7831243986605004759439767062340e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 255.5
Order of pole (three term test) = -6723
Radius of convergence (six term test) for eq 1 = 3.025e+10
Order of pole (six term test) = 9.554e+19
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = -0.096248489973891584380743066046067
y[1] (numeric) = -0.096248489973891584380743066046094
absolute error = 2.7e-32
relative error = 2.8052388154166402081130792628806e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 255.3
Order of pole (three term test) = -6719
Radius of convergence (six term test) for eq 1 = 3.301e+10
Order of pole (six term test) = 1.135e+20
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = -0.095489324000379122684781018840141
y[1] (numeric) = -0.095489324000379122684781018840163
absolute error = 2.2e-32
relative error = 2.3039224782775353056694388396367e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 255.2
Order of pole (three term test) = -6715
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = -0.094735736522604516412302114226203
y[1] (numeric) = -0.094735736522604516412302114226225
absolute error = 2.2e-32
relative error = 2.3222493229627942678804217028392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 255
Order of pole (three term test) = -6712
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = -0.093987691688488655072026890256781
y[1] (numeric) = -0.093987691688488655072026890256811
absolute error = 3.0e-32
relative error = 3.1919073083985862587696083031382e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 254.9
Order of pole (three term test) = -6708
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = -0.093245153807117243058000285592435
y[1] (numeric) = -0.093245153807117243058000285592461
absolute error = 2.6e-32
relative error = 2.7883486635436773211811613589161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 254.7
Order of pole (three term test) = -6704
Radius of convergence (six term test) for eq 1 = 4.231e+10
Order of pole (six term test) = 1.849e+20
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = -0.092508087349083130321647698895804
y[1] (numeric) = -0.092508087349083130321647698895834
absolute error = 3.0e-32
relative error = 3.2429597086786312356398064553945e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 254.5
Order of pole (three term test) = -6700
Radius of convergence (six term test) for eq 1 = 2.828e+10
Order of pole (six term test) = 8.247e+19
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = -0.091776456946805874296845163117692
y[1] (numeric) = -0.091776456946805874296845163117716
absolute error = 2.4e-32
relative error = 2.6150497413416742014886405943464e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 254.4
Order of pole (three term test) = -6696
Radius of convergence (six term test) for eq 1 = 4.933e+10
Order of pole (six term test) = 2.503e+20
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = -0.09105022739482895229091436644959
y[1] (numeric) = -0.091050227394828952290914366449615
absolute error = 2.5e-32
relative error = 2.7457372392482167294484494964528e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 254.2
Order of pole (three term test) = -6692
Radius of convergence (six term test) for eq 1 = 7.178e+10
Order of pole (six term test) = 5.290e+20
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = -0.090329363650095037466215141194639
y[1] (numeric) = -0.090329363650095037466215141194662
absolute error = 2.3e-32
relative error = 2.5462373552297023411320868603852e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 254.1
Order of pole (three term test) = -6688
Radius of convergence (six term test) for eq 1 = 3.549e+10
Order of pole (six term test) = 1.291e+20
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = -0.08961383083219974552842338090745
y[1] (numeric) = -0.089613830832199745528423380907472
absolute error = 2.2e-32
relative error = 2.4549781875963540114788549353806e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 253.9
Order of pole (three term test) = -6684
Radius of convergence (six term test) for eq 1 = 4.714e+10
Order of pole (six term test) = 2.272e+20
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = -0.088903594223624253307668775678096
y[1] (numeric) = -0.088903594223624253307668775678122
absolute error = 2.6e-32
relative error = 2.9245161826192004383488411633813e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 253.8
Order of pole (three term test) = -6680
Radius of convergence (six term test) for eq 1 = 4.765e+10
Order of pole (six term test) = 2.317e+20
TOP MAIN SOLVE Loop
bytes used=44013492, alloc=4390108, time=1.60
x[1] = 2.41
y[1] (analytic) = -0.088198619269947184566493579309495
y[1] (numeric) = -0.088198619269947184566493579309519
absolute error = 2.4e-32
relative error = 2.7211310334171824016033454512726e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 253.6
Order of pole (three term test) = -6676
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = -0.087498871580036152593121672564968
y[1] (numeric) = -0.087498871580036152593121672564996
absolute error = 2.8e-32
relative error = 3.2000412684623139251923221316552e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 253.5
Order of pole (three term test) = -6672
Radius of convergence (six term test) for eq 1 = 3.874e+10
Order of pole (six term test) = 1.525e+20
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = -0.086804316926219343438848690815511
y[1] (numeric) = -0.086804316926219343438848690815534
absolute error = 2.3e-32
relative error = 2.6496378077082504675656200459420e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 253.3
Order of pole (three term test) = -6668
Radius of convergence (six term test) for eq 1 = 6.007e+10
Order of pole (six term test) = 3.660e+20
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = -0.086114921244437518033542432632324
y[1] (numeric) = -0.086114921244437518033542432632351
absolute error = 2.7e-32
relative error = 3.1353451422617459667299097485398e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 253.1
Order of pole (three term test) = -6664
Radius of convergence (six term test) for eq 1 = 6.684e+10
Order of pole (six term test) = 4.521e+20
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = -0.085430650634376805862352781350995
y[1] (numeric) = -0.085430650634376805862352781351018
absolute error = 2.3e-32
relative error = 2.6922421670923025100715782064731e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 253
Order of pole (three term test) = -6661
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = -0.084751471359582657408857581611753
y[1] (numeric) = -0.084751471359582657408857581611778
absolute error = 2.5e-32
relative error = 2.9498012953580783439977318953652e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 252.8
Order of pole (three term test) = -6657
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = -0.084077349847555317164111821258835
y[1] (numeric) = -0.08407734984755531716411182125886
absolute error = 2.5e-32
relative error = 2.9734524274764489156027045524756e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 252.7
Order of pole (three term test) = -6653
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = -0.083408252689827173666529330407187
y[1] (numeric) = -0.083408252689827173666529330407215
absolute error = 2.8e-32
relative error = 3.3569819648571776702988672837041e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 252.5
Order of pole (three term test) = -6649
Radius of convergence (six term test) for eq 1 = 9.208e+10
Order of pole (six term test) = 8.514e+20
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = -0.082744146642022337773326904860512
y[1] (numeric) = -0.082744146642022337773326904860536
absolute error = 2.4e-32
relative error = 2.9005072834736796139713184808845e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 252.4
Order of pole (three term test) = -6645
Radius of convergence (six term test) for eq 1 = 3.547e+10
Order of pole (six term test) = 1.261e+20
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = -0.08208499862389879516952867446716
y[1] (numeric) = -0.082084998623898795169528674467185
absolute error = 2.5e-32
relative error = 3.0456234901758683595175439877920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 252.2
Order of pole (three term test) = -6641
Radius of convergence (six term test) for eq 1 = 5.675e+10
Order of pole (six term test) = 3.220e+20
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = -0.081430775719373473994402434001873
y[1] (numeric) = -0.081430775719373473994402434001897
absolute error = 2.4e-32
relative error = 2.9472886372480027871363876632457e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 252.1
Order of pole (three term test) = -6637
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = -0.080781445176530563406828561525371
y[1] (numeric) = -0.080781445176530563406828561525399
absolute error = 2.8e-32
relative error = 3.4661424958184384095236245918874e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 251.9
Order of pole (three term test) = -6633
Radius of convergence (six term test) for eq 1 = 6.342e+10
Order of pole (six term test) = 4.006e+20
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = -0.08013697440761341391964523592534
y[1] (numeric) = -0.080136974407613413919645235925364
absolute error = 2.4e-32
relative error = 2.9948722393641903955543594115487e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 251.7
Order of pole (three term test) = -6629
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = -0.079497330989000345407640125180843
y[1] (numeric) = -0.079497330989000345407640125180869
absolute error = 2.6e-32
relative error = 3.2705500520008013967039150343229e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 251.6
Order of pole (three term test) = -6625
Radius of convergence (six term test) for eq 1 = 1.724e+11
Order of pole (six term test) = 2.947e+21
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = -0.078862482661164683833747651948313
y[1] (numeric) = -0.078862482661164683833747651948341
absolute error = 2.8e-32
relative error = 3.5504842169758900718649020304662e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 251.4
Order of pole (three term test) = -6621
Radius of convergence (six term test) for eq 1 = 4.299e+10
Order of pole (six term test) = 1.829e+20
TOP MAIN SOLVE Loop
bytes used=48014316, alloc=4390108, time=1.76
x[1] = 2.56
y[1] (analytic) = -0.078232397328619342942351248972236
y[1] (numeric) = -0.078232397328619342942351248972266
absolute error = 3.0e-32
relative error = 3.8347284532242320958044264303476e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 251.3
Order of pole (three term test) = -6617
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = -0.077607043059846262436580269093602
y[1] (numeric) = -0.077607043059846262436580269093629
absolute error = 2.7e-32
relative error = 3.4790656795387877657988107811072e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 251.1
Order of pole (three term test) = -6613
Radius of convergence (six term test) for eq 1 = 7.440e+10
Order of pole (six term test) = 5.459e+20
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = -0.076986388087211009487339556331622
y[1] (numeric) = -0.076986388087211009487339556331646
absolute error = 2.4e-32
relative error = 3.1174342109429190969876412294131e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 251
Order of pole (three term test) = -6609
Radius of convergence (six term test) for eq 1 = 4.775e+10
Order of pole (six term test) = 2.244e+20
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = -0.076370400806862845814733715220247
y[1] (numeric) = -0.076370400806862845814733715220277
absolute error = 3.0e-32
relative error = 3.9282234587020945433758615451679e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 250.8
Order of pole (three term test) = -6605
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = -0.075759049778620558036774781573376
y[1] (numeric) = -0.075759049778620558036774781573402
absolute error = 2.6e-32
relative error = 3.4319332246082740229560927318351e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 250.7
Order of pole (three term test) = -6601
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = -0.075152303725844344495027483586668
y[1] (numeric) = -0.075152303725844344495027483586696
absolute error = 2.8e-32
relative error = 3.7257673566660070984090908239523e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 250.5
Order of pole (three term test) = -6597
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = -0.074550131535294047341395902981914
y[1] (numeric) = -0.074550131535294047341395902981943
absolute error = 2.9e-32
relative error = 3.8899998434302716336315160301556e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 250.3
Order of pole (three term test) = -6594
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = -0.073952502256974014303843441863639
y[1] (numeric) = -0.073952502256974014303843441863663
absolute error = 2.4e-32
relative error = 3.2453262928958843716840546939768e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 250.2
Order of pole (three term test) = -6590
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = -0.073359385103964870240727832094713
y[1] (numeric) = -0.07335938510396487024072783209474
absolute error = 2.7e-32
relative error = 3.6805106751829528728327087600527e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 250
Order of pole (three term test) = -6586
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = -0.072770749452242474342896566532256
y[1] (numeric) = -0.072770749452242474342896566532284
absolute error = 2.8e-32
relative error = 3.8476998259274026462728729574866e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 249.9
Order of pole (three term test) = -6582
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = -0.072186564840484334649006375337096
y[1] (numeric) = -0.072186564840484334649006375337121
absolute error = 2.5e-32
relative error = 3.4632483281680235282484848621851e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 249.7
Order of pole (three term test) = -6578
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = -0.071606800969863747401992618097381
y[1] (numeric) = -0.071606800969863747401992618097409
absolute error = 2.8e-32
relative error = 3.9102431083025210696316724299481e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 249.6
Order of pole (three term test) = -6574
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = -0.071031427703831924692518628200816
y[1] (numeric) = -0.071031427703831924692518628200842
absolute error = 2.6e-32
relative error = 3.6603515993523217374827140854764e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 249.4
Order of pole (three term test) = -6570
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = -0.070460415067888369807887457414605
y[1] (numeric) = -0.070460415067888369807887457414634
absolute error = 2.9e-32
relative error = 4.1157861434762481634759817867533e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 249.3
Order of pole (three term test) = -6566
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = -0.069893733249339755731613768890206
y[1] (numeric) = -0.069893733249339755731613768890232
absolute error = 2.6e-32
relative error = 3.7199329312182085279672482548670e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 249.1
Order of pole (three term test) = -6562
Radius of convergence (six term test) for eq 1 = 5.487e+10
Order of pole (six term test) = 2.895e+20
bytes used=52015288, alloc=4390108, time=1.91
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = -0.069331352597047558318954677142431
y[1] (numeric) = -0.069331352597047558318954677142459
absolute error = 2.8e-32
relative error = 4.0385769137860965777893889654304e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 248.9
Order of pole (three term test) = -6558
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = -0.06877324362116469180651611804696
y[1] (numeric) = -0.068773243621164691806516118046989
absolute error = 2.9e-32
relative error = 4.2167561791538599910530624946472e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 248.8
Order of pole (three term test) = -6554
Radius of convergence (six term test) for eq 1 = 6.008e+10
Order of pole (six term test) = 3.457e+20
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = -0.068219376992861390498924862781868
y[1] (numeric) = -0.068219376992861390498924862781894
absolute error = 2.6e-32
relative error = 3.8112338672809473222804586606171e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 248.6
Order of pole (three term test) = -6550
Radius of convergence (six term test) for eq 1 = 1.978e+11
Order of pole (six term test) = 3.740e+21
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = -0.067669723544040576711832513748314
y[1] (numeric) = -0.06766972354404057671183251374834
absolute error = 2.6e-32
relative error = 3.8421909590156326607121823980954e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 248.5
Order of pole (three term test) = -6546
Radius of convergence (six term test) for eq 1 = 3.583e+10
Order of pole (six term test) = 1.225e+20
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = -0.067124254267042951337551526835848
y[1] (numeric) = -0.067124254267042951337551526835877
absolute error = 2.9e-32
relative error = 4.3203459489662569209158880317957e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 248.3
Order of pole (three term test) = -6542
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = -0.066582940314342039736777032691134
y[1] (numeric) = -0.06658294031434203973677703269116
absolute error = 2.6e-32
relative error = 3.9049041507107445884633143827874e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 248.2
Order of pole (three term test) = -6538
Radius of convergence (six term test) for eq 1 = 6.090e+10
Order of pole (six term test) = 3.525e+20
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = -0.066045752998229422046492180032814
y[1] (numeric) = -0.066045752998229422046492180032841
absolute error = 2.7e-32
relative error = 4.0880751258485652467329909346148e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 248
Order of pole (three term test) = -6534
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = -0.065512663790490373429666667710763
y[1] (numeric) = -0.06551266379049037342966666771079
absolute error = 2.7e-32
relative error = 4.1213405833024974618169396449059e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 247.8
Order of pole (three term test) = -6530
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = -0.064983644322070136276123323056813
y[1] (numeric) = -0.064983644322070136276123323056843
absolute error = 3.0e-32
relative error = 4.6165462575959624192672429524392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 247.7
Order of pole (three term test) = -6526
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = -0.064458666382731042895358671474977
y[1] (numeric) = -0.064458666382731042895358671475006
absolute error = 2.9e-32
relative error = 4.4990071354888155308815326822342e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 247.5
Order of pole (three term test) = -6522
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = -0.063937701920700703820560384657685
y[1] (numeric) = -0.063937701920700703820560384657715
absolute error = 3.0e-32
relative error = 4.6920672934425706134475088950220e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 247.4
Order of pole (three term test) = -6518
Radius of convergence (six term test) for eq 1 = 4.222e+10
Order of pole (six term test) = 1.679e+20
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = -0.063420723042311473467974474582547
y[1] (numeric) = -0.063420723042311473467974474582577
absolute error = 3.0e-32
relative error = 4.7303150391371823485264661948761e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 247.2
Order of pole (three term test) = -6514
Radius of convergence (six term test) for eq 1 = 4.383e+10
Order of pole (six term test) = 1.805e+20
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = -0.062907702011631401566552439288916
y[1] (numeric) = -0.062907702011631401566552439288943
absolute error = 2.7e-32
relative error = 4.2920022726323399643887416410863e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 247.1
Order of pole (three term test) = -6510
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = -0.062398611250086875488874642174957
y[1] (numeric) = -0.062398611250086875488874642174987
absolute error = 3.0e-32
relative error = 4.8077993081870443083729701450169e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 246.9
Order of pole (three term test) = -6506
Radius of convergence (six term test) for eq 1 = 3.572e+10
Order of pole (six term test) = 1.195e+20
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = -0.061893423336077155375129370651819
y[1] (numeric) = -0.061893423336077155375129370651848
absolute error = 2.9e-32
relative error = 4.6854735829575844699088588023358e-29 %
Correct digits = 31
h = 0.01
bytes used=56016980, alloc=4390108, time=2.06
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 246.7
Order of pole (three term test) = -6502
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = -0.061392111004581000746862516048042
y[1] (numeric) = -0.061392111004581000746862516048071
absolute error = 2.9e-32
relative error = 4.7237339660524227807304755526971e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 246.6
Order of pole (three term test) = -6498
Radius of convergence (six term test) for eq 1 = 3.861e+10
Order of pole (six term test) = 1.391e+20
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = -0.060894647146755584155742699869714
y[1] (numeric) = -0.060894647146755584155742699869742
absolute error = 2.8e-32
relative error = 4.5981053034957632675965867063230e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 246.4
Order of pole (three term test) = -6494
Radius of convergence (six term test) for eq 1 = 2.996e+11
Order of pole (six term test) = 8.357e+21
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = -0.060401004809527884304159729033937
y[1] (numeric) = -0.060401004809527884304159729033966
absolute error = 2.9e-32
relative error = 4.8012446301928787887905150797960e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 246.3
Order of pole (three term test) = -6491
Radius of convergence (six term test) for eq 1 = 3.606e+10
Order of pole (six term test) = 1.208e+20
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = -0.05991115719517874800854593487176
y[1] (numeric) = -0.059911157195178748008545934871789
absolute error = 2.9e-32
relative error = 4.8405007276897878676429444960029e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 246.1
Order of pole (three term test) = -6487
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = -0.059425077660919807352342253300909
y[1] (numeric) = -0.059425077660919807352342253300938
absolute error = 2.9e-32
relative error = 4.8800945899430441420149207467566e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 246
Order of pole (three term test) = -6483
Radius of convergence (six term test) for eq 1 = 4.930e+10
Order of pole (six term test) = 2.251e+20
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = -0.058942739718463435392992350814033
y[1] (numeric) = -0.058942739718463435392992350814062
absolute error = 2.9e-32
relative error = 4.9200291907903859939548292122113e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 245.8
Order of pole (three term test) = -6479
Radius of convergence (six term test) for eq 1 = 3.565e+11
Order of pole (six term test) = 1.174e+22
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = -0.058464117033585920845713629427383
y[1] (numeric) = -0.058464117033585920845713629427411
absolute error = 2.8e-32
relative error = 4.7892624434770512426285461863034e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 245.7
Order of pole (three term test) = -6475
Radius of convergence (six term test) for eq 1 = 2.591e+11
Order of pole (six term test) = 6.195e+21
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = -0.057989183425684039265544837310934
y[1] (numeric) = -0.057989183425684039265544837310964
absolute error = 3.0e-32
relative error = 5.1733785902411369557709212875411e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 245.5
Order of pole (three term test) = -6471
Radius of convergence (six term test) for eq 1 = 5.785e+10
Order of pole (six term test) = 3.081e+20
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = -0.05751791286732519538779382717967
y[1] (numeric) = -0.057517912867325195387793827179699
absolute error = 2.9e-32
relative error = 5.0419075648473911255947663033030e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 245.3
Order of pole (three term test) = -6467
Radius of convergence (six term test) for eq 1 = 6.568e+10
Order of pole (six term test) = 3.965e+20
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = -0.05705027948379130846499949777876
y[1] (numeric) = -0.057050279483791308464999497778787
absolute error = 2.7e-32
relative error = 4.7326674372683896601843058079009e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 245.2
Order of pole (three term test) = -6463
Radius of convergence (six term test) for eq 1 = 5.446e+10
Order of pole (six term test) = 2.721e+20
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = -0.056586257552616609655379007825856
y[1] (numeric) = -0.056586257552616609655379007825883
absolute error = 2.7e-32
relative error = 4.7714765329539788310926787271342e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 245
Order of pole (three term test) = -6459
Radius of convergence (six term test) for eq 1 = 9.751e+10
Order of pole (six term test) = 8.707e+20
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = -0.056125821503119517772960904431163
y[1] (numeric) = -0.05612582150311951777296090443119
absolute error = 2.7e-32
relative error = 4.8106200099893982911212570566120e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 244.9
Order of pole (three term test) = -6455
Radius of convergence (six term test) for eq 1 = 4.111e+10
Order of pole (six term test) = 1.545e+20
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = -0.055668945915928757002718781136344
y[1] (numeric) = -0.055668945915928757002718781136371
absolute error = 2.7e-32
relative error = 4.8501008157717590745127351087899e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 244.7
Order of pole (three term test) = -6451
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = -0.055215605522503877514536309949837
y[1] (numeric) = -0.055215605522503877514536309949865
absolute error = 2.8e-32
relative error = 5.0710301435684185112597349135654e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 244.6
Order of pole (three term test) = -6447
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=60018832, alloc=4455632, time=2.21
x[1] = 3
y[1] (analytic) = -0.054765775204650337277276657215067
y[1] (numeric) = -0.054765775204650337277276657215096
absolute error = 2.9e-32
relative error = 5.2952779161131124044266123634807e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 244.4
Order of pole (three term test) = -6443
Radius of convergence (six term test) for eq 1 = 5.170e+10
Order of pole (six term test) = 2.430e+20
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = -0.054319429994029300778126850819468
y[1] (numeric) = -0.054319429994029300778126850819497
absolute error = 2.9e-32
relative error = 5.3387894540107712109425059620763e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 244.2
Order of pole (three term test) = -6439
Radius of convergence (six term test) for eq 1 = 4.690e+10
Order of pole (six term test) = 1.996e+20
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = -0.053876545071662307792275780226237
y[1] (numeric) = -0.053876545071662307792275780226266
absolute error = 2.9e-32
relative error = 5.3826762576231456059410457290410e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 244.1
Order of pole (three term test) = -6435
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = -0.053437095767430962823403986271071
y[1] (numeric) = -0.0534370957674309628234039862711
absolute error = 2.9e-32
relative error = 5.4269416373625279228306605358215e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 243.9
Order of pole (three term test) = -6431
Radius of convergence (six term test) for eq 1 = 6.901e+10
Order of pole (six term test) = 4.306e+20
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = -0.053001057559571793345960614651822
y[1] (numeric) = -0.053001057559571793345960614651849
absolute error = 2.7e-32
relative error = 5.0942379724504007915321184138301e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 243.8
Order of pole (three term test) = -6427
Radius of convergence (six term test) for eq 1 = 9.029e+10
Order of pole (six term test) = 7.358e+20
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = -0.052568406074166422525329754966104
y[1] (numeric) = -0.052568406074166422525329754966133
absolute error = 2.9e-32
relative error = 5.5166215157988986340375964155613e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 243.6
Order of pole (three term test) = -6423
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = -0.052139117084627199671302200085871
y[1] (numeric) = -0.052139117084627199671302200085899
absolute error = 2.8e-32
relative error = 5.3702482062657665024111262843118e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 243.4
Order of pole (three term test) = -6419
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = -0.051713166511178429293332153328767
y[1] (numeric) = -0.051713166511178429293332153328797
absolute error = 3.0e-32
relative error = 5.8012305228911355638131562710304e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 243.3
Order of pole (three term test) = -6415
Radius of convergence (six term test) for eq 1 = 6.242e+10
Order of pole (six term test) = 3.497e+20
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = -0.051290530420333337272439615438391
y[1] (numeric) = -0.051290530420333337272439615438419
absolute error = 2.8e-32
relative error = 5.4590973753899478462618178430373e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 243.1
Order of pole (three term test) = -6411
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = -0.050871185024366910343891386852752
y[1] (numeric) = -0.05087118502436691034389138685278
absolute error = 2.8e-32
relative error = 5.5040982407994256796351429401602e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 243
Order of pole (three term test) = -6407
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = -0.050455106680784742796535303239736
y[1] (numeric) = -0.050455106680784742796535303239765
absolute error = 2.9e-32
relative error = 5.7476838139447086494643862237183e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 242.8
Order of pole (three term test) = -6403
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = -0.050042271891788022038457095912319
y[1] (numeric) = -0.050042271891788022038457095912349
absolute error = 3.0e-32
relative error = 5.9949316579535679845117216501235e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 242.7
Order of pole (three term test) = -6399
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = -0.049632657303734782454065817198494
y[1] (numeric) = -0.049632657303734782454065817198524
absolute error = 3.0e-32
relative error = 6.0444073780717248314478570500760e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 242.5
Order of pole (three term test) = -6395
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = -0.04922623970659755478438578971336
y[1] (numeric) = -0.049226239706597554784385789713388
absolute error = 2.8e-32
relative error = 5.6880233320456722688075659275997e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 242.3
Order of pole (three term test) = -6391
Radius of convergence (six term test) for eq 1 = 1.323e+11
Order of pole (six term test) = 1.556e+21
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = -0.048822996033417536099839176219681
y[1] (numeric) = -0.04882299603341753609983917621971
absolute error = 2.9e-32
relative error = 5.9398239264445328080921405391883e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 242.2
Order of pole (three term test) = -6387
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=64021228, alloc=4455632, time=2.36
x[1] = 3.15
y[1] (analytic) = -0.048422903359755403302747066360455
y[1] (numeric) = -0.048422903359755403302747066360483
absolute error = 2.8e-32
relative error = 5.7823876837734157898640924937865e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 242
Order of pole (three term test) = -6383
Radius of convergence (six term test) for eq 1 = 6.786e+10
Order of pole (six term test) = 4.076e+20
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = -0.048025938903138890994766817864003
y[1] (numeric) = -0.04802593890313889099476681786403
absolute error = 2.7e-32
relative error = 5.6219619265445172657696340087248e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 241.9
Order of pole (three term test) = -6379
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = -0.047632080022507252472132432586239
y[1] (numeric) = -0.047632080022507252472132432586268
absolute error = 2.9e-32
relative error = 6.0883337419438398519541285331987e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 241.7
Order of pole (three term test) = -6375
Radius of convergence (six term test) for eq 1 = 6.625e+10
Order of pole (six term test) = 3.870e+20
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = -0.047241304217652720568490875210256
y[1] (numeric) = -0.047241304217652720568490875210284
absolute error = 2.8e-32
relative error = 5.9270167205792771069779411500704e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 241.6
Order of pole (three term test) = -6371
Radius of convergence (six term test) for eq 1 = 1.533e+11
Order of pole (six term test) = 2.069e+21
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = -0.046853589128659083050953005632225
y[1] (numeric) = -0.046853589128659083050953005632253
absolute error = 2.8e-32
relative error = 5.9760629912710681627469134647875e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 241.4
Order of pole (three term test) = -6367
Radius of convergence (six term test) for eq 1 = 5.150e+11
Order of pole (six term test) = 2.330e+22
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = -0.046468912535337485289330358844645
y[1] (numeric) = -0.046468912535337485289330358844672
absolute error = 2.7e-32
relative error = 5.8103360993153720471590098303073e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 241.2
Order of pole (three term test) = -6363
Radius of convergence (six term test) for eq 1 = 2.029e+11
Order of pole (six term test) = 3.611e+21
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = -0.046087252356659570961040090634769
y[1] (numeric) = -0.046087252356659570961040090634796
absolute error = 2.7e-32
relative error = 5.8584529602790524523232131180407e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 241.1
Order of pole (three term test) = -6359
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = -0.045708586650188069624466240332695
y[1] (numeric) = -0.045708586650188069624466240332723
absolute error = 2.8e-32
relative error = 6.1257636807470162704099487730361e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 240.9
Order of pole (three term test) = -6355
Radius of convergence (six term test) for eq 1 = 1.352e+11
Order of pole (six term test) = 1.599e+21
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = -0.04533289361150493809130672120713
y[1] (numeric) = -0.045332893611504938091306721207157
absolute error = 2.7e-32
relative error = 5.9559401240488491031882491097717e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 240.8
Order of pole (three term test) = -6351
Radius of convergence (six term test) for eq 1 = 6.965e+11
Order of pole (six term test) = 4.233e+22
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = -0.044960151573637160653257211739887
y[1] (numeric) = -0.044960151573637160653257211739914
absolute error = 2.7e-32
relative error = 6.0053178325652538334867935244729e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 240.6
Order of pole (three term test) = -6347
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = -0.044590339006480311369934810557736
y[1] (numeric) = -0.044590339006480311369934810557763
absolute error = 2.7e-32
relative error = 6.0551232849061971861318513658537e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 240.5
Order of pole (three term test) = -6343
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = -0.044223434516219979802879653366151
y[1] (numeric) = -0.044223434516219979802879653366179
absolute error = 2.8e-32
relative error = 6.3314847221398746333157398568906e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 240.3
Order of pole (three term test) = -6339
Radius of convergence (six term test) for eq 1 = 6.600e+10
Order of pole (six term test) = 3.781e+20
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = -0.043859416844751159784449635604978
y[1] (numeric) = -0.043859416844751159784449635605006
absolute error = 2.8e-32
relative error = 6.3840338094579288369292572829824e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 240.1
Order of pole (three term test) = -6335
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = -0.043498264869095699040104098021788
y[1] (numeric) = -0.043498264869095699040104098021816
absolute error = 2.8e-32
relative error = 6.4370383702116856409005810481142e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 240
Order of pole (three term test) = -6331
Radius of convergence (six term test) for eq 1 = 5.364e+10
Order of pole (six term test) = 2.489e+20
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = -0.04313995760081790573762311711766
y[1] (numeric) = -0.043139957600817905737623117117688
absolute error = 2.8e-32
relative error = 6.4905024383865268522096745753988e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 239.8
Order of pole (three term test) = -6327
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=68023752, alloc=4455632, time=2.52
x[1] = 3.3
y[1] (analytic) = -0.042784474185438406316900297500158
y[1] (numeric) = -0.042784474185438406316900297500185
absolute error = 2.7e-32
relative error = 6.3107004384289910390008279911745e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 239.7
Order of pole (three term test) = -6323
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = -0.04243179390184634725875313500178
y[1] (numeric) = -0.042431793901846347258753135001808
absolute error = 2.8e-32
relative error = 6.5988254149164378549684300827249e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 239.5
Order of pole (three term test) = -6319
Radius of convergence (six term test) for eq 1 = 6.481e+10
Order of pole (six term test) = 3.615e+20
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = -0.042081896161710031780394553883857
y[1] (numeric) = -0.042081896161710031780394553883884
absolute error = 2.7e-32
relative error = 6.4160606965631639043504681106394e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 239.3
Order of pole (three term test) = -6315
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = -0.041734760508886080798484516553766
y[1] (numeric) = -0.041734760508886080798484516553794
absolute error = 2.8e-32
relative error = 6.7090357434873255425402760862263e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 239.2
Order of pole (three term test) = -6311
Radius of convergence (six term test) for eq 1 = 6.896e+10
Order of pole (six term test) = 4.079e+20
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = -0.041390366618827205877717963286282
y[1] (numeric) = -0.04139036661882720587771796328631
absolute error = 2.8e-32
relative error = 6.7648591417075441947235525964452e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 239
Order of pole (three term test) = -6307
Radius of convergence (six term test) for eq 1 = 5.667e+10
Order of pole (six term test) = 2.749e+20
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = -0.041048694297988680283394924794674
y[1] (numeric) = -0.041048694297988680283394924794701
absolute error = 2.7e-32
relative error = 6.5775539177924488546250522361823e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 238.9
Order of pole (three term test) = -6303
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = -0.040709723483233592680054437771227
y[1] (numeric) = -0.040709723483233592680054437771254
absolute error = 2.7e-32
relative error = 6.6323221308835520418968931633249e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 238.7
Order of pole (three term test) = -6299
Radius of convergence (six term test) for eq 1 = 6.195e+10
Order of pole (six term test) = 3.275e+20
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = -0.040373434241236966464733626417377
y[1] (numeric) = -0.040373434241236966464733626417405
absolute error = 2.8e-32
relative error = 6.9352534720470022624127011002412e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 238.6
Order of pole (three term test) = -6295
Radius of convergence (six term test) for eq 1 = 6.002e+10
Order of pole (six term test) = 3.068e+20
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = -0.04003980676788882619243845861026
y[1] (numeric) = -0.040039806767888826192438458610287
absolute error = 2.7e-32
relative error = 6.7432892862144113618524894667034e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 238.4
Order of pole (three term test) = -6291
Radius of convergence (six term test) for eq 1 = 8.806e+10
Order of pole (six term test) = 6.594e+20
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = -0.039708821387696291042688390025546
y[1] (numeric) = -0.039708821387696291042688390025574
absolute error = 2.8e-32
relative error = 7.0513299114628849445686438630769e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 238.2
Order of pole (three term test) = -6287
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = -0.039380458553184773789232155135719
y[1] (numeric) = -0.039380458553184773789232155135746
absolute error = 2.7e-32
relative error = 6.8561923837264352576304604399212e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 238.1
Order of pole (three term test) = -6283
Radius of convergence (six term test) for eq 1 = 3.238e+11
Order of pole (six term test) = 8.884e+21
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = -0.039054698844298362269938724810878
y[1] (numeric) = -0.039054698844298362269938724810906
absolute error = 2.8e-32
relative error = 7.1694318042572104708023934521923e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 237.9
Order of pole (three term test) = -6279
Radius of convergence (six term test) for eq 1 = 3.757e+10
Order of pole (six term test) = 1.194e+20
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = -0.03873152296779945891016185029374
y[1] (numeric) = -0.038731522967799458910161850293767
absolute error = 2.7e-32
relative error = 6.9710659254084094439323776207608e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 237.8
Order of pole (three term test) = -6275
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = -0.038410911756667752430278084209698
y[1] (numeric) = -0.038410911756667752430278084209725
absolute error = 2.7e-32
relative error = 7.0292525652721764441029699785521e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 237.6
Order of pole (three term test) = -6271
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = -0.038092846169498594466329608519083
y[1] (numeric) = -0.03809284616949859446632960851911
absolute error = 2.7e-32
relative error = 7.0879450382521505051543178739402e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 237.4
Order of pole (three term test) = -6267
NO COMPLEX POLE (six term test) for Equation 1
bytes used=72024960, alloc=4455632, time=2.66
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = -0.037777307289900852451490929142885
y[1] (numeric) = -0.037777307289900852451490929142912
absolute error = 2.7e-32
relative error = 7.1471478347579341774374560781832e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 237.3
Order of pole (three term test) = -6263
Radius of convergence (six term test) for eq 1 = 9.100e+10
Order of pole (six term test) = 6.960e+20
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = -0.037464276325894308745152223607566
y[1] (numeric) = -0.037464276325894308745152223607593
absolute error = 2.7e-32
relative error = 7.2068654857049300596892913156926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 237.1
Order of pole (three term test) = -6259
Radius of convergence (six term test) for eq 1 = 5.796e+10
Order of pole (six term test) = 2.818e+20
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = -0.03715373460930667465550490141511
y[1] (numeric) = -0.037153734609306674655504901415138
absolute error = 2.8e-32
relative error = 7.5362545096573557145864246247316e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 237
Order of pole (three term test) = -6255
Radius of convergence (six term test) for eq 1 = 5.662e+10
Order of pole (six term test) = 2.685e+20
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = -0.036845663595170286680363110870559
y[1] (numeric) = -0.036845663595170286680363110870586
absolute error = 2.7e-32
relative error = 7.3278636793338003774360529484176e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 236.8
Order of pole (three term test) = -6250
Radius of convergence (six term test) for eq 1 = 1.534e+11
Order of pole (six term test) = 1.967e+21
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = -0.036540044861118550989298119352908
y[1] (numeric) = -0.036540044861118550989298119352935
absolute error = 2.7e-32
relative error = 7.3891534897183718195905866825155e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 236.6
Order of pole (three term test) = -6246
Radius of convergence (six term test) for eq 1 = 6.182e+10
Order of pole (six term test) = 3.190e+20
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = -0.036236860106782200887743550836343
y[1] (numeric) = -0.036236860106782200887743550836371
absolute error = 2.8e-32
relative error = 7.7269387903615398751524248484242e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 236.5
Order of pole (three term test) = -6242
Radius of convergence (six term test) for eq 1 = 9.336e+10
Order of pole (six term test) = 7.263e+20
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = -0.035936091153185430740294416559987
y[1] (numeric) = -0.035936091153185430740294416560015
absolute error = 2.8e-32
relative error = 7.7916097999206117504227683598956e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 236.3
Order of pole (three term test) = -6238
Radius of convergence (six term test) for eq 1 = 1.627e+11
Order of pole (six term test) = 2.203e+21
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = -0.035637719942141968585720903201987
y[1] (numeric) = -0.035637719942141968585720903202015
absolute error = 2.8e-32
relative error = 7.8568438288022218330444205960535e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 236.2
Order of pole (three term test) = -6234
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = -0.035341728535651148450001280697606
y[1] (numeric) = -0.035341728535651148450001280697634
absolute error = 2.8e-32
relative error = 7.9226458807058227384143244793415e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 236
Order of pole (three term test) = -6230
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = -0.03504809911529404215570242667988
y[1] (numeric) = -0.035048099115294042155702426679908
absolute error = 2.8e-32
relative error = 7.9890210045033676583713308632399e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 235.9
Order of pole (three term test) = -6226
Radius of convergence (six term test) for eq 1 = 1.022e+11
Order of pole (six term test) = 8.655e+20
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = -0.034756813981629709236059742249032
y[1] (numeric) = -0.03475681398162970923605974224906
absolute error = 2.8e-32
relative error = 8.0559742946517074372691465250293e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 235.7
Order of pole (three term test) = -6222
Radius of convergence (six term test) for eq 1 = 1.032e+11
Order of pole (six term test) = 8.805e+20
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = -0.034467855553591622389892062091893
y[1] (numeric) = -0.034467855553591622389892062091921
absolute error = 2.8e-32
relative error = 8.1235108916087881306316385616100e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 235.5
Order of pole (three term test) = -6218
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = -0.034181206367884324758795914620488
y[1] (numeric) = -0.034181206367884324758795914620516
absolute error = 2.8e-32
relative error = 8.1916359822536843199373196504001e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 235.4
Order of pole (three term test) = -6214
Radius of convergence (six term test) for eq 1 = 7.986e+10
Order of pole (six term test) = 5.254e+20
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = -0.033896849078380374170664469168011
y[1] (numeric) = -0.033896849078380374170664469168039
absolute error = 2.8e-32
relative error = 8.2603548003105037866268433960144e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 235.2
Order of pole (three term test) = -6210
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
bytes used=76027044, alloc=4455632, time=2.81
y[1] (analytic) = -0.033614766455517628373239917409908
y[1] (numeric) = -0.033614766455517628373239917409936
absolute error = 2.8e-32
relative error = 8.3296726267761994810676356414238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 235.1
Order of pole (three term test) = -6206
Radius of convergence (six term test) for eq 1 = 2.235e+11
Order of pole (six term test) = 4.100e+21
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = -0.033334941385696924177906936171374
y[1] (numeric) = -0.033334941385696924177906936171403
absolute error = 2.9e-32
relative error = 8.6995803185791938100430181235766e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 234.9
Order of pole (three term test) = -6202
Radius of convergence (six term test) for eq 1 = 6.112e+10
Order of pole (six term test) = 3.062e+20
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = -0.033057356870680202347045156623923
y[1] (numeric) = -0.033057356870680202347045156623952
absolute error = 2.9e-32
relative error = 8.7726311917336552525659084337669e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 234.7
Order of pole (three term test) = -6198
Radius of convergence (six term test) for eq 1 = 1.505e+11
Order of pole (six term test) = 1.854e+21
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = -0.032781996026989128987758901638798
y[1] (numeric) = -0.032781996026989128987758901638827
absolute error = 2.9e-32
relative error = 8.8463191735257838100775773098569e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 234.6
Order of pole (three term test) = -6194
Radius of convergence (six term test) for eq 1 = 5.559e+10
Order of pole (six term test) = 2.525e+20
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = -0.032508842085304263160474289527232
y[1] (numeric) = -0.032508842085304263160474289527261
absolute error = 2.9e-32
relative error = 8.9206499339173794770863963886895e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 234.4
Order of pole (three term test) = -6190
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = -0.032237878389864819372521306020379
y[1] (numeric) = -0.032237878389864819372521306020407
absolute error = 2.8e-32
relative error = 8.6854350839672021780517718964864e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 234.3
Order of pole (three term test) = -6186
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = -0.031969088397869072604188478655587
y[1] (numeric) = -0.031969088397869072604188478655616
absolute error = 2.9e-32
relative error = 9.0712627270075740495492004469674e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 234.1
Order of pole (three term test) = -6182
Radius of convergence (six term test) for eq 1 = 6.311e+10
Order of pole (six term test) = 3.238e+20
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = -0.031702455678875452507639872093658
y[1] (numeric) = -0.031702455678875452507639872093687
absolute error = 2.9e-32
relative error = 9.1475563577000121387213147854864e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 233.9
Order of pole (three term test) = -6178
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = -0.031437963914204372427310412600276
y[1] (numeric) = -0.031437963914204372427310412600304
absolute error = 2.8e-32
relative error = 8.9064292065520745302675138243746e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 233.8
Order of pole (three term test) = -6174
Radius of convergence (six term test) for eq 1 = 5.669e+10
Order of pole (six term test) = 2.605e+20
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = -0.031175596896340837913740796745567
y[1] (numeric) = -0.031175596896340837913740796745596
absolute error = 2.9e-32
relative error = 9.3021474765744762810643424653121e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 233.6
Order of pole (three term test) = -6170
Radius of convergence (six term test) for eq 1 = 6.258e+10
Order of pole (six term test) = 3.169e+20
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = -0.03091533852833787844107476239294
y[1] (numeric) = -0.030915338528337878441074762392968
absolute error = 2.8e-32
relative error = 9.0569928497902113405926865791974e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 233.5
Order of pole (three term test) = -6166
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = -0.030657172823220845091419154899419
y[1] (numeric) = -0.030657172823220845091419154899448
absolute error = 2.9e-32
relative error = 9.4594502132415671398220281284850e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 233.3
Order of pole (three term test) = -6162
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = -0.030401083903392616036763369913487
y[1] (numeric) = -0.030401083903392616036763369913515
absolute error = 2.8e-32
relative error = 9.2101979287900762908332361499110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 233.1
Order of pole (three term test) = -6158
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = -0.030147056000039750730974234095278
y[1] (numeric) = -0.030147056000039750730974234095306
absolute error = 2.8e-32
relative error = 9.2878057479188283901543664350113e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 233
Order of pole (three term test) = -6154
Radius of convergence (six term test) for eq 1 = 3.454e+10
Order of pole (six term test) = 9.587e+19
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = -0.029895073452539632820332480736991
y[1] (numeric) = -0.029895073452539632820332480737019
absolute error = 2.8e-32
relative error = 9.3660917222537737589642866963533e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 232.8
Order of pole (three term test) = -6150
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=80027828, alloc=4455632, time=2.96
x[1] = 3.74
y[1] (analytic) = -0.029645120707868640890967389881705
y[1] (numeric) = -0.029645120707868640890967389881733
absolute error = 2.8e-32
relative error = 9.4450618959928943634718386203728e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 232.7
Order of pole (three term test) = -6146
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = -0.029397182320011385295188981375541
y[1] (numeric) = -0.029397182320011385295188981375568
absolute error = 2.7e-32
relative error = 9.1845537120135611399919252862665e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 232.5
Order of pole (three term test) = -6141
Radius of convergence (six term test) for eq 1 = 4.638e+10
Order of pole (six term test) = 1.721e+20
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = -0.029151242949371048435926822903941
y[1] (numeric) = -0.029151242949371048435926822903968
absolute error = 2.7e-32
relative error = 9.2620407462188631999255404079188e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 232.3
Order of pole (three term test) = -6137
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = -0.028907287362180865039077822987969
y[1] (numeric) = -0.028907287362180865039077822987996
absolute error = 2.7e-32
relative error = 9.3402053474321664161841803876036e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 232.2
Order of pole (three term test) = -6133
Radius of convergence (six term test) for eq 1 = 5.480e+10
Order of pole (six term test) = 2.395e+20
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = -0.028665300429916778107361403631793
y[1] (numeric) = -0.02866530042991677810736140363182
absolute error = 2.7e-32
relative error = 9.4190535578065061801951245835308e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 232
Order of pole (three term test) = -6129
Radius of convergence (six term test) for eq 1 = 5.643e+10
Order of pole (six term test) = 2.535e+20
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = -0.028425267128711305426100546560153
y[1] (numeric) = -0.02842526712871130542610054656018
absolute error = 2.7e-32
relative error = 9.4985914741776705791141099643286e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 231.9
Order of pole (three term test) = -6125
Radius of convergence (six term test) for eq 1 = 3.429e+10
Order of pole (six term test) = 9.347e+19
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = -0.028187172538768650681014986401437
y[1] (numeric) = -0.028187172538768650681014986401464
absolute error = 2.7e-32
relative error = 9.5788252485644620794766775847995e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 231.7
Order of pole (three term test) = -6121
Radius of convergence (six term test) for eq 1 = 1.249e+11
Order of pole (six term test) = 1.238e+21
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = -0.027951001843781092450454110242328
y[1] (numeric) = -0.027951001843781092450454110242355
absolute error = 2.7e-32
relative error = 9.6597610886735768707754470073982e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 231.6
Order of pole (three term test) = -6117
Radius of convergence (six term test) for eq 1 = 5.426e+10
Order of pole (six term test) = 2.333e+20
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = -0.027716740330346683549339936304052
y[1] (numeric) = -0.027716740330346683549339936304079
absolute error = 2.7e-32
relative error = 9.7414052584091447902761370023715e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 231.4
Order of pole (three term test) = -6113
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = -0.027484373387388292429265073364723
y[1] (numeric) = -0.027484373387388292429265073364751
absolute error = 2.8e-32
relative error = 1.0187607192401305490780486005600e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 231.2
Order of pole (three term test) = -6109
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = -0.027253886505574017578529136859446
y[1] (numeric) = -0.027253886505574017578529136859473
absolute error = 2.7e-32
relative error = 9.9068439264535382066041613020524e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 231.1
Order of pole (three term test) = -6105
Radius of convergence (six term test) for eq 1 = 1.453e+11
Order of pole (six term test) = 1.666e+21
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = -0.027025265276739005117234162991433
y[1] (numeric) = -0.02702526527673900511723416299146
absolute error = 2.7e-32
relative error = 9.9906512382097683728379752638690e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 230.9
Order of pole (three term test) = -6101
Radius of convergence (six term test) for eq 1 = 6.414e+10
Order of pole (six term test) = 3.239e+20
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = -0.026798495393308699045731654620683
y[1] (numeric) = -0.026798495393308699045731654620711
absolute error = 2.8e-32
relative error = 1.0448347785596688368866062316006e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 230.8
Order of pole (three term test) = -6097
Radius of convergence (six term test) for eq 1 = 5.071e+10
Order of pole (six term test) = 2.022e+20
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = -0.026573562647723552879559613167534
y[1] (numeric) = -0.026573562647723552879559613167562
absolute error = 2.8e-32
relative error = 1.0536788149630604424880040737197e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 230.6
Order of pole (three term test) = -6093
Radius of convergence (six term test) for eq 1 = 6.232e+10
Order of pole (six term test) = 3.048e+20
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = -0.026350452931865230690367900440014
y[1] (numeric) = -0.026350452931865230690367900440041
absolute error = 2.7e-32
relative error = 1.0246503189077741130986306405578e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 230.4
Order of pole (three term test) = -6089
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=84029016, alloc=4455632, time=3.11
x[1] = 3.89
y[1] (analytic) = -0.026129152236484324870047189866362
y[1] (numeric) = -0.026129152236484324870047189866389
absolute error = 2.7e-32
relative error = 1.0333285885295468591047777723355e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 230.3
Order of pole (three term test) = -6085
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = -0.025909646650629617244195255991877
y[1] (numeric) = -0.025909646650629617244195255991904
absolute error = 2.7e-32
relative error = 1.0420829108197771052762188567289e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 230.1
Order of pole (three term test) = -6081
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = -0.025691922361078909481021029343645
y[1] (numeric) = -0.025691922361078909481021029343672
absolute error = 2.7e-32
relative error = 1.0509139651185742941539920983134e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 230
Order of pole (three term test) = -6077
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = -0.025475965651771448072650269329411
y[1] (numeric) = -0.025475965651771448072650269329438
absolute error = 2.7e-32
relative error = 1.0598224369219378181554080409185e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 229.8
Order of pole (three term test) = -6073
Radius of convergence (six term test) for eq 1 = 4.186e+10
Order of pole (six term test) = 1.365e+20
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = -0.025261762903241968507407359071699
y[1] (numeric) = -0.025261762903241968507407359071726
absolute error = 2.7e-32
relative error = 1.0688090179381326876206088809018e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 229.6
Order of pole (three term test) = -6068
Radius of convergence (six term test) for eq 1 = 4.147e+10
Order of pole (six term test) = 1.337e+20
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = -0.025049300592056382603857978028571
y[1] (numeric) = -0.025049300592056382603857978028599
absolute error = 2.8e-32
relative error = 1.1177956804462373377612443001773e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 229.5
Order of pole (three term test) = -6064
Radius of convergence (six term test) for eq 1 = 6.253e+10
Order of pole (six term test) = 3.036e+20
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = -0.024838565290249132340061509709132
y[1] (numeric) = -0.02483856529024913234006150970916
absolute error = 2.8e-32
relative error = 1.1272792801358760876738583580121e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 229.3
Order of pole (three term test) = -6060
Radius of convergence (six term test) for eq 1 = 8.678e+10
Order of pole (six term test) = 5.838e+20
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = -0.024629543664762232884456092621648
y[1] (numeric) = -0.024629543664762232884456092621676
absolute error = 2.8e-32
relative error = 1.1368460732002890160588872812061e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 229.2
Order of pole (three term test) = -6056
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = -0.024422222476886026917941151330309
y[1] (numeric) = -0.024422222476886026917941151330337
absolute error = 2.8e-32
relative error = 1.1464968033314779705602264309272e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 229
Order of pole (three term test) = -6052
Radius of convergence (six term test) for eq 1 = 7.806e+10
Order of pole (six term test) = 4.709e+20
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = -0.024216588581701671729891786202869
y[1] (numeric) = -0.024216588581701671729891786202896
absolute error = 2.7e-32
relative error = 1.1149382130727325245015194591379e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 228.8
Order of pole (three term test) = -6048
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = -0.024012628927525379973898074805517
y[1] (numeric) = -0.024012628927525379973898074805544
absolute error = 2.7e-32
relative error = 1.1244083303619552235270194450302e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 228.7
Order of pole (three term test) = -6044
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = -0.023810330555354434381833427655214
y[1] (numeric) = -0.023810330555354434381833427655241
absolute error = 2.7e-32
relative error = 1.1339615776114572731607515788286e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 228.5
Order of pole (three term test) = -6040
Radius of convergence (six term test) for eq 1 = 1.047e+11
Order of pole (six term test) = 8.438e+20
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = -0.023609680598314996157284670523026
y[1] (numeric) = -0.023609680598314996157284670523054
absolute error = 2.8e-32
relative error = 1.1859542056658884827874981190340e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 228.3
Order of pole (three term test) = -6036
Radius of convergence (six term test) for eq 1 = 6.394e+10
Order of pole (six term test) = 3.141e+20
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = -0.023410666281111726201289239559235
y[1] (numeric) = -0.023410666281111726201289239559263
absolute error = 2.8e-32
relative error = 1.1960360146857954110645773354417e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 228.2
Order of pole (three term test) = -6032
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = -0.023213274919479237764590218685376
y[1] (numeric) = -0.023213274919479237764590218685404
absolute error = 2.8e-32
relative error = 1.2062063667071818199054845995742e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 228
Order of pole (three term test) = -6028
Radius of convergence (six term test) for eq 1 = 8.130e+10
Order of pole (six term test) = 5.061e+20
TOP MAIN SOLVE Loop
bytes used=88029900, alloc=4455632, time=3.27
x[1] = 4.04
y[1] (analytic) = -0.023017493919635398571108044482309
y[1] (numeric) = -0.023017493919635398571108044482337
absolute error = 2.8e-32
relative error = 1.2164660539397038433741432549529e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 227.9
Order of pole (three term test) = -6024
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = -0.02282331077773649991691033432962
y[1] (numeric) = -0.022823310777736499916910334329648
absolute error = 2.8e-32
relative error = 1.2268158757805294117265203046568e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 227.7
Order of pole (three term test) = -6020
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = -0.022630713079334309717511879425232
y[1] (numeric) = -0.02263071307933430971751187942526
absolute error = 2.8e-32
relative error = 1.2372566388802287674731317867139e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 227.5
Order of pole (three term test) = -6016
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = -0.022439688498835025953730424700265
y[1] (numeric) = -0.022439688498835025953730424700293
absolute error = 2.8e-32
relative error = 1.2477891572092741832563937485163e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 227.4
Order of pole (three term test) = -6011
Radius of convergence (six term test) for eq 1 = 5.346e+10
Order of pole (six term test) = 2.175e+20
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = -0.022250224798960146452437070590735
y[1] (numeric) = -0.022250224798960146452437070590763
absolute error = 2.8e-32
relative error = 1.2584142521251545523430438617742e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 227.2
Order of pole (three term test) = -6007
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = -0.022062309830209270433251194618407
y[1] (numeric) = -0.022062309830209270433251194618435
absolute error = 2.8e-32
relative error = 1.2691327524401105756315805005542e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 227.1
Order of pole (three term test) = -6003
Radius of convergence (six term test) for eq 1 = 1.735e+11
Order of pole (six term test) = 2.283e+21
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = -0.021875931530324846755418481470155
y[1] (numeric) = -0.021875931530324846755418481470183
absolute error = 2.8e-32
relative error = 1.2799454944894963226739713271420e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 226.9
Order of pole (three term test) = -5999
Radius of convergence (six term test) for eq 1 = 6.755e+10
Order of pole (six term test) = 3.456e+20
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = -0.021691077923758883310658287677234
y[1] (numeric) = -0.021691077923758883310658287677262
absolute error = 2.8e-32
relative error = 1.2908533222007729983144935875283e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 226.7
Order of pole (three term test) = -5995
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = -0.021507737121141631527555992470023
y[1] (numeric) = -0.021507737121141631527555992470051
absolute error = 2.8e-32
relative error = 1.3018570871631408011612496745797e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 226.6
Order of pole (three term test) = -5991
Radius of convergence (six term test) for eq 1 = 1.266e+11
Order of pole (six term test) = 1.211e+21
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = -0.021325897318752259480991545218319
y[1] (numeric) = -0.021325897318752259480991545218347
absolute error = 2.8e-32
relative error = 1.3129576486978148152324655336941e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 226.4
Order of pole (three term test) = -5987
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = -0.021145546797991526636022942942347
y[1] (numeric) = -0.021145546797991526636022942942374
absolute error = 2.7e-32
relative error = 1.2768645927172026842019481352487e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 226.3
Order of pole (three term test) = -5983
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = -0.020966673924856472799470157044775
y[1] (numeric) = -0.020966673924856472799470157044803
absolute error = 2.8e-32
relative error = 1.3354526378552278543413058316783e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 226.1
Order of pole (three term test) = -5979
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = -0.02078926714941713340405982458783
y[1] (numeric) = -0.020789267149417133404059824587858
absolute error = 2.8e-32
relative error = 1.3468488234220912971890913792920e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 225.9
Order of pole (three term test) = -5975
Radius of convergence (six term test) for eq 1 = 8.449e+10
Order of pole (six term test) = 5.360e+20
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = -0.020613315005295292809284005921241
y[1] (numeric) = -0.020613315005295292809284005921269
absolute error = 2.8e-32
relative error = 1.3583453215946665437381222633898e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 225.8
Order of pole (three term test) = -5971
Radius of convergence (six term test) for eq 1 = 1.575e+11
Order of pole (six term test) = 1.860e+21
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = -0.020438806109145286869989081455812
y[1] (numeric) = -0.02043880610914528686998908145584
absolute error = 2.8e-32
relative error = 1.3699430314313455902895363173985e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 225.6
Order of pole (three term test) = -5967
NO COMPLEX POLE (six term test) for Equation 1
bytes used=92031748, alloc=4455632, time=3.42
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = -0.020265729160136865598036407199233
y[1] (numeric) = -0.020265729160136865598036407199262
absolute error = 2.9e-32
relative error = 1.4309872480208428421786504715186e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 225.5
Order of pole (three term test) = -5963
Radius of convergence (six term test) for eq 1 = 7.785e+10
Order of pole (six term test) = 4.530e+20
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = -0.020094072939440126324059042706496
y[1] (numeric) = -0.020094072939440126324059042706525
absolute error = 2.9e-32
relative error = 1.4432116419304694833624106753476e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 225.3
Order of pole (three term test) = -5958
Radius of convergence (six term test) for eq 1 = 4.790e+10
Order of pole (six term test) = 1.712e+20
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = -0.019923826309712527355274440914421
y[1] (numeric) = -0.01992382630971252735527444091445
absolute error = 2.9e-32
relative error = 1.4555437067759917145604015263479e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 225.1
Order of pole (three term test) = -5954
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = -0.019754978214587991721398528012411
y[1] (numeric) = -0.019754978214587991721398528012439
absolute error = 2.8e-32
relative error = 1.4173642560295764824905934131820e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 225
Order of pole (three term test) = -5950
Radius of convergence (six term test) for eq 1 = 5.003e+10
Order of pole (six term test) = 1.863e+20
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = -0.01958751767816811020384051417679
y[1] (numeric) = -0.019587517678168110203840514176819
absolute error = 2.9e-32
relative error = 1.4805347199417142502521058782976e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 224.8
Order of pole (three term test) = -5946
Radius of convergence (six term test) for eq 1 = 6.080e+10
Order of pole (six term test) = 2.746e+20
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = -0.019421433804515452453439787555739
y[1] (numeric) = -0.019421433804515452453439787555767
absolute error = 2.8e-32
relative error = 1.4417061212797813391886674938225e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 224.7
Order of pole (three term test) = -5942
Radius of convergence (six term test) for eq 1 = 9.409e+10
Order of pole (six term test) = 6.568e+20
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = -0.019256715777148994618937376905602
y[1] (numeric) = -0.01925671577714899461893737690563
absolute error = 2.8e-32
relative error = 1.4540381820053777976655501036020e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 224.5
Order of pole (three term test) = -5938
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = -0.019093352858541671532057027098704
y[1] (numeric) = -0.019093352858541671532057027098732
absolute error = 2.8e-32
relative error = 1.4664789472779171167768607718208e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 224.3
Order of pole (three term test) = -5934
Radius of convergence (six term test) for eq 1 = 4.471e+10
Order of pole (six term test) = 1.478e+20
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = -0.018931334389620061125408486772067
y[1] (numeric) = -0.018931334389620061125408486772095
absolute error = 2.8e-32
relative error = 1.4790293924210770207014569345015e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 224.2
Order of pole (three term test) = -5930
Radius of convergence (six term test) for eq 1 = 6.717e+10
Order of pole (six term test) = 3.333e+20
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = -0.018770649789266208396322979640463
y[1] (numeric) = -0.018770649789266208396322979640491
absolute error = 2.8e-32
relative error = 1.4916905016261874419307494324906e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 224
Order of pole (three term test) = -5926
Radius of convergence (six term test) for eq 1 = 4.722e+10
Order of pole (six term test) = 1.645e+20
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = -0.018611288553821595873094076641628
y[1] (numeric) = -0.018611288553821595873094076641656
absolute error = 2.8e-32
relative error = 1.5044632680336660184477616015002e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 223.9
Order of pole (three term test) = -5922
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = -0.018453240256593267189833581355044
y[1] (numeric) = -0.018453240256593267189833581355072
absolute error = 2.8e-32
relative error = 1.5173486938152075834774519358664e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 223.7
Order of pole (three term test) = -5918
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = -0.018296494547362110032170067351987
y[1] (numeric) = -0.018296494547362110032170067352016
absolute error = 2.9e-32
relative error = 1.5850030684801894848936268818877e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 223.5
Order of pole (three term test) = -5913
Radius of convergence (six term test) for eq 1 = 8.172e+10
Order of pole (six term test) = 4.903e+20
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = -0.018141041151893304378227034880409
y[1] (numeric) = -0.018141041151893304378227034880438
absolute error = 2.9e-32
relative error = 1.5985852056221917357387472533123e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 223.4
Order of pole (three term test) = -5909
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = -0.017986869871448941627629132798142
y[1] (numeric) = -0.017986869871448941627629132798171
absolute error = 2.9e-32
relative error = 1.6122871965640061621908502385988e-28 %
Correct digits = 30
h = 0.01
bytes used=96032732, alloc=4455632, time=3.57
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 223.2
Order of pole (three term test) = -5905
Radius of convergence (six term test) for eq 1 = 1.308e+11
Order of pole (six term test) = 1.253e+21
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = -0.01783397058230281988561052837111
y[1] (numeric) = -0.017833970582302819885610528371139
absolute error = 2.9e-32
relative error = 1.6261101175515879585526225183671e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 223
Order of pole (three term test) = -5901
Radius of convergence (six term test) for eq 1 = 6.318e+10
Order of pole (six term test) = 2.918e+20
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = -0.017682333235257420349552457792092
y[1] (numeric) = -0.017682333235257420349552457792121
absolute error = 2.9e-32
relative error = 1.6400550546223102244659088195521e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 222.9
Order of pole (three term test) = -5897
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = -0.017531947855163069431371542193595
y[1] (numeric) = -0.017531947855163069431371542193625
absolute error = 3.0e-32
relative error = 1.7111618314085478332132263438029e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 222.7
Order of pole (three term test) = -5893
Radius of convergence (six term test) for eq 1 = 5.654e+10
Order of pole (six term test) = 2.330e+20
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = -0.017382804540439290941032014524905
y[1] (numeric) = -0.017382804540439290941032014524934
absolute error = 2.9e-32
relative error = 1.6683153706603850572253184486884e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 222.6
Order of pole (three term test) = -5889
Radius of convergence (six term test) for eq 1 = 8.640e+10
Order of pole (six term test) = 5.434e+20
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = -0.017234893462598352353980084014123
y[1] (numeric) = -0.017234893462598352353980084014152
absolute error = 2.9e-32
relative error = 1.6826329714734382035273392568965e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 222.4
Order of pole (three term test) = -5885
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = -0.017088204865771008888414870576956
y[1] (numeric) = -0.017088204865771008888414870576986
absolute error = 3.0e-32
relative error = 1.7555969299087882372813807981306e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 222.2
Order of pole (three term test) = -5881
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = -0.016942729066234448826936353006427
y[1] (numeric) = -0.016942729066234448826936353006457
absolute error = 3.0e-32
relative error = 1.7706710579340895096608872114388e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 222.1
Order of pole (three term test) = -5877
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = -0.016798456451942443231166338333738
y[1] (numeric) = -0.016798456451942443231166338333767
absolute error = 2.9e-32
relative error = 1.7263490894514099774068787823057e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 221.9
Order of pole (three term test) = -5873
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = -0.016655377482057702917344373215563
y[1] (numeric) = -0.016655377482057702917344373215592
absolute error = 2.9e-32
relative error = 1.7411793897340818534317773007065e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 221.8
Order of pole (three term test) = -5868
Radius of convergence (six term test) for eq 1 = 8.961e+10
Order of pole (six term test) = 5.802e+20
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = -0.016513482686486445285578617995082
y[1] (numeric) = -0.016513482686486445285578617995112
absolute error = 3.0e-32
relative error = 1.8166973357201045692073897441053e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 221.6
Order of pole (three term test) = -5864
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = -0.016372762665415173325304852386465
y[1] (numeric) = -0.016372762665415173325304852386495
absolute error = 3.0e-32
relative error = 1.8323114194631412361578645914531e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 221.4
Order of pole (three term test) = -5860
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = -0.01623320808884966885449885381994
y[1] (numeric) = -0.01623320808884966885449885381997
absolute error = 3.0e-32
relative error = 1.8480635396158397331605444702810e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 221.3
Order of pole (three term test) = -5856
Radius of convergence (six term test) for eq 1 = 8.403e+10
Order of pole (six term test) = 5.080e+20
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = -0.016094809696156201790223261198965
y[1] (numeric) = -0.016094809696156201790223261198995
absolute error = 3.0e-32
relative error = 1.8639549374208920687992314774935e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 221.1
Order of pole (three term test) = -5852
Radius of convergence (six term test) for eq 1 = 5.146e+10
Order of pole (six term test) = 1.903e+20
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = -0.015957558295604956993095572196783
y[1] (numeric) = -0.015957558295604956993095572196812
absolute error = 2.9e-32
relative error = 1.8173206365780410374621925928330e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 220.9
Order of pole (three term test) = -5848
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=100033952, alloc=4521156, time=3.72
x[1] = 4.48
y[1] (analytic) = -0.015821444763915679978165961256329
y[1] (numeric) = -0.015821444763915679978165961256358
absolute error = 2.9e-32
relative error = 1.8329552346661123687887156475396e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 220.8
Order of pole (three term test) = -5844
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = -0.01568646004580554253941995203708
y[1] (numeric) = -0.015686460045805542539419952037109
absolute error = 2.9e-32
relative error = 1.8487281333913454560251504950110e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 220.6
Order of pole (three term test) = -5840
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = -0.015552595153539229094600388001703
y[1] (numeric) = -0.015552595153539229094600388001731
absolute error = 2.8e-32
relative error = 1.8003426260104362710023091349115e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 220.5
Order of pole (three term test) = -5836
Radius of convergence (six term test) for eq 1 = 1.834e+11
Order of pole (six term test) = 2.402e+21
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = -0.015419841166481244321205314129138
y[1] (numeric) = -0.015419841166481244321205314129167
absolute error = 2.9e-32
relative error = 1.8806938208312104204458480264222e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 220.3
Order of pole (three term test) = -5831
Radius of convergence (six term test) for eq 1 = 6.098e+10
Order of pole (six term test) = 2.652e+20
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = -0.015288189230650442423293935846499
y[1] (numeric) = -0.015288189230650442423293935846528
absolute error = 2.9e-32
relative error = 1.8968891320274548195296070175555e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 220.1
Order of pole (three term test) = -5827
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = -0.015157630558276778142053299633143
y[1] (numeric) = -0.015157630558276778142053299633172
absolute error = 2.9e-32
relative error = 1.9132277890335991897465626369579e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 220
Order of pole (three term test) = -5823
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = -0.015028156427360279400876190406069
y[1] (numeric) = -0.015028156427360279400876190406098
absolute error = 2.9e-32
relative error = 1.9297110820062110634770182742681e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 219.8
Order of pole (three term test) = -5819
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = -0.014899758181232241257909305138172
y[1] (numeric) = -0.014899758181232241257909305138202
absolute error = 3.0e-32
relative error = 2.0134554960622144182200340198433e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 219.7
Order of pole (three term test) = -5815
Radius of convergence (six term test) for eq 1 = 7.392e+10
Order of pole (six term test) = 3.876e+20
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = -0.014772427228118640625584264824498
y[1] (numeric) = -0.014772427228118640625584264824528
absolute error = 3.0e-32
relative error = 2.0308104779759124479641578021605e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 219.5
Order of pole (three term test) = -5811
Radius of convergence (six term test) for eq 1 = 5.050e+10
Order of pole (six term test) = 1.806e+20
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = -0.014646155040705771007477564796187
y[1] (numeric) = -0.014646155040705771007477564796217
absolute error = 3.0e-32
relative error = 2.0483191606685569895714658922348e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 219.3
Order of pole (three term test) = -5807
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = -0.014520933155708096297895094806434
y[1] (numeric) = -0.014520933155708096297895094806463
absolute error = 2.9e-32
relative error = 1.9971168305116992301071356496545e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 219.2
Order of pole (three term test) = -5803
Radius of convergence (six term test) for eq 1 = 1.021e+11
Order of pole (six term test) = 7.358e+20
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = -0.01439675317343832248877919429881
y[1] (numeric) = -0.014396753173438322488779194298839
absolute error = 2.9e-32
relative error = 2.0143430710130066721717250627696e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 219
Order of pole (three term test) = -5799
Radius of convergence (six term test) for eq 1 = 7.182e+10
Order of pole (six term test) = 3.638e+20
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = -0.014273606757379685931828993950801
y[1] (numeric) = -0.01427360675737968593182899395083
absolute error = 2.9e-32
relative error = 2.0317219391662538403719489796756e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 218.8
Order of pole (three term test) = -5795
Radius of convergence (six term test) for eq 1 = 5.645e+11
Order of pole (six term test) = 2.244e+22
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = -0.014151485633760456611046510750785
y[1] (numeric) = -0.014151485633760456611046510750814
absolute error = 2.9e-32
relative error = 2.0492548097435241647474368357527e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 218.7
Order of pole (three term test) = -5790
Radius of convergence (six term test) for eq 1 = 6.578e+10
Order of pole (six term test) = 3.043e+20
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = -0.014030381591130654692210908615478
y[1] (numeric) = -0.014030381591130654692210908615507
absolute error = 2.9e-32
relative error = 2.0669430700539486267323027378104e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 218.5
Order of pole (three term test) = -5786
Radius of convergence (six term test) for eq 1 = 1.825e+11
Order of pole (six term test) = 2.340e+21
TOP MAIN SOLVE Loop
bytes used=104034748, alloc=4521156, time=3.87
x[1] = 4.63
y[1] (analytic) = -0.013910286479940978430981617088102
y[1] (numeric) = -0.01391028647994097843098161708813
absolute error = 2.8e-32
relative error = 2.0128988745398437293615450163318e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 218.4
Order of pole (three term test) = -5782
Radius of convergence (six term test) for eq 1 = 6.361e+10
Order of pole (six term test) = 2.838e+20
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = -0.013791192212123941340378523185078
y[1] (numeric) = -0.013791192212123941340378523185107
absolute error = 2.9e-32
relative error = 2.1027913724896010621099190884388e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 218.2
Order of pole (three term test) = -5778
Radius of convergence (six term test) for eq 1 = 1.304e+11
Order of pole (six term test) = 1.190e+21
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = -0.013673090760677216341225911229106
y[1] (numeric) = -0.013673090760677216341225911229136
absolute error = 3.0e-32
relative error = 2.1940906065128851662167423097464e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 218
Order of pole (three term test) = -5774
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = -0.013555974159249184445718696953557
y[1] (numeric) = -0.013555974159249184445718696953586
absolute error = 2.9e-32
relative error = 2.1392782000999479145931000154506e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 217.9
Order of pole (three term test) = -5770
Radius of convergence (six term test) for eq 1 = 9.364e+10
Order of pole (six term test) = 6.123e+20
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = -0.013439834501726685354518029175181
y[1] (numeric) = -0.01343983450172668535451802917521
absolute error = 2.9e-32
relative error = 2.1577646656492845468690026221946e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 217.7
Order of pole (three term test) = -5766
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = -0.013324663941824967181652518632892
y[1] (numeric) = -0.01332466394182496718165251863292
absolute error = 2.8e-32
relative error = 2.1013663175481989254465604104886e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 217.6
Order of pole (three term test) = -5762
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = -0.013210454692679832358935953237933
y[1] (numeric) = -0.013210454692679832358935953237961
absolute error = 2.8e-32
relative error = 2.1195334037605336806735498372937e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 217.4
Order of pole (three term test) = -5757
Radius of convergence (six term test) for eq 1 = 9.632e+10
Order of pole (six term test) = 6.452e+20
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = -0.013097199026441976612557866979598
y[1] (numeric) = -0.013097199026441976612557866979628
absolute error = 3.0e-32
relative error = 2.2905660927525728933276812594869e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 217.2
Order of pole (three term test) = -5753
Radius of convergence (six term test) for eq 1 = 6.012e+10
Order of pole (six term test) = 2.510e+20
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = -0.012984889273873517748905972756003
y[1] (numeric) = -0.012984889273873517748905972756032
absolute error = 2.9e-32
relative error = 2.2333652130827158148985070599445e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 217.1
Order of pole (three term test) = -5749
Radius of convergence (six term test) for eq 1 = 1.395e+11
Order of pole (six term test) = 1.349e+21
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = -0.012873517823946710834486196633319
y[1] (numeric) = -0.012873517823946710834486196633348
absolute error = 2.9e-32
relative error = 2.2526865147967222626139050420824e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 216.9
Order of pole (three term test) = -5745
Radius of convergence (six term test) for eq 1 = 9.500e+10
Order of pole (six term test) = 6.250e+20
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = -0.012763077123444846205964525113938
y[1] (numeric) = -0.012763077123444846205964525113968
absolute error = 3.0e-32
relative error = 2.3505303391838146692212518493419e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 216.7
Order of pole (three term test) = -5741
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = -0.012653559676565326600813465055423
y[1] (numeric) = -0.012653559676565326600813465055452
absolute error = 2.9e-32
relative error = 2.2918451993954431439024823618192e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 216.6
Order of pole (three term test) = -5737
Radius of convergence (six term test) for eq 1 = 7.974e+10
Order of pole (six term test) = 4.392e+20
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = -0.012544958044524919556753680738013
y[1] (numeric) = -0.012544958044524919556753680738042
absolute error = 2.9e-32
relative error = 2.3116856905437531626682853427306e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 216.4
Order of pole (three term test) = -5733
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = -0.01243726484516718108908806397543
y[1] (numeric) = -0.012437264845167181089088063975459
absolute error = 2.9e-32
relative error = 2.3317023767704597318336101781536e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 216.3
Order of pole (three term test) = -5729
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = -0.012330472752572046519081539157613
y[1] (numeric) = -0.012330472752572046519081539157641
absolute error = 2.8e-32
relative error = 2.2707969566016359423227961258738e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 216.1
Order of pole (three term test) = -5724
Radius of convergence (six term test) for eq 1 = 1.419e+11
Order of pole (six term test) = 1.385e+21
TOP MAIN SOLVE Loop
bytes used=108037256, alloc=4521156, time=4.01
x[1] = 4.78
y[1] (analytic) = -0.012224574496667584193696403546793
y[1] (numeric) = -0.012224574496667584193696403546822
absolute error = 2.9e-32
relative error = 2.3722707083101659207200893117204e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 215.9
Order of pole (three term test) = -5720
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = -0.012119562862843907707201713226515
y[1] (numeric) = -0.012119562862843907707201713226544
absolute error = 2.9e-32
relative error = 2.3928255769775367046237010096440e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 215.8
Order of pole (three term test) = -5716
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = -0.012015430691569242108388559078469
y[1] (numeric) = -0.012015430691569242108388559078498
absolute error = 2.9e-32
relative error = 2.4135630877008983164071201182455e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 215.6
Order of pole (three term test) = -5712
Radius of convergence (six term test) for eq 1 = 8.787e+10
Order of pole (six term test) = 5.288e+20
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = -0.011912170878008139453294092111419
y[1] (numeric) = -0.011912170878008139453294092111448
absolute error = 2.9e-32
relative error = 2.4344848891933587173605047447278e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 215.4
Order of pole (three term test) = -5708
Radius of convergence (six term test) for eq 1 = 1.117e+11
Order of pole (six term test) = 8.537e+20
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = -0.011809776371641838942419547171497
y[1] (numeric) = -0.011809776371641838942419547171527
absolute error = 3.0e-32
relative error = 2.5402682536849161909158155582476e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 215.3
Order of pole (three term test) = -5704
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = -0.011708240175890766763375600986895
y[1] (numeric) = -0.011708240175890766763375600986925
absolute error = 3.0e-32
relative error = 2.5622979670142947108717638071974e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 215.1
Order of pole (three term test) = -5700
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = -0.011607555347739170644657127860712
y[1] (numeric) = -0.011607555347739170644657127860742
absolute error = 3.0e-32
relative error = 2.5845235367189669857046016205843e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 215
Order of pole (three term test) = -5696
Radius of convergence (six term test) for eq 1 = 2.272e+11
Order of pole (six term test) = 3.516e+21
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = -0.011507714997361884013794340265994
y[1] (numeric) = -0.011507714997361884013794340266024
absolute error = 3.0e-32
relative error = 2.6069467315516093201554691876630e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 214.8
Order of pole (three term test) = -5691
Radius of convergence (six term test) for eq 1 = 3.142e+11
Order of pole (six term test) = 6.716e+21
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = -0.01140871228775321454340458344703
y[1] (numeric) = -0.011408712287753214543404583447059
absolute error = 2.9e-32
relative error = 2.5419170252132935683069550665493e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 214.6
Order of pole (three term test) = -5687
Radius of convergence (six term test) for eq 1 = 1.148e+11
Order of pole (six term test) = 8.956e+20
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = -0.011310540434357951761635451765616
y[1] (numeric) = -0.011310540434357951761635451765646
absolute error = 3.0e-32
relative error = 2.6523931525737889598075771882682e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 214.5
Order of pole (three term test) = -5683
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = -0.011213192704704488299102758818536
y[1] (numeric) = -0.011213192704704488299102758818566
absolute error = 3.0e-32
relative error = 2.6754199976794760626678051035973e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 214.3
Order of pole (three term test) = -5679
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = -0.011116662418040049242644154694593
y[1] (numeric) = -0.011116662418040049242644154694623
absolute error = 3.0e-32
relative error = 2.6986517060476884081821215287243e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 214.1
Order of pole (three term test) = -5675
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = -0.01102094294496802396698934870179
y[1] (numeric) = -0.01102094294496802396698934870182
absolute error = 3.0e-32
relative error = 2.7220901287486922602714586711017e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 214
Order of pole (three term test) = -5671
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = -0.010926027707087394718750038925556
y[1] (numeric) = -0.010926027707087394718750038925586
absolute error = 3.0e-32
relative error = 2.7457371337745992662099910316373e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 213.8
Order of pole (three term test) = -5667
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = -0.010831910176634256132916406215345
y[1] (numeric) = -0.010831910176634256132916406215375
absolute error = 3.0e-32
relative error = 2.7695946061954647836740266151244e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 213.7
Order of pole (three term test) = -5663
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=112037948, alloc=4521156, time=4.16
x[1] = 4.93
y[1] (analytic) = -0.010738583876125419770272588360867
y[1] (numeric) = -0.010738583876125419770272588360897
absolute error = 3.0e-32
relative error = 2.7936644483168368229890617865817e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 213.5
Order of pole (three term test) = -5658
Radius of convergence (six term test) for eq 1 = 2.955e+11
Order of pole (six term test) = 5.876e+21
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = -0.010646042378004097674771645595919
y[1] (numeric) = -0.010646042378004097674771645595949
absolute error = 3.0e-32
relative error = 2.8179485798387691673714846206516e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 213.3
Order of pole (three term test) = -5654
Radius of convergence (six term test) for eq 1 = 6.037e+10
Order of pole (six term test) = 2.450e+20
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = -0.010554279304287658862902436070549
y[1] (numeric) = -0.010554279304287658862902436070579
absolute error = 3.0e-32
relative error = 2.8424489380163123614292395268143e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 213.2
Order of pole (three term test) = -5650
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = -0.010463288326217452572398347251641
y[1] (numeric) = -0.010463288326217452572398347251672
absolute error = 3.1e-32
relative error = 2.9627397270822129330854487928443e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 213
Order of pole (three term test) = -5646
Radius of convergence (six term test) for eq 1 = 2.033e+11
Order of pole (six term test) = 2.771e+21
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = -0.010373063163910692015243310046742
y[1] (numeric) = -0.010373063163910692015243310046772
absolute error = 3.0e-32
relative error = 2.8921061721068189741462992135910e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 212.8
Order of pole (three term test) = -5642
Radius of convergence (six term test) for eq 1 = 1.886e+11
Order of pole (six term test) = 2.382e+21
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = -0.010283597586014392299786809817067
y[1] (numeric) = -0.010283597586014392299786809817098
absolute error = 3.1e-32
relative error = 3.0145092454959287512544943648609e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 212.7
Order of pole (three term test) = -5638
Radius of convergence (six term test) for eq 1 = 1.360e+11
Order of pole (six term test) = 1.236e+21
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = -0.010194885409361356108850068090735
y[1] (numeric) = -0.010194885409361356108850068090766
absolute error = 3.1e-32
relative error = 3.0407404061191846476027022169111e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 212.5
Order of pole (three term test) = -5634
Radius of convergence (six term test) for eq 1 = 1.261e+11
Order of pole (six term test) = 1.062e+21
Finished!
diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);
Iterations = 400
Total Elapsed Time = 4 Seconds
Elapsed Time(since restart) = 4 Seconds
Time to Timeout = 2 Minutes 55 Seconds
Percent Done = 100.2 %
> quit
bytes used=113934428, alloc=4521156, time=4.23