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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
\ MAPLE / All rights reserved. Maple is a trademark of
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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_2,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_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_2, array_const_0D0, array_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_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_2,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_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_2, array_const_0D0, array_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_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_2,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_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_2, array_const_0D0, array_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_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_2,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_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_2, array_const_0D0, array_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_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_2,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_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_2, array_const_0D0, array_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_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_2,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_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_2, array_const_0D0, array_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_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_2,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_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 - 2 - 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 - 2 - 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 - 2 - 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_2, array_const_0D0, array_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_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 - 12;
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 - 3;
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 - 3;
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_2,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_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_2, array_const_0D0, array_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_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_2,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * expt(glob_h , (2)) * factorial_3(0,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[3,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1;
> array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1;
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * expt(glob_h , (2)) * factorial_3(1,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[3,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2;
> array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2;
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * expt(glob_h , (2)) * factorial_3(2,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3;
> array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3;
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * expt(glob_h , (2)) * factorial_3(3,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[3,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4;
> array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4;
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,7]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * expt(glob_h , (2)) * factorial_3(4,6);
> array_y[7] := temporary;
> array_y_higher[1,7] := temporary;
> temporary := temporary / glob_h * (6.0);
> array_y_higher[2,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[3,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> 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_tmp2[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_2, array_const_0D0, array_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 3] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*expt(glob_h, 2)*factorial_3(0, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[3, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2];
array_tmp1_g[2] := -array_tmp1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 4] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*expt(glob_h, 2)*factorial_3(1, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[3, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2];
array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2];
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 5] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*expt(glob_h, 2)*factorial_3(2, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2];
array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2];
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 6] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*expt(glob_h, 2)*factorial_3(3, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[3, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2];
array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2];
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 7] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*expt(glob_h, 2)*factorial_3(4, 6);
array_y[7] := temporary;
array_y_higher[1, 7] := temporary;
temporary := temporary*6.0/glob_h;
array_y_higher[2, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[3, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 2;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 13
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s
", str)
end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-42.4g %s
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then printf("%-30s = %-32d %s
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " |
")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,m,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_int(ALWAYS,"m",4, m ,4," ");
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, m, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_int(ALWAYS, "m", 4, m, 4, " ");
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file)
fprintf(file, "
")
end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(2.0 - sin(x));
> end;
exact_soln_y := proc(x) return 2.0 - sin(x) end proc
> exact_soln_yp := proc(x)
> return(- cos(x));
> end;
exact_soln_yp := proc(x) return -cos(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_2,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_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/h2sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 2 ) = sin(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 := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(2.0 - sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yp := proc(x)");
> omniout_str(ALWAYS,"return(- cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(2 + 1),[]);
> array_last_rel_error:= Array(0..(2 + 1),[]);
> array_type_pole:= Array(0..(2 + 1),[]);
> array_type_real_pole:= Array(0..(2 + 1),[]);
> array_type_complex_pole:= Array(0..(2 + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) 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 <=3) 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 <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_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_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_2[1] := 2;
> 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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> array_y_init[1 + 1] := exact_soln_yp(x_start);
> glob_look_poles := true;
> glob_max_iter := 100;
> #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] := true;
> 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 := 2;
> #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 := 2;
> #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 := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> 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 := 2;
> calc_term := 2;
> #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 := 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 := 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 := 3;
> #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 := 3;
> #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 , 2 ) = sin(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,"2013-05-26T02:15:18-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"h2sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 2 ) = sin(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,"h2sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"h2sin 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_2, array_const_0D0, array_y_init, array_norms,
array_fact_1, array_pole, array_real_pole, array_complex_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_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/h2sinpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 2 ) = sin(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 := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(2.0 - sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yp := proc(x)");
omniout_str(ALWAYS, "return(- cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 3 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 <= 3 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 <= 3 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_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_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
array_y_init[2] := exact_soln_yp(x_start);
glob_look_poles := true;
glob_max_iter := 100;
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] := true;
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 := 2;
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 := 2;
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 := 3;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
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 := 2;
calc_term := 2;
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 := 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 := 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 := 3;
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 := 3;
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 , 2 ) = sin(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, "2013-05-26T02:15:18-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "h2sin")
;
logitem_str(html_log_file, "diff ( y , x , 2 ) = sin(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,
"h2sin diffeq.mxt");
logitem_str(html_log_file,
"h2sin 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/h2sinpostode.ode#################
diff ( y , x , 2 ) = sin(x);
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
array_y_init[1 + 1] := exact_soln_yp(x_start);
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(2.0 - sin(x));
end;
exact_soln_yp := proc(x)
return(- cos(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 4.9
estimated_steps = 4900000
step_error = 2.0408163265306122448979591836735e-17
est_needed_step_err = 2.0408163265306122448979591836735e-17
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.4754661255148762938611236228242e-184
estimated_step_error = 2.4754661255148762938611236228242e-184
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.6612575021518590873308215131969e-176
estimated_step_error = 1.6612575021518590873308215131969e-176
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 = 1.1148514493392458816356641790437e-168
estimated_step_error = 1.1148514493392458816356641790437e-168
best_h = 8.000e-06
opt_iter = 4
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.4816469528579360567578132996291e-161
estimated_step_error = 7.4816469528579360567578132996291e-161
best_h = 1.60000e-05
opt_iter = 5
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.0208556920251995696960833738275e-153
estimated_step_error = 5.0208556920251995696960833738275e-153
best_h = 3.200000e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.3694491681902006751037040039290e-145
estimated_step_error = 3.3694491681902006751037040039290e-145
best_h = 6.4000000e-05
opt_iter = 7
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.2612124147513860369452514057993e-137
estimated_step_error = 2.2612124147513860369452514057993e-137
best_h = 0.000128
opt_iter = 8
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.5174918888357446027651485871533e-129
estimated_step_error = 1.5174918888357446027651485871533e-129
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 = 1.0183956259651806708160109218667e-121
estimated_step_error = 1.0183956259651806708160109218667e-121
best_h = 0.000512
opt_iter = 10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.8346602579086747397477922391410e-114
estimated_step_error = 6.8346602579086747397477922391410e-114
best_h = 0.001024
opt_iter = 11
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.5870962482045285209495447279895e-106
estimated_step_error = 4.5870962482045285209495447279895e-106
best_h = 0.002048
opt_iter = 12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.0789298685249199270989121799078e-98
estimated_step_error = 3.0789298685249199270989121799078e-98
best_h = 0.004096
opt_iter = 13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.0670155792488052717117746940106e-90
estimated_step_error = 2.0670155792488052717117746940106e-90
best_h = 0.008192
opt_iter = 14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.3881985285577433917451112053891e-82
estimated_step_error = 1.3881985285577433917451112053891e-82
best_h = 0.016384
opt_iter = 15
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 9.3301063828012164504416923464795e-75
estimated_step_error = 9.3301063828012164504416923464795e-75
best_h = 0.032768
opt_iter = 16
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.2802036274121662687299408666559e-67
estimated_step_error = 6.2802036274121662687299408666559e-67
best_h = 0.065536
opt_iter = 17
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.2399049767166217549514514166790e-59
estimated_step_error = 4.2399049767166217549514514166790e-59
best_h = 0.131072
opt_iter = 18
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.8793456610032358787721666337866e-51
estimated_step_error = 2.8793456610032358787721666337866e-51
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 1.9001665833531718476931858015894
y[1] (numeric) = 1.9001665833531718476931858015894
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 1.8902216991628251913350505099166
y[1] (numeric) = 1.8902216991628251913350505099166
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 1.880287792711080640032649385729
y[1] (numeric) = 1.8802877927110806400326493857291
absolute error = 1e-31
relative error = 5.3183347989413713575080521335103e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 1.8703658573803051404587941892917
y[1] (numeric) = 1.8703658573803051404587941892918
absolute error = 1e-31
relative error = 5.3465475540738982178064340154123e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=4000044, alloc=3079628, time=0.13
x[1] = 0.14
y[1] (analytic) = 1.8604568853557635182820116482946
y[1] (numeric) = 1.8604568853557635182820116482947
absolute error = 1e-31
relative error = 5.3750237797570689896767742806961e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 1.8505618675264007785022745613124
y[1] (numeric) = 1.8505618675264007785022745613124
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 1.840681793385754036688536840314
y[1] (numeric) = 1.8406817933857540366885368403141
absolute error = 1e-31
relative error = 5.4327695508988430654522163131111e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 1.8308176509330039898423756233292
y[1] (numeric) = 1.8308176509330039898423756233292
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 1.8209704265741758216581972603008
y[1] (numeric) = 1.8209704265741758216581972603008
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 1.8111411050234994220071488470187
y[1] (numeric) = 1.8111411050234994220071488470187
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 1.8013306692049387845405873728816
y[1] (numeric) = 1.8013306692049387845405873728816
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 1.7915401001539004293912875737724
y[1] (numeric) = 1.7915401001539004293912875737723
absolute error = 1e-31
relative error = 5.5817896563637956946170305261845e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 1.781770376919130680048208994543
y[1] (numeric) = 1.7817703769191306800482089945429
absolute error = 1e-31
relative error = 5.6123954744892869017108246806504e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 1.7720224764648116045953827876399
y[1] (numeric) = 1.7720224764648116045953827876398
absolute error = 1e-31
relative error = 5.6432692772328825427864142904146e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 1.7622973735728654116392079155102
y[1] (numeric) = 1.7622973735728654116392079155101
absolute error = 1e-31
relative error = 5.6744112259136449823538591549678e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 1.7525960407454770704031512951506
y[1] (numeric) = 1.7525960407454770704031512951505
absolute error = 1e-31
relative error = 5.7058214029437388071982080540761e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 1.7429194481078449026466115356348
y[1] (numeric) = 1.7429194481078449026466115356347
absolute error = 1e-31
relative error = 5.7374998086436177581179166049324e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 1.7332685633111688712677134789795
y[1] (numeric) = 1.7332685633111688712677134789794
absolute error = 1e-31
relative error = 5.7694463579818172061008975590405e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 1.7236443514358862666803304415422
y[1] (numeric) = 1.7236443514358862666803304415421
absolute error = 1e-31
relative error = 5.8016608772392488174463624822497e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 1.7140477748951644673160597944956
y[1] (numeric) = 1.7140477748951644673160597944956
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 1.704479793338660424894679254315
y[1] (numeric) = 1.7044797933386604248946792543149
absolute error = 1e-31
relative error = 5.8668926666548728258811238080615e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 1.694941363556556498434356676041
y[1] (numeric) = 1.694941363556556498434356676041
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 1.6854334393838822333382424565828
y[1] (numeric) = 1.6854334393838822333382424565828
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 1.6759569716051316532998043038298
y[1] (numeric) = 1.6759569716051316532998043038297
absolute error = 1e-31
relative error = 5.9667402978864047331973137372584e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=8001816, alloc=4324584, time=0.27
x[1] = 0.34
y[1] (analytic) = 1.6665129078591856032182285129692
y[1] (numeric) = 1.6665129078591856032182285129691
absolute error = 1e-31
relative error = 6.0005535827778684886823350370458e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 1.6571021925445486508103650930824
y[1] (numeric) = 1.6571021925445486508103650930823
absolute error = 1e-31
relative error = 6.0346308423167241315662992119687e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 1.6477257667249100231500865640793
y[1] (numeric) = 1.6477257667249100231500865640792
absolute error = 1e-31
relative error = 6.0689710642059244495356624871930e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 1.6383845680350380219627075308728
y[1] (numeric) = 1.6383845680350380219627075308728
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 1.6290795305870173281545145336508
y[1] (numeric) = 1.6290795305870173281545145336508
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 1.6198115848768385717688179021528
y[1] (numeric) = 1.6198115848768385717688179021528
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 1.6105816576913495083336882432043
y[1] (numeric) = 1.6105816576913495083336882432043
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 1.6013906720155771064062023599489
y[1] (numeric) = 1.6013906720155771064062023599489
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 1.5922395469404298140272128419137
y[1] (numeric) = 1.5922395469404298140272128419137
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 1.5831291975707892337830813273754
y[1] (numeric) = 1.5831291975707892337830813273755
absolute error = 1e-31
relative error = 6.3166038598393372456581954222242e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 1.5740605349340003972302792492201
y[1] (numeric) = 1.5740605349340003972302792492201
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 1.5650344658887697895791557537681
y[1] (numeric) = 1.5650344658887697895791557537681
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 1.5560518930344802347584863560711
y[1] (numeric) = 1.5560518930344802347584863560711
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 1.5471137146209317092967251996036
y[1] (numeric) = 1.5471137146209317092967251996036
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 1.5382208244585171108633570574114
y[1] (numeric) = 1.5382208244585171108633570574114
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 1.529374111828841963818641662812
y[1] (numeric) = 1.5293741118288419638186416628121
absolute error = 1e-31
relative error = 6.5386225140439266104400847887623e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 1.5205744613957969997267120647844
y[1] (numeric) = 1.5205744613957969997267120647845
absolute error = 1e-31
relative error = 6.5764618924485909237902113823204e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 1.5118227531170925054998697623254
y[1] (numeric) = 1.5118227531170925054998697623255
absolute error = 1e-31
relative error = 6.6145320140088458331137476957297e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 1.5031198621562632856655410574522
y[1] (numeric) = 1.5031198621562632856655410574523
absolute error = 1e-31
relative error = 6.6528293928966837244105802564533e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 1.4944666587951530381863389775339
y[1] (numeric) = 1.494466658795153038186338977534
absolute error = 1e-31
relative error = 6.6913503497375131401807390081828e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 1.4858640083468868953227193170418
y[1] (numeric) = 1.4858640083468868953227193170418
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=12002736, alloc=4390108, time=0.42
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 1.4773127710693408322116218922427
y[1] (numeric) = 1.4773127710693408322116218922428
absolute error = 1e-31
relative error = 6.7690472835766398638118706558234e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 1.468813802079116596148130558888
y[1] (numeric) = 1.4688138020791165961481305588881
absolute error = 1e-31
relative error = 6.8082148913939448479855016447645e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = 1.4603679512660307590055365069212
y[1] (numeric) = 1.4603679512660307590055365069213
absolute error = 1e-31
relative error = 6.8475893293404181350439372032216e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 1.4519760632081264438173039404235
y[1] (numeric) = 1.4519760632081264438173039404237
absolute error = 2e-31
relative error = 1.3774331758479683225430606027572e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 1.4436389770872162242774566211242
y[1] (numeric) = 1.4436389770872162242774566211244
absolute error = 2e-31
relative error = 1.3853879202093417130283971786780e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 1.4353575266049646427990545543413
y[1] (numeric) = 1.4353575266049646427990545543415
absolute error = 2e-31
relative error = 1.3933810656433299819825634796768e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 1.4271325398995187388090239678373
y[1] (numeric) = 1.4271325398995187388090239678374
absolute error = 1e-31
relative error = 7.0070576631264241170121706897226e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 1.4189648394626949241570367724178
y[1] (numeric) = 1.4189648394626949241570367724179
absolute error = 1e-31
relative error = 7.0473909725533431406255199515245e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 1.4108552420577304868818879092054
y[1] (numeric) = 1.4108552420577304868818879092055
absolute error = 1e-31
relative error = 7.0878993832244712442558428402154e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 1.4028045586376079481164537607921
y[1] (numeric) = 1.4028045586376079481164537607922
absolute error = 1e-31
relative error = 7.1285767774464009033693188678593e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 1.3948135942639604396274783213941
y[1] (numeric) = 1.3948135942639604396274783213942
absolute error = 1e-31
relative error = 7.1694167888268786062237311519017e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.44
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 1.3868831480265662113848545206037
y[1] (numeric) = 1.3868831480265662113848545206038
absolute error = 1e-31
relative error = 7.2104127981000217975347512558099e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.75
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 1.3790140129634403196425560858734
y[1] (numeric) = 1.3790140129634403196425560858735
absolute error = 1e-31
relative error = 7.2515579290673347493969154514838e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.05
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 1.3712069759815314862958218125798
y[1] (numeric) = 1.3712069759815314862958218125798
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.36
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 1.3634628177780320597625707929913
y[1] (numeric) = 1.3634628177780320597625707929913
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.68
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 1.3557823127623089463273856486013
y[1] (numeric) = 1.3557823127623089463273856486013
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 = 16
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 1.3481662289784633187898720271472
y[1] (numeric) = 1.3481662289784633187898720271472
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 = 16.33
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 1.3406153280285268463819961673518
y[1] (numeric) = 1.3406153280285268463819961673519
absolute error = 1e-31
relative error = 7.4592612742282555787001396766268e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.66
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 1.3331303649963021262674058692385
y[1] (numeric) = 1.3331303649963021262674058692385
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
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 1.3257120883718549325161188423918
y[1] (numeric) = 1.3257120883718549325161188423919
absolute error = 1e-31
relative error = 7.5431159508255574774124732185496e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=16003976, alloc=4390108, time=0.57
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 1.3183612399766658332667580472201
y[1] (numeric) = 1.3183612399766658332667580472202
absolute error = 1e-31
relative error = 7.5851744550507217016141048019607e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 1.3110785548894486608522443612303
y[1] (numeric) = 1.3110785548894486608522443612304
absolute error = 1e-31
relative error = 7.6273080378797051696723404179719e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.06
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 1.3038647613726432529801162655478
y[1] (numeric) = 1.3038647613726432529801162655479
absolute error = 1e-31
relative error = 7.6695070656503538546832971896404e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.42
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 1.2967205807995898156321026748821
y[1] (numeric) = 1.2967205807995898156321026748822
absolute error = 1e-31
relative error = 7.7117616146986376604776257099294e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 1.2896467275823921901859711250308
y[1] (numeric) = 1.2896467275823921901859711250309
absolute error = 1e-31
relative error = 7.7540614697997796397824347279354e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 1.2826439091004772383728253894186
y[1] (numeric) = 1.2826439091004772383728253894187
absolute error = 1e-31
relative error = 7.7963961229216266042458024472232e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 1.2757128256298574890718231474855
y[1] (numeric) = 1.2757128256298574890718231474855
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 = 17.14
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 1.2688541702731041206186866353123
y[1] (numeric) = 1.2688541702731041206186866353123
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 = 16.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 1.2620686288900372812714197738619
y[1] (numeric) = 1.2620686288900372812714197738619
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 = 16.46
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = 1.2553568800291406787434273293704
y[1] (numeric) = 1.2553568800291406787434273293703
absolute error = 1e-31
relative error = 7.9658622652132749428314198936047e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.13
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 1.2487195948597072972879284757645
y[1] (numeric) = 1.2487195948597072972879284757645
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.81
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 1.2421574371047230277054112704714
y[1] (numeric) = 1.2421574371047230277054112704713
absolute error = 1e-31
relative error = 8.0505093004220577648799519603411e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.5
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 1.2356710629744949218551971762772
y[1] (numeric) = 1.2356710629744949218551971762771
absolute error = 1e-31
relative error = 8.0927686175057792835902096492073e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 1.229261121101030708790354869244
y[1] (numeric) = 1.229261121101030708790354869244
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 = 14.88
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 1.2229282524731761345096662870268
y[1] (numeric) = 1.2229282524731761345096662870268
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 = 14.58
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 1.2166730903725166115386176842864
y[1] (numeric) = 1.2166730903725166115386176842864
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 = 14.28
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 1.2104962603100495881210424821284
y[1] (numeric) = 1.2104962603100495881210424821284
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 = 13.99
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 1.2043983799636339697317238975184
y[1] (numeric) = 1.2043983799636339697317238975183
absolute error = 1e-31
relative error = 8.3029005737303827439379037656877e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.71
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 1.1983800591162228479156807840894
y[1] (numeric) = 1.1983800591162228479156807840893
absolute error = 1e-31
relative error = 8.3445981297241921485040255542078e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.42
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 1.1924418995948857131297802013658
y[1] (numeric) = 1.1924418995948857131297802013658
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 = 13.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=20006248, alloc=4390108, time=0.72
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 1.1865844952106262493145778978974
y[1] (numeric) = 1.1865844952106262493145778978974
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 1.1808084316990017283667778535696
y[1] (numeric) = 1.1808084316990017283667778535695
absolute error = 1e-31
relative error = 8.4687742156545562352183626230611e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 1.1751142866615499425233799621437
y[1] (numeric) = 1.1751142866615499425233799621436
absolute error = 1e-31
relative error = 8.5098105890700875148035034838214e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 1.1695026295080295319154667122808
y[1] (numeric) = 1.1695026295080295319154667122808
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 1.1639740213994794832107405884529
y[1] (numeric) = 1.1639740213994794832107405884528
absolute error = 1e-31
relative error = 8.5912570350811713515856332349457e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 1.1585290151921034933474976783697
y[1] (numeric) = 1.1585290151921034933474976783696
absolute error = 1e-31
relative error = 8.6316353486769018868443454348184e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 1.153168155381984809876901215218
y[1] (numeric) = 1.1531681553819848098769012152179
absolute error = 1e-31
relative error = 8.6717621825825727657112539839197e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 1.1478919780506370763834500145446
y[1] (numeric) = 1.1478919780506370763834500145445
absolute error = 1e-31
relative error = 8.7116211204665017494348770073118e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 1.1427010108113966278537256147056
y[1] (numeric) = 1.1427010108113966278537256147055
absolute error = 1e-31
relative error = 8.7511955493058586179115167898098e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 1.1375957727566615967192083078838
y[1] (numeric) = 1.1375957727566615967192083078838
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 1.1325767744059831056185905149997
y[1] (numeric) = 1.1325767744059831056185905149997
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 1.1276445176550137377170540780026
y[1] (numeric) = 1.1276445176550137377170540780026
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 1.1227994957253183896929367422232
y[1] (numeric) = 1.1227994957253183896929367422232
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 1.1180421931150525262646650123752
y[1] (numeric) = 1.1180421931150525262646650123753
absolute error = 1e-31
relative error = 8.9442062755595364839371538812101e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 1.113373085550512768391399371364
y[1] (numeric) = 1.113373085550512768391399371364
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 1.1087926399385646600481974221283
y[1] (numeric) = 1.1087926399385646600481974221283
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 1.1043013143199523707593740406606
y[1] (numeric) = 1.1043013143199523707593740406606
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 1.0998995578234950028808967526608
y[1] (numeric) = 1.0998995578234950028808967526608
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 1.0955878106211740839629184775886
y[1] (numeric) = 1.0955878106211740839629184775886
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 1.0913665038841167354057844218978
y[1] (numeric) = 1.0913665038841167354057844218978
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=24007412, alloc=4455632, time=0.87
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 1.0872360597394789190559669502463
y[1] (numeric) = 1.0872360597394789190559669502463
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 1.0831968912282330733813383331257
y[1] (numeric) = 1.0831968912282330733813383331256
absolute error = 1e-31
relative error = 9.2319319608285025952245884734830e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 1.079249402263864360426986991038
y[1] (numeric) = 1.0792494022638643604269869910379
absolute error = 1e-31
relative error = 9.2656989005726706769964517663026e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 1.0753939875919796538924619741252
y[1] (numeric) = 1.0753939875919796538924619741252
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 1.0716310327508333073979788883973
y[1] (numeric) = 1.0716310327508333073979788883973
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 1.0679609140327736503298655645052
y[1] (numeric) = 1.0679609140327736503298655645051
absolute error = 1e-31
relative error = 9.3636385644850663363063136267275e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 1.0643839984466140665835351114564
y[1] (numeric) = 1.0643839984466140665835351114563
absolute error = 1e-31
relative error = 9.3951055395366942645505830501522e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 1.0609006436809324190647547281116
y[1] (numeric) = 1.0609006436809324190647547281115
absolute error = 1e-31
relative error = 9.4259533723192990544686068275284e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 1.0575111980683024899761764346108
y[1] (numeric) = 1.0575111980683024899761764346106
absolute error = 2e-31
relative error = 1.8912329284581477139699967145741e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 1.0542160005504610137152940369182
y[1] (numeric) = 1.0542160005504610137152940369181
absolute error = 1e-31
relative error = 9.4857220861554745940426854983962e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 1.051015380644413785651509152964
y[1] (numeric) = 1.0510153806444137856515091529638
absolute error = 2e-31
relative error = 1.9029217239178088983737124935182e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 1.0479096584094842361431837785746
y[1] (numeric) = 1.0479096584094842361431837785744
absolute error = 2e-31
relative error = 1.9085614718310709219314623010111e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 1.0448991444153077649098182578171
y[1] (numeric) = 1.0448991444153077649098182578169
absolute error = 2e-31
relative error = 1.9140603288742629909865044030434e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 1.0419841397107750362992461408397
y[1] (numeric) = 1.0419841397107750362992461408395
absolute error = 2e-31
relative error = 1.9194150119743115640560059734074e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = 1.0391649357939273410944387087146
y[1] (numeric) = 1.0391649357939273410944387087144
absolute error = 2e-31
relative error = 1.9246222915248672641928361964855e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 1.0364418145828070352986513699604
y[1] (numeric) = 1.0364418145828070352986513699602
absolute error = 2e-31
relative error = 1.9296789958296390243499471928966e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 1.0338150483872659708307421940625
y[1] (numeric) = 1.0338150483872659708307421940623
absolute error = 2e-31
relative error = 1.9345820155355314750670358066434e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = 1.0312848998817347372641001540272
y[1] (numeric) = 1.031284899881734737264100154027
absolute error = 2e-31
relative error = 1.9393283080449982074614976171725e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 1.0288516220789554376623169622362
y[1] (numeric) = 1.028851622078955437662316962236
absolute error = 2e-31
relative error = 1.9439149018968231243576115863232e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = 1.0265154583046806252121296519104
y[1] (numeric) = 1.0265154583046806252121296519102
absolute error = 2e-31
relative error = 1.9483389011043795557596016189940e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=28008900, alloc=4455632, time=1.03
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 1.0242766421733409307388864607348
y[1] (numeric) = 1.0242766421733409307388864607345
absolute error = 3e-31
relative error = 2.9288962341604411991785023845206e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 1.0221353975646838143215075605734
y[1] (numeric) = 1.0221353975646838143215075605731
absolute error = 3e-31
relative error = 2.9350319019845420639826053018050e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 1.0200919386013857771123114951081
y[1] (numeric) = 1.0200919386013857771123114951078
absolute error = 3e-31
relative error = 2.9409113889412757215057056335432e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = 1.018146469627640272121868914794
y[1] (numeric) = 1.0181464696276402721218689147937
absolute error = 3e-31
relative error = 2.9465308671130288669200228675943e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 1.0162991851887234551599617755571
y[1] (numeric) = 1.0162991851887234551599617755568
absolute error = 3e-31
relative error = 2.9518866527900538970174285918522e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 1.0145502700115398193405254211939
y[1] (numeric) = 1.0145502700115398193405254211936
absolute error = 3e-31
relative error = 2.9569752122444135175837937085527e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 1.0128998989861496585709111380578
y[1] (numeric) = 1.0128998989861496585709111380575
absolute error = 3e-31
relative error = 2.9617931673236565764627202914017e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 1.0113482371482802072637265266643
y[1] (numeric) = 1.011348237148280207263726526664
absolute error = 3e-31
relative error = 2.9663373008481853814870574227256e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 1.0098954396628222051427085045182
y[1] (numeric) = 1.0098954396628222051427085045179
absolute error = 3e-31
relative error = 2.9706045617966369820816309077550e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 1.008541651808313537472395536042
y[1] (numeric) = 1.0085416518083135374723955360417
absolute error = 3e-31
relative error = 2.9745920702640341039792535588451e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 1.007287008962411502334645865677
y[1] (numeric) = 1.0072870089624115023346458656767
absolute error = 3e-31
relative error = 2.9782971221779647854306015042498e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 1.00613163658835515771316769875
y[1] (numeric) = 1.0061316365883551577131676987497
absolute error = 3e-31
relative error = 2.9817171937586219684380167549566e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 1.0050756502224191021400715372644
y[1] (numeric) = 1.0050756502224191021400715372642
absolute error = 2e-31
relative error = 1.9898999638061157254199550962272e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 1.0041191554623599435159248674373
y[1] (numeric) = 1.0041191554623599435159248674371
absolute error = 2e-31
relative error = 1.9917954847490919065040001904711e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 1.0032622479568566114467992829563
y[1] (numeric) = 1.0032622479568566114467992829561
absolute error = 2e-31
relative error = 1.9934967194001365468947766415826e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 1.0025050133959455690582766288585
y[1] (numeric) = 1.0025050133959455690582766288583
absolute error = 2e-31
relative error = 1.9950024920325137596289569408302e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 1.0018475275024518807572621351633
y[1] (numeric) = 1.0018475275024518807572621351631
absolute error = 2e-31
relative error = 1.9963117591215548332151907586272e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = 1.0012898560244169928276876058832
y[1] (numeric) = 1.001289856024416992827687605883
absolute error = 2e-31
relative error = 1.9974236111218816961762799851789e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 1.000832054728523984075734931291
y[1] (numeric) = 1.0008320547285239840757349312909
absolute error = 1e-31
relative error = 9.9916863701098214806101470613926e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=32009752, alloc=4455632, time=1.17
x[1] = 1.54
y[1] (analytic) = 1.00047416939452094399403646156
y[1] (numeric) = 1.0004741693945209439940364615598
absolute error = 2e-31
relative error = 1.9990521106710672849013650899954e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 1.0002162358106430361023886523655
y[1] (numeric) = 1.0002162358106430361023886523654
absolute error = 1e-31
relative error = 9.9978381093717421618923489186190e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = 1.0000582797700337042548299765865
y[1] (numeric) = 1.0000582797700337042548299765864
absolute error = 1e-31
relative error = 9.9994172362629995338209765379344e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 1.0000003170681653797894700761767
y[1] (numeric) = 1.0000003170681653797894700761766
absolute error = 1e-31
relative error = 9.9999968293193515240015167242419e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 1.0000423535012599474482057677483
y[1] (numeric) = 1.0000423535012599474482057677482
absolute error = 1e-31
relative error = 9.9995764829248315022761687989208e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.008862
Order of pole (three term test) = -0.8909
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 1.0001843848657091280184156562545
y[1] (numeric) = 1.0001843848657091280184156562544
absolute error = 1e-31
relative error = 9.9981564912580205433015006954264e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01849
Order of pole (three term test) = -0.8974
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 1.0004263969584948356578861744538
y[1] (numeric) = 1.0004263969584948356578861744537
absolute error = 1e-31
relative error = 9.9957378477837932759914505641782e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02811
Order of pole (three term test) = -0.9087
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = 1.0007683655786094678675868521557
y[1] (numeric) = 1.0007683655786094678675868521556
absolute error = 1e-31
relative error = 9.9923222435376919052644159982900e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03771
Order of pole (three term test) = -0.9245
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 1.0012102565294759860844811087532
y[1] (numeric) = 1.0012102565294759860844811087531
absolute error = 1e-31
relative error = 9.9879120642084597372303990719157e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0473
Order of pole (three term test) = -0.945
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 1.0017520256223675448883300150669
y[1] (numeric) = 1.0017520256223675448883300150668
absolute error = 1e-31
relative error = 9.9825103860281285872373635527405e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05688
Order of pole (three term test) = -0.9701
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 1.0023936186808263278624180256321
y[1] (numeric) = 1.002393618680826327862418025632
absolute error = 1e-31
relative error = 9.9761209704828689295933709540155e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06643
Order of pole (three term test) = -0.9997
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 1.0031349715460811482282969597978
y[1] (numeric) = 1.0031349715460811482282969597977
absolute error = 1e-31
relative error = 9.9687482578615579986076723695363e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07595
Order of pole (three term test) = -1.034
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 1.003976010083463272498999409387
y[1] (numeric) = 1.0039760100834632724989994093869
absolute error = 1e-31
relative error = 9.9603973596626802277597843121470e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08544
Order of pole (three term test) = -1.073
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = 1.0049166501898198255737027534658
y[1] (numeric) = 1.0049166501898198255737027534656
absolute error = 2e-31
relative error = 1.9902148099767456056340734115580e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0949
Order of pole (three term test) = -1.116
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 1.0059567978019240359395121308064
y[1] (numeric) = 1.0059567978019240359395121308063
absolute error = 1e-31
relative error = 9.9407847552207013604854046055065e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1043
Order of pole (three term test) = -1.164
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 1.0070963489058814799628507060544
y[1] (numeric) = 1.0070963489058814799628507060543
absolute error = 1e-31
relative error = 9.9295365442085951641114556557187e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1137
Order of pole (three term test) = -1.217
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 1.0083351895475313846538666013521
y[1] (numeric) = 1.008335189547531384653866601352
absolute error = 1e-31
relative error = 9.9173371153368988267654364733717e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.123
Order of pole (three term test) = -1.274
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 1.0096731958438419487822477761389
y[1] (numeric) = 1.0096731958438419487822477761387
absolute error = 2e-31
relative error = 1.9808389568354193996803142916981e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1323
Order of pole (three term test) = -1.335
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 1.0111102339952985428218293429145
y[1] (numeric) = 1.0111102339952985428218293429144
absolute error = 1e-31
relative error = 9.8901184695619429052991666087528e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1416
Order of pole (three term test) = -1.401
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 1.0126461602992835489143223237779
y[1] (numeric) = 1.0126461602992835489143223237778
absolute error = 1e-31
relative error = 9.8751176788588619494933498397890e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1507
Order of pole (three term test) = -1.472
NO COMPLEX POLE (six term test) for Equation 1
bytes used=36011940, alloc=4455632, time=1.33
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 1.0142808211644465028793173043344
y[1] (numeric) = 1.0142808211644465028793173043343
absolute error = 1e-31
relative error = 9.8592024923822242212629733056395e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1598
Order of pole (three term test) = -1.546
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 1.016014053126063101268337063032
y[1] (numeric) = 1.0160140531260631012683370630319
absolute error = 1e-31
relative error = 9.8423835469913904883693668757750e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1689
Order of pole (three term test) = -1.625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 1.017845682862381537575031900544
y[1] (numeric) = 1.0178456828623815375750319005439
absolute error = 1e-31
relative error = 9.8246720189233796230325443107708e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1779
Order of pole (three term test) = -1.709
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 1.0197755272119545329815185511016
y[1] (numeric) = 1.0197755272119545329815185511014
absolute error = 2e-31
relative error = 1.9612159211821440340859640625036e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1868
Order of pole (three term test) = -1.797
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 1.0218033931919553284522313526944
y[1] (numeric) = 1.0218033931919553284522313526942
absolute error = 2e-31
relative error = 1.9573237017273060532375797803809e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1956
Order of pole (three term test) = -1.889
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = 1.0239290780174758065913395668914
y[1] (numeric) = 1.0239290780174758065913395668912
absolute error = 2e-31
relative error = 1.9532602823160230645229315978679e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2044
Order of pole (three term test) = -1.985
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 1.0261523691218048134676268211566
y[1] (numeric) = 1.0261523691218048134676268211565
absolute error = 1e-31
relative error = 9.7451414633073802920258216134393e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.213
Order of pole (three term test) = -2.086
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 1.0284730441776846525915487309096
y[1] (numeric) = 1.0284730441776846525915487309095
absolute error = 1e-31
relative error = 9.7231522562611228430518876962136e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2216
Order of pole (three term test) = -2.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 1.030890871119543625412784681502
y[1] (numeric) = 1.0308908711195436254127846815018
absolute error = 2e-31
relative error = 1.9400695612213613744365071964483e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2301
Order of pole (three term test) = -2.299
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 1.0334056081667023951027610702572
y[1] (numeric) = 1.033405608166702395102761070257
absolute error = 2e-31
relative error = 1.9353485061379430492390498131561e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2385
Order of pole (three term test) = -2.412
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = 1.0360170038475518530051063282729
y[1] (numeric) = 1.0360170038475518530051063282727
absolute error = 2e-31
relative error = 1.9304702457318901416318874396617e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2469
Order of pole (three term test) = -2.529
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = 1.0387247970247000699875408313639
y[1] (numeric) = 1.0387247970247000699875408313637
absolute error = 2e-31
relative error = 1.9254378115635199871884098298489e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2551
Order of pole (three term test) = -2.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 1.0415287169210858180210222340968
y[1] (numeric) = 1.0415287169210858180210222340966
absolute error = 2e-31
relative error = 1.9202543026488008947382125042391e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2632
Order of pole (three term test) = -2.774
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 1.0444284831470560506557495078274
y[1] (numeric) = 1.0444284831470560506557495078272
absolute error = 2e-31
relative error = 1.9149228810513002868787773146847e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2712
Order of pole (three term test) = -2.903
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 1.0474238057284046346685425741849
y[1] (numeric) = 1.0474238057284046346685425741847
absolute error = 2e-31
relative error = 1.9094467674516430576402226878162e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2791
Order of pole (three term test) = -3.035
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 1.0505143851353695290317983278617
y[1] (numeric) = 1.0505143851353695290317983278615
absolute error = 2e-31
relative error = 1.9038292367051018847973816747845e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2869
Order of pole (three term test) = -3.172
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = 1.053699912312585511510290388365
y[1] (numeric) = 1.0536999123125855115102903883649
absolute error = 1e-31
relative error = 9.4903680669885530400988182963611e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2946
Order of pole (three term test) = -3.312
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 1.0569800687099894576381134230518
y[1] (numeric) = 1.0569800687099894576381134230516
absolute error = 2e-31
relative error = 1.8921832674110273082452595348258e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3021
Order of pole (three term test) = -3.455
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 1.060354526314675081573628660313
y[1] (numeric) = 1.0603545263146750815736286603128
absolute error = 2e-31
relative error = 1.8861616095053777717999277182591e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3095
Order of pole (three term test) = -3.602
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=40012816, alloc=4455632, time=1.47
x[1] = 1.93
y[1] (analytic) = 1.0638229476836939533848706272512
y[1] (numeric) = 1.063822947683693953384870627251
absolute error = 2e-31
relative error = 1.8800120869310850688716581891393e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3168
Order of pole (three term test) = -3.753
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 1.0673849859777995126910206611343
y[1] (numeric) = 1.0673849859777995126910206611341
absolute error = 2e-31
relative error = 1.8737381790768395731068915679150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.324
Order of pole (three term test) = -3.908
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 1.0710402849961307042867029649085
y[1] (numeric) = 1.0710402849961307042867029649083
absolute error = 2e-31
relative error = 1.8673433931639885084121023148604e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3311
Order of pole (three term test) = -4.065
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 1.07478847921183176741444371051
y[1] (numeric) = 1.0747884792118317674144437105098
absolute error = 2e-31
relative error = 1.8608312599951276788250591960230e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.338
Order of pole (three term test) = -4.226
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 1.0786291938086046167360490028468
y[1] (numeric) = 1.0786291938086046167360490028467
absolute error = 1e-31
relative error = 9.2710266488248154153911476411645e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3448
Order of pole (three term test) = -4.391
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = 1.082562044718190159795264782598
y[1] (numeric) = 1.0825620447181901597952647825979
absolute error = 1e-31
relative error = 9.2373458397048965031866718913917e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3514
Order of pole (three term test) = -4.558
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 1.0865866386587748028712067289424
y[1] (numeric) = 1.0865866386587748028712067289423
absolute error = 1e-31
relative error = 9.2031317561050375180245510294952e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3579
Order of pole (three term test) = -4.729
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 1.0907025731743183046039801340883
y[1] (numeric) = 1.0907025731743183046039801340882
absolute error = 1e-31
relative error = 9.1684023178716565217284135664528e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3643
Order of pole (three term test) = -4.903
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 1.0949094366747990446399002897263
y[1] (numeric) = 1.0949094366747990446399002897262
absolute error = 1e-31
relative error = 9.1331754618625297186739971270557e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3705
Order of pole (three term test) = -5.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 1.0992068084773726828029864754463
y[1] (numeric) = 1.0992068084773726828029864754462
absolute error = 1e-31
relative error = 9.0974691230779902138296500159890e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3766
Order of pole (three term test) = -5.259
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 1.1035942588484400929611111680324
y[1] (numeric) = 1.1035942588484400929611111680323
absolute error = 1e-31
relative error = 9.0613012162954084105951319593129e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3825
Order of pole (three term test) = -5.442
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 1.1080713490466203648284743514158
y[1] (numeric) = 1.1080713490466203648284743514157
absolute error = 1e-31
relative error = 9.0246896182307712366763275374182e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3883
Order of pole (three term test) = -5.628
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 1.1126376313666245764400333953197
y[1] (numeric) = 1.1126376313666245764400333953196
absolute error = 1e-31
relative error = 8.9876521502488224193674338292929e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3939
Order of pole (three term test) = -5.816
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 1.1172926491840259499572024148001
y[1] (numeric) = 1.1172926491840259499572024148
absolute error = 1e-31
relative error = 8.9502065616408881744829677320517e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3993
Order of pole (three term test) = -6.007
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 1.1220359370009219138265488795562
y[1] (numeric) = 1.1220359370009219138265488795561
absolute error = 1e-31
relative error = 8.9123705134872017583125678542797e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4046
Order of pole (three term test) = -6.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 1.1268670204924835051233231949754
y[1] (numeric) = 1.1268670204924835051233231949753
absolute error = 1e-31
relative error = 8.8741615631182655504150329073605e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4097
Order of pole (three term test) = -6.396
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 1.1317854165543874571783779412725
y[1] (numeric) = 1.1317854165543874571783779412724
absolute error = 1e-31
relative error = 8.8355971491875592111441236343972e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4147
Order of pole (three term test) = -6.595
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 1.136790633351126229319240686731
y[1] (numeric) = 1.1367906333511262293192406867309
absolute error = 1e-31
relative error = 8.7966945773657248305076080518435e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4195
Order of pole (three term test) = -6.796
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 1.1418821703651911477626244916893
y[1] (numeric) = 1.1418821703651911477626244916892
absolute error = 1e-31
relative error = 8.7574710066642419958080078846701e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4241
Order of pole (three term test) = -6.999
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 1.1470595184471237393852726663458
y[1] (numeric) = 1.1470595184471237393852726663457
absolute error = 1e-31
relative error = 8.7179434363945537924301266434375e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4286
Order of pole (three term test) = -7.204
NO COMPLEX POLE (six term test) for Equation 1
bytes used=44014776, alloc=4455632, time=1.63
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 1.1523221598664302532814700036841
y[1] (numeric) = 1.152322159866430253281470003684
absolute error = 1e-31
relative error = 8.6781286937666246491495187561309e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4329
Order of pole (three term test) = -7.411
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 1.1576695683633542786974933629311
y[1] (numeric) = 1.157669568363354278697493362931
absolute error = 1e-31
relative error = 8.6380434221290076815724737400717e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.437
Order of pole (three term test) = -7.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 1.1631012092015022821243518629562
y[1] (numeric) = 1.1631012092015022821243518629561
absolute error = 1e-31
relative error = 8.5977040698506771209927103107695e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4409
Order of pole (three term test) = -7.832
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 1.1686165392213168010389618796537
y[1] (numeric) = 1.1686165392213168010389618796536
absolute error = 1e-31
relative error = 8.5571268798431442128242908543691e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4447
Order of pole (three term test) = -8.045
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 1.1742150068943919470189435760566
y[1] (numeric) = 1.1742150068943919470189435760565
absolute error = 1e-31
relative error = 8.5163278797197256446965923559502e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4483
Order of pole (three term test) = -8.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 1.1798960523786257867259902539161
y[1] (numeric) = 1.1798960523786257867259902539159
absolute error = 2e-31
relative error = 1.6950645745174549002745308845274e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4517
Order of pole (three term test) = -8.476
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 1.185659107574204085565672354095
y[1] (numeric) = 1.1856591075742040855656723540948
absolute error = 2e-31
relative error = 1.6868254856928433431067718806665e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4549
Order of pole (three term test) = -8.694
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 1.1915035961804098156959630895839
y[1] (numeric) = 1.1915035961804098156959630895837
absolute error = 2e-31
relative error = 1.6785513752634724366811827568224e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4579
Order of pole (three term test) = -8.914
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 1.197428933753252747481025957444
y[1] (numeric) = 1.1974289337532527474810259574439
absolute error = 1e-31
relative error = 8.3512262967086797853149864283113e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4608
Order of pole (three term test) = -9.135
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 1.2034345277639133614791432503908
y[1] (numeric) = 1.2034345277639133614791432503907
absolute error = 1e-31
relative error = 8.3095505150420396187232622215618e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4635
Order of pole (three term test) = -9.358
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 1.2095197776579952366222898728115
y[1] (numeric) = 1.2095197776579952366222898728113
absolute error = 2e-31
relative error = 1.6535488190797666911758987541566e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.466
Order of pole (three term test) = -9.581
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 1.2156840749155799893979113293955
y[1] (numeric) = 1.2156840749155799893979113293953
absolute error = 2e-31
relative error = 1.6451642669900769941906820949254e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.24
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4683
Order of pole (three term test) = -9.806
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 1.2219268031120787585890333244122
y[1] (numeric) = 1.221926803112078758589033324412
absolute error = 2e-31
relative error = 1.6367592517868306837939268878298e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4704
Order of pole (three term test) = -10.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 1.2282473379798741504749383622597
y[1] (numeric) = 1.2282473379798741504749383622594
absolute error = 3e-31
relative error = 2.4425047848539749766298407804515e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.83
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4723
Order of pole (three term test) = -10.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 1.2346450474707464803492573980653
y[1] (numeric) = 1.234645047470746480349257398065
absolute error = 3e-31
relative error = 2.4298481625514167147473360540465e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.14
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4741
Order of pole (three term test) = -10.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 1.2411192918190780677833464236991
y[1] (numeric) = 1.2411192918190780677833464236988
absolute error = 3e-31
relative error = 2.4171729661884263124842877167660e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4756
Order of pole (three term test) = -10.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 1.2476694236058292652580917220264
y[1] (numeric) = 1.2476694236058292652580917220261
absolute error = 3e-31
relative error = 2.4044830651775087953710199861926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.477
Order of pole (three term test) = -10.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 1.2542947878232798226145937883565
y[1] (numeric) = 1.2542947878232798226145937883563
absolute error = 2e-31
relative error = 1.5945214948001395357834523084085e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4781
Order of pole (three term test) = -11.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 1.2609947219405291132412358079017
y[1] (numeric) = 1.2609947219405291132412358079015
absolute error = 2e-31
relative error = 1.5860494617473297940840820977354e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4791
Order of pole (three term test) = -11.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=48015644, alloc=4455632, time=1.78
x[1] = 2.32
y[1] (analytic) = 1.2677685559697486720291013222753
y[1] (numeric) = 1.2677685559697486720291013222751
absolute error = 2e-31
relative error = 1.5775750160250257375909146549629e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4799
Order of pole (three term test) = -11.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 1.2746156125331804198971558075246
y[1] (numeric) = 1.2746156125331804198971558075244
absolute error = 2e-31
relative error = 1.5691005039748299697037300697748e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4805
Order of pole (three term test) = -11.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 1.281535206930873875120571313206
y[1] (numeric) = 1.2815352069308738751205713132058
absolute error = 2e-31
relative error = 1.5606282130865251997311524377762e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4809
Order of pole (three term test) = -12.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 1.2885266472091555777975088179868
y[1] (numeric) = 1.2885266472091555777975088179866
absolute error = 2e-31
relative error = 1.5521603719502721316793572166083e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.78
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4811
Order of pole (three term test) = -12.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 1.2955892342298238805689692870673
y[1] (numeric) = 1.2955892342298238805689692870671
absolute error = 2e-31
relative error = 1.5436991502857927197396722141095e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.14
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4811
Order of pole (three term test) = -12.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 1.3027222617400621861703035797108
y[1] (numeric) = 1.3027222617400621861703035797106
absolute error = 2e-31
relative error = 1.5352466590450180394948277279094e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4809
Order of pole (three term test) = -12.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 1.3099250164430636405488868929798
y[1] (numeric) = 1.3099250164430636405488868929796
absolute error = 2e-31
relative error = 1.5268049505846892232996978194540e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.12
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4806
Order of pole (three term test) = -13.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 1.317196778069360219137499688987
y[1] (numeric) = 1.3171967780693602191374996889867
absolute error = 3e-31
relative error = 2.2775640283581286287456995604136e-29 %
Correct digits = 31
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 = 0.48
Order of pole (three term test) = -13.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 1.3245368194488490734342284746587
y[1] (numeric) = 1.3245368194488490734342284746585
absolute error = 2e-31
relative error = 1.5099617999537505081387090020650e-29 %
Correct digits = 31
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 = 0.4792
Order of pole (three term test) = -13.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 1.3319444065835089353142501993453
y[1] (numeric) = 1.3319444065835089353142501993451
absolute error = 2e-31
relative error = 1.5015641719837846510687760196275e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.06
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4783
Order of pole (three term test) = -13.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 1.3394187987207993074936658934398
y[1] (numeric) = 1.3394187987207993074936658934396
absolute error = 2e-31
relative error = 1.4931849559749969387642282528645e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4772
Order of pole (three term test) = -13.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 1.3469592484277351002875029528101
y[1] (numeric) = 1.3469592484277351002875029528099
absolute error = 2e-31
relative error = 1.4848259161029108119433157477930e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4758
Order of pole (three term test) = -14.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 1.3545650016656293072599389270175
y[1] (numeric) = 1.3545650016656293072599389270173
absolute error = 2e-31
relative error = 1.4764887602593578374401521970997e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.06
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4743
Order of pole (three term test) = -14.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 1.3622352978654962455614671443662
y[1] (numeric) = 1.3622352978654962455614671443661
absolute error = 1e-31
relative error = 7.3408757030955861657117043410000e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4726
Order of pole (three term test) = -14.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = 1.3699693700041078206918062813841
y[1] (numeric) = 1.369969370004107820691806281384
absolute error = 1e-31
relative error = 7.2994332712489880244329142880175e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4707
Order of pole (three term test) = -14.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 1.3777664446806952101254575951442
y[1] (numeric) = 1.3777664446806952101254575951442
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4686
Order of pole (three term test) = -15.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 1.3856257421942882956954651193344
y[1] (numeric) = 1.3856257421942882956954651193344
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 = 14.79
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4664
Order of pole (three term test) = -15.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 1.3935464766216851108565897602082
y[1] (numeric) = 1.3935464766216851108565897602082
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 = 14.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4639
Order of pole (three term test) = -15.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 1.4015278558960435059481452978138
y[1] (numeric) = 1.4015278558960435059481452978138
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 = 14.19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4613
Order of pole (three term test) = -15.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 1.409569081886087172355462844976
y[1] (numeric) = 1.4095690818860871723554628449759
absolute error = 1e-31
relative error = 7.0943667312987639542377352834993e-30 %
Correct digits = 32
h = 0.01
bytes used=52016804, alloc=4455632, time=1.94
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4584
Order of pole (three term test) = -15.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 1.4176693504759181050335724177029
y[1] (numeric) = 1.4176693504759181050335724177028
absolute error = 1e-31
relative error = 7.0538309914388387682412280900112e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4554
Order of pole (three term test) = -16.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 1.4258278516454275222133594125978
y[1] (numeric) = 1.4258278516454275222133594125977
absolute error = 1e-31
relative error = 7.0134693949622631030302952972107e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4522
Order of pole (three term test) = -16.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 1.434043769551297201265234252018
y[1] (numeric) = 1.4340437695512972012652342520179
absolute error = 1e-31
relative error = 6.9732878537793402054763906478023e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4489
Order of pole (three term test) = -16.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 1.4423162826085831306542297182338
y[1] (numeric) = 1.4423162826085831306542297182337
absolute error = 1e-31
relative error = 6.9332920390484196344500982761377e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4453
Order of pole (three term test) = -16.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 1.4506445635728733196893166168627
y[1] (numeric) = 1.4506445635728733196893166168627
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4416
Order of pole (three term test) = -17.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 1.4590277796230115503544274512542
y[1] (numeric) = 1.4590277796230115503544274512541
absolute error = 1e-31
relative error = 6.8538790965198985139647128826792e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4377
Order of pole (three term test) = -17.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 1.4674650924443787989149412355284
y[1] (numeric) = 1.4674650924443787989149412355283
absolute error = 1e-31
relative error = 6.8144721475744603618970045814936e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4336
Order of pole (three term test) = -17.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 1.4759556583127239992268697511241
y[1] (numeric) = 1.475955658312723999226869751124
absolute error = 1e-31
relative error = 6.7752712919788882070367464552326e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4293
Order of pole (three term test) = -17.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 1.4844986281785357647422730647906
y[1] (numeric) = 1.4844986281785357647422730647905
absolute error = 1e-31
relative error = 6.7362810649881805808873011215890e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4249
Order of pole (three term test) = -17.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 1.4930931477519466321090133004445
y[1] (numeric) = 1.4930931477519466321090133004444
absolute error = 1e-31
relative error = 6.6975057886082662990920505365338e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4203
Order of pole (three term test) = -18.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 1.5017383575881613360112399900024
y[1] (numeric) = 1.5017383575881613360112399900023
absolute error = 1e-31
relative error = 6.6589495763165509401463446228451e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4155
Order of pole (three term test) = -18.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 1.5104333931734005724943129463884
y[1] (numeric) = 1.5104333931734005724943129463883
absolute error = 1e-31
relative error = 6.6206163377983403315557961826744e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4106
Order of pole (three term test) = -18.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 1.5191773850113516564694497304671
y[1] (numeric) = 1.5191773850113516564694497304671
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4055
Order of pole (three term test) = -18.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 1.5279694587101174284043892216026
y[1] (numeric) = 1.5279694587101174284043892216026
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4003
Order of pole (three term test) = -18.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 1.5368087350696547153818594062036
y[1] (numeric) = 1.5368087350696547153818594062036
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3948
Order of pole (three term test) = -19.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 1.5456943301696936027526086788087
y[1] (numeric) = 1.5456943301696936027526086788087
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3893
Order of pole (three term test) = -19.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 1.5546253554581287245291011680706
y[1] (numeric) = 1.5546253554581287245291011680705
absolute error = 1e-31
relative error = 6.4324179230005705016290684055123e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3835
Order of pole (three term test) = -19.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 1.563600917839873733464495881239
y[1] (numeric) = 1.563600917839873733464495881239
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3777
Order of pole (three term test) = -19.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 1.5726201197661700654439469141421
y[1] (numeric) = 1.5726201197661700654439469141421
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3716
Order of pole (three term test) = -19.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=56018968, alloc=4521156, time=2.09
x[1] = 2.71
y[1] (analytic) = 1.5816820593243410673862093188914
y[1] (numeric) = 1.5816820593243410673862093188914
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3654
Order of pole (three term test) = -19.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 1.5907858303279825133175553259926
y[1] (numeric) = 1.5907858303279825133175553259926
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3591
Order of pole (three term test) = -20.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 1.5999305224075804896415520421056
y[1] (numeric) = 1.5999305224075804896415520421056
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3526
Order of pole (three term test) = -20.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 1.6091152211015475878916882983597
y[1] (numeric) = 1.6091152211015475878916882983598
absolute error = 1e-31
relative error = 6.2145953682262277417322175301373e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.346
Order of pole (three term test) = -20.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 1.6183390079476683014234386276222
y[1] (numeric) = 1.6183390079476683014234386276223
absolute error = 1e-31
relative error = 6.1791750374241530520595923960859e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3393
Order of pole (three term test) = -20.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 1.6276009605749444815822994075502
y[1] (numeric) = 1.6276009605749444815822994075503
absolute error = 1e-31
relative error = 6.1440121026148412611078434980163e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3324
Order of pole (three term test) = -20.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 1.6369001527958316688787179908275
y[1] (numeric) = 1.6369001527958316688787179908276
absolute error = 1e-31
relative error = 6.1091081107909740708660567715408e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3254
Order of pole (three term test) = -20.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 1.6462356546988570756136606827727
y[1] (numeric) = 1.6462356546988570756136606827727
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3182
Order of pole (three term test) = -21.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 1.6556065327416099582337384044377
y[1] (numeric) = 1.6556065327416099582337384044378
absolute error = 1e-31
relative error = 6.0400824726394681135127997087224e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3109
Order of pole (three term test) = -21.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 1.6650118498440950804561462472876
y[1] (numeric) = 1.6650118498440950804561462472877
absolute error = 1e-31
relative error = 6.0059632614244512548398502724673e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3035
Order of pole (three term test) = -21.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 1.6744506654824399318948987187937
y[1] (numeric) = 1.6744506654824399318948987187938
absolute error = 1e-31
relative error = 5.9721078716396918658318061085178e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.296
Order of pole (three term test) = -21.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 1.6839220357829463315445871439754
y[1] (numeric) = 1.6839220357829463315445871439756
absolute error = 2e-31
relative error = 1.1877034432120201729970674826554e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2884
Order of pole (three term test) = -21.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = 1.6934250136164770110396869221319
y[1] (numeric) = 1.6934250136164770110396869221321
absolute error = 2e-31
relative error = 1.1810384185413688381692624608973e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2806
Order of pole (three term test) = -21.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 1.7029586486931677391097439319027
y[1] (numeric) = 1.7029586486931677391097439319029
absolute error = 2e-31
relative error = 1.1744266377429531939905676878077e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2728
Order of pole (three term test) = -22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 1.7125219876574555160969210733083
y[1] (numeric) = 1.7125219876574555160969210733085
absolute error = 2e-31
relative error = 1.1678682168255154780525394786383e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2648
Order of pole (three term test) = -22.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 1.7221140741834133357956430902468
y[1] (numeric) = 1.722114074183413335795643090247
absolute error = 2e-31
relative error = 1.1613632511239731567520299696745e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2567
Order of pole (three term test) = -22.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 1.7317339490703819812176010790129
y[1] (numeric) = 1.7317339490703819812176010790131
absolute error = 2e-31
relative error = 1.1549118160290308071198176879722e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2485
Order of pole (three term test) = -22.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = 1.7413806503388892911822330798823
y[1] (numeric) = 1.7413806503388892911822330798826
absolute error = 3e-31
relative error = 1.7227709515528218217877423912640e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2402
Order of pole (three term test) = -22.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 1.7510532133268473058859541594195
y[1] (numeric) = 1.7510532133268473058859541594198
absolute error = 3e-31
relative error = 1.7132546156608590424228143517360e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2319
Order of pole (three term test) = -22.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = 1.7607506707860176718157430812604
y[1] (numeric) = 1.7607506707860176718157430812607
absolute error = 3e-31
relative error = 1.7038187460469734514064612664989e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2234
Order of pole (three term test) = -22.72
NO COMPLEX POLE (six term test) for Equation 1
bytes used=60021128, alloc=4521156, time=2.24
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 1.770472052978735659546981776173
y[1] (numeric) = 1.7704720529787356595469817761733
absolute error = 3e-31
relative error = 1.6944633466270431129408163968218e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2148
Order of pole (three term test) = -22.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = 1.7802163877748831221043709069354
y[1] (numeric) = 1.7802163877748831221043709069357
absolute error = 3e-31
relative error = 1.6851883965351769082208563521285e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2062
Order of pole (three term test) = -22.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 1.7899827007491006966708959657409
y[1] (numeric) = 1.7899827007491006966708959657412
absolute error = 3e-31
relative error = 1.6759938510827573018095474544628e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1974
Order of pole (three term test) = -23.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = 1.7997700152782295285056829055769
y[1] (numeric) = 1.7997700152782295285056829055772
absolute error = 3e-31
relative error = 1.6668796426949166963075958005790e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1886
Order of pole (three term test) = -23.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 1.8095773526389727729795526859426
y[1] (numeric) = 1.8095773526389727729795526859429
absolute error = 3e-31
relative error = 1.6578456818245378589996841627726e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1798
Order of pole (three term test) = -23.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 1.8194037321057671096594554911986
y[1] (numeric) = 1.8194037321057671096594554911989
absolute error = 3e-31
relative error = 1.6488918578438979886927269127956e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1708
Order of pole (three term test) = -23.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = 1.829248171048854481371935501332
y[1] (numeric) = 1.8292481710488544813719355013323
absolute error = 3e-31
relative error = 1.6400180399141029231180126653474e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1618
Order of pole (three term test) = -23.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 1.8391096850325442511534460454587
y[1] (numeric) = 1.8391096850325442511534460454589
absolute error = 2e-31
relative error = 1.0874827185549885727899443756766e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1527
Order of pole (three term test) = -23.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 1.8489872879136559509537049643895
y[1] (numeric) = 1.8489872879136559509537049643897
absolute error = 2e-31
relative error = 1.0816732019054292405699791783073e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1435
Order of pole (three term test) = -23.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = 1.8588799919401327778992551971919
y[1] (numeric) = 1.8588799919401327778992551971921
absolute error = 2e-31
relative error = 1.0759166856772603011498430164056e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1343
Order of pole (three term test) = -23.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = 1.8687868078498159768497818753152
y[1] (numeric) = 1.8687868078498159768497818753154
absolute error = 2e-31
relative error = 1.0702130342525025460859540834299e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1251
Order of pole (three term test) = -23.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = 1.8787067449693702318912420036609
y[1] (numeric) = 1.8787067449693702318912420036611
absolute error = 2e-31
relative error = 1.0645621012195851196019036224713e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1158
Order of pole (three term test) = -23.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = 1.8886388113133501743090949670827
y[1] (numeric) = 1.888638811313350174309094967083
absolute error = 3e-31
relative error = 1.5884455948005297535891525039634e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1064
Order of pole (three term test) = -23.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = 1.8985820136833981004733916873912
y[1] (numeric) = 1.8985820136833981004733916873915
absolute error = 3e-31
relative error = 1.5801266304950211609385354833513e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09702
Order of pole (three term test) = -23.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = 1.9085353577675629799465984113036
y[1] (numeric) = 1.9085353577675629799465984113039
absolute error = 3e-31
relative error = 1.5718859950853289334560547934053e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08758
Order of pole (three term test) = -23.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = 1.9184978482397308219961099111643
y[1] (numeric) = 1.9184978482397308219961099111646
absolute error = 3e-31
relative error = 1.5637234113932283656187558161187e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07811
Order of pole (three term test) = -23.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = 1.9284684888591564575576592096811
y[1] (numeric) = 1.9284684888591564575576592096814
absolute error = 3e-31
relative error = 1.5556385895497521140529217514828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0686
Order of pole (three term test) = -23.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = 1.9384462825700867835543703628643
y[1] (numeric) = 1.9384462825700867835543703628646
absolute error = 3e-31
relative error = 1.5476312276358019248473577767135e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05907
Order of pole (three term test) = -23.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = 1.9484302316014655073300414894254
y[1] (numeric) = 1.9484302316014655073300414894257
absolute error = 3e-31
relative error = 1.5397010123037466613286953054743e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04952
Order of pole (three term test) = -23.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = 1.9584193375667094208053017284033
y[1] (numeric) = 1.9584193375667094208053017284036
bytes used=64022228, alloc=4521156, time=2.39
absolute error = 3e-31
relative error = 1.5318476193803470001475905855040e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03995
Order of pole (three term test) = -24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = 1.9684126015635462268123731272966
y[1] (numeric) = 1.9684126015635462268123731272969
absolute error = 3e-31
relative error = 1.5240707144513528236023024540394e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03036
Order of pole (three term test) = -24.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = 1.9784090242739039339090018957981
y[1] (numeric) = 1.9784090242739039339090018957984
absolute error = 3e-31
relative error = 1.5163699534281240240110362712408e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02076
Order of pole (three term test) = -24.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = 1.9884076060638418308153185168817
y[1] (numeric) = 1.988407606063841830815318516882
absolute error = 3e-31
relative error = 1.5087449830966292119713830959392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01115
Order of pole (three term test) = -24.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = 1.9984073470835130474594585636756
y[1] (numeric) = 1.9984073470835130474594585636759
absolute error = 3e-31
relative error = 1.5011954416491797424499906991389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.001531
Order of pole (three term test) = -24.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = 2.0084072473671487064591415165711
y[1] (numeric) = 2.0084072473671487064591415165714
absolute error = 3e-31
relative error = 1.4937209591992585963911750930038e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = 2.0184063069330536667073792711874
y[1] (numeric) = 2.0184063069330536667073792711877
absolute error = 3e-31
relative error = 1.4863211582798050341417576216364e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = 2.0284035258836038595712852748967
y[1] (numeric) = 2.0284035258836038595712852748971
absolute error = 4e-31
relative error = 1.9719942057670888285071329700036e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = 2.0383979045052352180536952467261
y[1] (numeric) = 2.0383979045052352180536952467265
absolute error = 4e-31
relative error = 1.9623254081841736894288733898356e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = 2.0483884433684142001080071484512
y[1] (numeric) = 2.0483884433684142001080071484515
absolute error = 3e-31
relative error = 1.4645659663392433526855810023099e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = 2.0583741434275799091372174146191
y[1] (numeric) = 2.0583741434275799091372174146194
absolute error = 3e-31
relative error = 1.4574609818040349168091891769389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = 2.0683540061210478175483883606769
y[1] (numeric) = 2.0683540061210478175483883606772
absolute error = 3e-31
relative error = 1.4504286940832452315088194504278e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = 2.078327033470865103073444147916
y[1] (numeric) = 2.0783270334708651030734441479164
absolute error = 4e-31
relative error = 1.9246249197460933419836995342545e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = 2.0882922281826076124058757285297
y[1] (numeric) = 2.0882922281826076124058757285301
absolute error = 4e-31
relative error = 1.9154407347869638964703345581997e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = 2.0982485937451084725401549594376
y[1] (numeric) = 2.098248593745108472540154959438
absolute error = 4e-31
relative error = 1.9063518078477563484444549202852e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = 2.1081951345301083770358308425608
y[1] (numeric) = 2.1081951345301083770358308425612
absolute error = 4e-31
relative error = 1.8973575711678854758667450351170e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = 2.1181308558918175822607231103361
y[1] (numeric) = 2.1181308558918175822607231103365
absolute error = 4e-31
relative error = 1.8884574524154412738511458032464e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 2.1280547642663796574965568907536
y[1] (numeric) = 2.128054764266379657496556890754
absolute error = 4e-31
relative error = 1.8796508751404008715947671893279e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = 2.1379658672712270426149140705852
y[1] (numeric) = 2.1379658672712270426149140705856
absolute error = 4e-31
relative error = 1.8709372592114218352327105496977e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = 2.1478631738043184778505297837426
y[1] (numeric) = 2.147863173804318477850529783743
absolute error = 4e-31
relative error = 1.8623160212366585478591265447495e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=68023444, alloc=4521156, time=2.55
x[1] = 3.3
y[1] (analytic) = 2.1577456941432483820116542776025
y[1] (numeric) = 2.1577456941432483820116542776028
absolute error = 3e-31
relative error = 1.3903399312267778551319724657314e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = 2.167612440044218268272249994317
y[1] (numeric) = 2.1676124400442182682722499943173
absolute error = 3e-31
relative error = 1.3840112487723134765317983306563e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = 2.1774624248408603004869205523084
y[1] (numeric) = 2.1774624248408603004869205523087
absolute error = 3e-31
relative error = 1.3777505254628009503429835109994e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = 2.187294663542903107755292824136
y[1] (numeric) = 2.1872946635429031077552928241362
absolute error = 2e-31
relative error = 9.1437154460042901261055184556537e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = 2.1971081729346699907366169105927
y[1] (numeric) = 2.197108172934669990736616910593
absolute error = 3e-31
relative error = 1.3654311776524458049451470340747e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = 2.2069019716733996699760341160255
y[1] (numeric) = 2.2069019716733996699760341160258
absolute error = 3e-31
relative error = 1.3593716614994130936736211112135e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = 2.2166750803873797442496139819055
y[1] (numeric) = 2.2166750803873797442496139819058
absolute error = 3e-31
relative error = 1.3533783216779468878566655480414e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = 2.2264265217738830456641034843086
y[1] (numeric) = 2.2264265217738830456641034843088
absolute error = 2e-31
relative error = 8.9830047407381763451525377308338e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = 2.2361553206968970979574917775896
y[1] (numeric) = 2.2361553206968970979574917775899
absolute error = 3e-31
relative error = 1.3415883826285604121151437612264e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = 2.2458605042846369051360013715579
y[1] (numeric) = 2.2458605042846369051360013715582
absolute error = 3e-31
relative error = 1.3357908891832867885876503564558e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = 2.2555411020268313192499024293637
y[1] (numeric) = 2.255541102026831319249902429364
absolute error = 3e-31
relative error = 1.3300577840519940988312272228855e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = 2.2651961458717732587524443075741
y[1] (numeric) = 2.2651961458717732587524443075744
absolute error = 3e-31
relative error = 1.3243886210328304333166492340441e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = 2.2748246703231240725009433576662
y[1] (numeric) = 2.2748246703231240725009433576665
absolute error = 3e-31
relative error = 1.3187829546326616375908511428869e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = 2.2844257125364623690442969145914
y[1] (numeric) = 2.2844257125364623690442969145917
absolute error = 3e-31
relative error = 1.3132403402468339823810584486506e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = 2.2939983124155676563944518105603
y[1] (numeric) = 2.2939983124155676563944518105606
absolute error = 3e-31
relative error = 1.3077603343312909563886028954252e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = 2.3035415127084291639980863662199
y[1] (numeric) = 2.3035415127084291639980863662202
absolute error = 3e-31
relative error = 1.3023424945672880911965582855957e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = 2.3130543591029702461063157759749
y[1] (numeric) = 2.3130543591029702461063157759752
absolute error = 3e-31
relative error = 1.2969863800189440309011387721811e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = 2.3225359003224787941818539871573
y[1] (numeric) = 2.3225359003224787941818539871575
absolute error = 2e-31
relative error = 8.6112770085590693232832046162743e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = 2.3319851882207341153819164354428
y[1] (numeric) = 2.331985188220734115381916435443
absolute error = 2e-31
relative error = 8.5763838042469159575955942277252e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = 2.3414012778768207645082874807375
y[1] (numeric) = 2.3414012778768207645082874807378
absolute error = 3e-31
relative error = 1.2812840021683064887414201364956e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=72026100, alloc=4521156, time=2.70
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = 2.3507832276896198481203688000436
y[1] (numeric) = 2.3507832276896198481203688000439
absolute error = 3e-31
relative error = 1.2761704119134960776885389716211e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = 2.3601300994719683517595399234174
y[1] (numeric) = 2.3601300994719683517595399234176
absolute error = 2e-31
relative error = 8.4741091198636031996418726495869e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = 2.369440958544477074430574321433
y[1] (numeric) = 2.3694409585444770744305743214332
absolute error = 2e-31
relative error = 8.4408096044249154406476790211745e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = 2.3787148738289977886248442540066
y[1] (numeric) = 2.3787148738289977886248442540069
absolute error = 3e-31
relative error = 1.2611852025673529540441428740416e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = 2.3879509179417302792472011004845
y[1] (numeric) = 2.3879509179417302792472011004848
absolute error = 3e-31
relative error = 1.2563072287037704815155214040809e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = 2.397148167285959950820227423437
y[1] (numeric) = 2.3971481672859599508202274234372
absolute error = 2e-31
relative error = 8.3432473106757966243636680829139e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = 2.4063057021444167292824214226859
y[1] (numeric) = 2.4063057021444167292824214226862
absolute error = 3e-31
relative error = 1.2467243864013218972953617409547e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = 2.4154226067712460225670994560663
y[1] (numeric) = 2.4154226067712460225670994560666
absolute error = 3e-31
relative error = 1.2420186809504829286022276898179e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = 2.4244979694835825429426009483438
y[1] (numeric) = 2.4244979694835825429426009483441
absolute error = 3e-31
relative error = 1.2373695658895516603203837910094e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = 2.433530882752717833807872932044
y[1] (numeric) = 2.4335308827527178338078729320444
absolute error = 4e-31
relative error = 1.6437021729822272544834400254788e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = 2.4425204432948523842667273474927
y[1] (numeric) = 2.4425204432948523842667273474931
absolute error = 4e-31
relative error = 1.6376526186221706152567925343490e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = 2.4514657521614232563449401863925
y[1] (numeric) = 2.4514657521614232563449401863929
absolute error = 4e-31
relative error = 1.6316768841144346543836531447295e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = 2.4603659148289981921627435407948
y[1] (numeric) = 2.4603659148289981921627435407952
absolute error = 4e-31
relative error = 1.6257744329375536675681479437587e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = 2.4692200412887272117269048145319
y[1] (numeric) = 2.4692200412887272117269048145323
absolute error = 4e-31
relative error = 1.6199447327960019072873402584753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = 2.4780272461353427562571566388729
y[1] (numeric) = 2.4780272461353427562571566388733
absolute error = 4e-31
relative error = 1.6141872557044239406630751683389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = 2.4867866486556994771068113882953
y[1] (numeric) = 2.4867866486556994771068113882957
absolute error = 4e-31
relative error = 1.6085014780670104441971123229382e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = 2.4954973729168448163724511464104
y[1] (numeric) = 2.4954973729168448163724511464107
absolute error = 3e-31
relative error = 1.2021651605641527015453820193119e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = 2.5041585478536115722080240589139
y[1] (numeric) = 2.5041585478536115722080240589143
absolute error = 4e-31
relative error = 1.5973429491629107994373512264015e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = 2.512769307355723689659809225044
y[1] (numeric) = 2.5127693073557236896598092250444
absolute error = 4e-31
relative error = 1.5918691733023999501666787955418e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = 2.5213287903544065665157545481247
y[1] (numeric) = 2.521328790354406566515754548125
bytes used=76027628, alloc=4521156, time=2.85
absolute error = 3e-31
relative error = 1.1898487858770334261420865155302e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = 2.5298361409084932132107776257012
y[1] (numeric) = 2.5298361409084932132107776257015
absolute error = 3e-31
relative error = 1.1858475541118111883668557127704e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = 2.5382905082900176562437940432504
y[1] (numeric) = 2.5382905082900176562437940432507
absolute error = 3e-31
relative error = 1.1818978128004049434092435710949e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = 2.5466910470692870258374589670562
y[1] (numeric) = 2.5466910470692870258374589670566
absolute error = 4e-31
relative error = 1.5706655915734929948786361825289e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = 2.5550369171994238207027492321657
y[1] (numeric) = 2.5550369171994238207027492321661
absolute error = 4e-31
relative error = 1.5655351095217834799742226069236e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = 2.5633272841003698957523611196795
y[1] (numeric) = 2.5633272841003698957523611196798
absolute error = 3e-31
relative error = 1.1703538672600231661833077071557e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = 2.5715613187423437724341555733503
y[1] (numeric) = 2.5715613187423437724341555733506
absolute error = 3e-31
relative error = 1.1666064418277958297658476369490e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = 2.579738197728742926023165037754
y[1] (numeric) = 2.5797381977287429260231650377543
absolute error = 3e-31
relative error = 1.1629087023796696178972914497436e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = 2.5878571033784827597125177264744
y[1] (numeric) = 2.5878571033784827597125177264748
absolute error = 4e-31
relative error = 1.5456803989594114064837901361261e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.81
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = 2.5959172238077640316744858109002
y[1] (numeric) = 2.5959172238077640316744858109006
absolute error = 4e-31
relative error = 1.5408811819248566248127361725789e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = 2.6039177530112605584170907202327
y[1] (numeric) = 2.6039177530112605584170907202331
absolute error = 4e-31
relative error = 1.5361468292822465844187662314991e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = 2.6118578909427190757335860861189
y[1] (numeric) = 2.6118578909427190757335860861193
absolute error = 4e-31
relative error = 1.5314768900218562510425285073613e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = 2.6197368435949631973258897105178
y[1] (numeric) = 2.6197368435949631973258897105182
absolute error = 4e-31
relative error = 1.5268709182678651195208746180819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = 2.6275538230792934707727719568899
y[1] (numeric) = 2.6275538230792934707727719568903
absolute error = 4e-31
relative error = 1.5223284732992848351239595534496e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.31
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = 2.6353080477042755909033702386223
y[1] (numeric) = 2.6353080477042755909033702386227
absolute error = 4e-31
relative error = 1.5178491195686072727321121583404e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.63
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = 2.6429987420539088918203488788627
y[1] (numeric) = 2.6429987420539088918203488788632
absolute error = 5e-31
relative error = 1.8917905333978458884897552566624e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = 2.650625137065167300788642218662
y[1] (numeric) = 2.6506251370651673007886422186625
absolute error = 5e-31
relative error = 1.8863474619938578766871305114309e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.28
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = 2.6581864701049049999590093452957
y[1] (numeric) = 2.6581864701049049999590093452962
absolute error = 5e-31
relative error = 1.8809816603282446242382567568474e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.61
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = 2.6656819850461191054243159231035
y[1] (numeric) = 2.665681985046119105424315923104
absolute error = 5e-31
relative error = 1.8756926100145793402940851260611e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = 2.6731109323435617374041895193685
y[1] (numeric) = 2.673110932343561737404189519369
absolute error = 5e-31
relative error = 1.8704797992114809511405133272082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.29
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=80031056, alloc=4521156, time=3.00
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = 2.6804725691086939204140398081587
y[1] (numeric) = 2.6804725691086939204140398081591
absolute error = 4e-31
relative error = 1.4922741781051216082223280703541e-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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = 2.6877661591839738180908881253787
y[1] (numeric) = 2.6877661591839738180908881253791
absolute error = 4e-31
relative error = 1.4882247052379104006719488842426e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = 2.6949909732164718739144304480765
y[1] (numeric) = 2.6949909732164718739144304480769
absolute error = 4e-31
relative error = 1.4842350270383279915971643575688e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.37
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = 2.7021462887308054963706074378206
y[1] (numeric) = 2.7021462887308054963706074378211
absolute error = 5e-31
relative error = 1.8503809437898690982710154637242e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.25
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = 2.7092313902013859951499438928516
y[1] (numeric) = 2.709231390201385995149943892852
absolute error = 4e-31
relative error = 1.4764335059998942981099486778994e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = 2.7162455691239705437472433545408
y[1] (numeric) = 2.7162455691239705437472433545412
absolute error = 4e-31
relative error = 1.4726209019790722707104758292942e-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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = 2.7231881240865120133260043354428
y[1] (numeric) = 2.7231881240865120133260043354432
absolute error = 4e-31
relative error = 1.4688665702601034829202771758315e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = 2.7300583608392995929232130587317
y[1] (numeric) = 2.7300583608392995929232130587321
absolute error = 4e-31
relative error = 1.4651701433848774189185562588834e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = 2.7368555923643831819909425517513
y[1] (numeric) = 2.7368555923643831819909425517518
absolute error = 5e-31
relative error = 1.8269140739283489519669009078486e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = 2.7435791389442746128933574013766
y[1] (numeric) = 2.7435791389442746128933574013771
absolute error = 5e-31
relative error = 1.8224369507066572008060372587058e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = 2.7502283282299188332941252986201
y[1] (numeric) = 2.7502283282299188332941252986206
absolute error = 5e-31
relative error = 1.8180308699016500216557688404903e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.86
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = 2.7568024953079282513726390945118
y[1] (numeric) = 2.7568024953079282513726390945123
absolute error = 5e-31
relative error = 1.8136953983863511946844377922598e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.55
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = 2.7633009827670735204905561792977
y[1] (numeric) = 2.7633009827670735204905561792982
absolute error = 5e-31
relative error = 1.8094301095616351775960624350521e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.23
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = 2.7697231407640241142855973335445
y[1] (numeric) = 2.769723140764024114285597333545
absolute error = 5e-31
relative error = 1.8052345833456687105490248112883e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.93
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = 2.7760683270883321181898793012325
y[1] (numeric) = 2.776068327088332118189879301233
absolute error = 5e-31
relative error = 1.8011084061624050507003523419730e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.63
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = 2.7823359072266527390477822306665
y[1] (numeric) = 2.782335907226652739047782230667
absolute error = 5e-31
relative error = 1.7970511709291948658663066648257e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.33
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = 2.7885252544261951108359071094194
y[1] (numeric) = 2.7885252544261951108359071094199
absolute error = 5e-31
relative error = 1.7930624770435754995176770211872e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.04
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = 2.7946357497573970514574266927463
y[1] (numeric) = 2.7946357497573970514574266927469
absolute error = 6e-31
relative error = 2.1469703164431576920901021593594e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.75
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = 2.8006667821758175031873792802757
y[1] (numeric) = 2.8006667821758175031873792802763
absolute error = 6e-31
relative error = 2.1423469718659797009887486017372e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.47
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=84031860, alloc=4521156, time=3.16
x[1] = 4.08
y[1] (analytic) = 2.8066177485832404675764376733801
y[1] (numeric) = 2.8066177485832404675764376733807
absolute error = 6e-31
relative error = 2.1378044812225515488277156232223e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = 2.8124880538879843244705827123527
y[1] (numeric) = 2.8124880538879843244705827123533
absolute error = 6e-31
relative error = 2.1333423947190098143186618718764e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = 2.8182771110644105042650370243584
y[1] (numeric) = 2.818277111064410504265037024359
absolute error = 6e-31
relative error = 2.1289602702460697078816182994905e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = 2.823984341211625562574823983696
y[1] (numeric) = 2.8239843412116255625748239836966
absolute error = 6e-31
relative error = 2.1246576733586668725074759569088e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = 2.8296091736113707871634030609722
y[1] (numeric) = 2.8296091736113707871634030609728
absolute error = 6e-31
relative error = 2.1204341772550609723102528401622e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = 2.8351510457850935482169298759564
y[1] (numeric) = 2.8351510457850935482169298759569
absolute error = 5e-31
relative error = 1.7635744689628799169030321398445e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = 2.8406094035501946848766728281409
y[1] (numeric) = 2.8406094035501946848766728281414
absolute error = 5e-31
relative error = 1.7601856819001578139261377331335e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = 2.8459837010754463033378057292122
y[1] (numeric) = 2.8459837010754463033378057292127
absolute error = 5e-31
relative error = 1.7568617831896189320385983924521e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = 2.8512734009355744447809479026467
y[1] (numeric) = 2.8512734009355744447809479026472
absolute error = 5e-31
relative error = 1.7536024424593496956586414218881e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = 2.8564779741650011649151440014129
y[1] (numeric) = 2.8564779741650011649151440014134
absolute error = 5e-31
relative error = 1.7504073356146175382858298481496e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = 2.8615969003107406509691141628009
y[1] (numeric) = 2.8615969003107406509691141628014
absolute error = 5e-31
relative error = 1.7472761448186676024621927144277e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = 2.8666296674844440865631553259225
y[1] (numeric) = 2.866629667484444086563155325923
absolute error = 5e-31
relative error = 1.7442085584733566765653433217767e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = 2.8715757724135880600185770979088
y[1] (numeric) = 2.8715757724135880600185770979093
absolute error = 5e-31
relative error = 1.7412042711996591895533211654727e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = 2.8764347204918013973064980899522
y[1] (numeric) = 2.8764347204918013973064980899527
absolute error = 5e-31
relative error = 1.7382629838180787345217784744760e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = 2.8812060258283253869946467312212
y[1] (numeric) = 2.8812060258283253869946467312217
absolute error = 5e-31
relative error = 1.7353844033289972876993529862170e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = 2.8858892112966024512108885972993
y[1] (numeric) = 2.8858892112966024512108885972997
absolute error = 4e-31
relative error = 1.3860545943143944238593422705468e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = 2.8904838085819884037968743245822
y[1] (numeric) = 2.8904838085819884037968743245826
absolute error = 4e-31
relative error = 1.3838513774489251682209714684393e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = 2.8949893582285835244657528284383
y[1] (numeric) = 2.8949893582285835244657528284387
absolute error = 4e-31
relative error = 1.3816976524043466555870350729263e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = 2.8994054096851777658955598188531
y[1] (numeric) = 2.8994054096851777658955598188535
absolute error = 4e-31
relative error = 1.3795932043992173604878060848541e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = 2.9037315213503054992758598196613
y[1] (numeric) = 2.9037315213503054992758598196617
absolute error = 4e-31
relative error = 1.3775378235174797088140739302907e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=88033872, alloc=4521156, time=3.31
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = 2.9079672606164052928706325232994
y[1] (numeric) = 2.9079672606164052928706325232998
absolute error = 4e-31
relative error = 1.3755313046929267089747197672844e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = 2.912112203913080307656346885248
y[1] (numeric) = 2.9121122039130803076563468852484
absolute error = 4e-31
relative error = 1.3735734476937725101079084693597e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = 2.9161659367494549840317093602846
y[1] (numeric) = 2.916165936749454984031709360285
absolute error = 4e-31
relative error = 1.3716640571073454634797382564341e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = 2.920128053755623783965712426991
y[1] (numeric) = 2.9201280537556237839657124269914
absolute error = 4e-31
relative error = 1.3698029423249215014589212180544e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = 2.923998158723187843744309098984
y[1] (numeric) = 2.9239981587231878437443090989844
absolute error = 4e-31
relative error = 1.3679899175267149129578554968052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = 2.927775864644875483684219186773
y[1] (numeric) = 2.9277758646448754836842191867734
absolute error = 4e-31
relative error = 1.3662248016670428840599217714619e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = 2.9314607937532426127959129109888
y[1] (numeric) = 2.9314607937532426127959129109893
absolute error = 5e-31
relative error = 1.7056342730745993585168277462861e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = 2.9350525775584491583875557983414
y[1] (numeric) = 2.9350525775584491583875557983419
absolute error = 5e-31
relative error = 1.7035469954542676712380116506700e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = 2.938550856885107742998434718885
y[1] (numeric) = 2.9385508568851077429984347188854
absolute error = 4e-31
relative error = 1.3612151685678289021293341545024e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = 2.9419552819082009238248788504083
y[1] (numeric) = 2.9419552819082009238248788504087
absolute error = 4e-31
relative error = 1.3596399729793084235772782883184e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = 2.9452655121880634029446639109382
y[1] (numeric) = 2.9452655121880634029446639109386
absolute error = 4e-31
relative error = 1.3581118522072956197011332548214e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = 2.9484812167044257101480289636141
y[1] (numeric) = 2.9484812167044257101480289636146
absolute error = 5e-31
relative error = 1.6957883169385072014580747633318e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = 2.9516020738895159540353923333804
y[1] (numeric) = 2.9516020738895159540353923333809
absolute error = 5e-31
relative error = 1.6939952862315136905097022503707e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = 2.9546277716602163312342415645362
y[1] (numeric) = 2.9546277716602163312342415645367
absolute error = 5e-31
relative error = 1.6922605439366331442329403366347e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = 2.9575580074492711781110727318389
y[1] (numeric) = 2.9575580074492711781110727318394
absolute error = 5e-31
relative error = 1.6905839166658378146440552429141e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = 2.9603924882355434441992145343005
y[1] (numeric) = 2.960392488235543444199214534301
absolute error = 5e-31
relative error = 1.6889652368291563206346436511829e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = 2.9631309305733165617204080330778
y[1] (numeric) = 2.9631309305733165617204080330784
absolute error = 6e-31
relative error = 2.0248852111435723067656226300004e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = 2.9657730606206387810376080186917
y[1] (numeric) = 2.9657730606206387810376080186923
absolute error = 6e-31
relative error = 2.0230812935985052382939362617242e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = 2.9683186141667071376290809282464
y[1] (numeric) = 2.968318614166707137629080928247
absolute error = 6e-31
relative error = 2.0213463512185579467687720751171e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = 2.9707673366582883122099217992716
y[1] (numeric) = 2.9707673366582883122099217992721
absolute error = 5e-31
relative error = 1.6830668421258206432496303094357e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=92035000, alloc=4521156, time=3.46
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = 2.9731189832251737419369954185327
y[1] (numeric) = 2.9731189832251737419369954185332
absolute error = 5e-31
relative error = 1.6817355875129190229286913799555e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = 2.9753733187046664372073936936592
y[1] (numeric) = 2.9753733187046664372073936936597
absolute error = 5e-31
relative error = 1.6804613957406723156609473794523e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = 2.9775301176650970553891350144986
y[1] (numeric) = 2.9775301176650970553891350144991
absolute error = 5e-31
relative error = 1.6792441394080245562131658303424e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = 2.9795891644283668798963291970477
y[1] (numeric) = 2.9795891644283668798963291970481
absolute error = 4e-31
relative error = 1.3424669574429059167018316629050e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = 2.9815502530915154503296862467421
y[1] (numeric) = 2.9815502530915154503296862467425
absolute error = 4e-31
relative error = 1.3415839615154808995959010262389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = 2.983413187547310686937327855437
y[1] (numeric) = 2.9834131875473106869373278554374
absolute error = 4e-31
relative error = 1.3407462354513603136616020037508e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = 2.9851777815038594504006139307825
y[1] (numeric) = 2.985177781503859450400613930783
absolute error = 5e-31
relative error = 1.6749421193538169994470913104356e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = 2.9868438585032365759053476540251
y[1] (numeric) = 2.9868438585032365759053476540256
absolute error = 5e-31
relative error = 1.6740078279504016954285300042168e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = 2.9884112519391305186104760890381
y[1] (numeric) = 2.9884112519391305186104760890386
absolute error = 5e-31
relative error = 1.6731298266781664978308828902740e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = 2.9898798050735038459644441280651
y[1] (numeric) = 2.9898798050735038459644441280656
absolute error = 5e-31
relative error = 1.6723080277392886461949088181726e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = 2.9912493710522669108338538360973
y[1] (numeric) = 2.9912493710522669108338538360978
absolute error = 5e-31
relative error = 1.6715423489553768952859860783310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = 2.9925198129199631380901776786878
y[1] (numeric) = 2.9925198129199631380901776786883
absolute error = 5e-31
relative error = 1.6708327137594554690373838547307e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = 2.9936910036334644561381046599088
y[1] (numeric) = 2.9936910036334644561381046599093
absolute error = 5e-31
relative error = 1.6701790511884706144088444517800e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = 2.9947628260746755038537793574031
y[1] (numeric) = 2.9947628260746755038537793574036
absolute error = 5e-31
relative error = 1.6695812958763243228215460724023e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = 2.9957351730622453425228268344515
y[1] (numeric) = 2.9957351730622453425228268344519
absolute error = 4e-31
relative error = 1.3352315104379515382768843542427e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = 2.9966079473622855016167293539807
y[1] (numeric) = 2.9966079473622855016167293539811
absolute error = 4e-31
relative error = 1.3348426188086879128421085544093e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = 2.9973810616980932866119089318828
y[1] (numeric) = 2.9973810616980932866119089318832
absolute error = 4e-31
relative error = 1.3344983229239119022284253262715e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = 2.998054438758879376528836550896
y[1] (numeric) = 2.9980544387588793765288365508964
absolute error = 4e-31
relative error = 1.3341985883538196804098189874292e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = 2.9986280112074988384386870978325
y[1] (numeric) = 2.9986280112074988384386870978329
absolute error = 4e-31
relative error = 1.3339433851247407349866332120199e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=96036520, alloc=4521156, time=3.62
x[1] = 4.67
y[1] (analytic) = 2.9991017216871847858425318492734
y[1] (numeric) = 2.9991017216871847858425318492738
absolute error = 4e-31
relative error = 1.3337326877161560565222952274297e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = 2.9994755228272840075628419497597
y[1] (numeric) = 2.9994755228272840075628419497601
absolute error = 4e-31
relative error = 1.3335664750581557778628327059585e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = 2.9997493772479939935891934069429
y[1] (numeric) = 2.9997493772479939935891934069433
absolute error = 4e-31
relative error = 1.3334447305293377234179399549796e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = 2.999923257564100884179536541575
y[1] (numeric) = 2.9999232575641008841795365415754
absolute error = 4e-31
relative error = 1.3333674419551480703284184399386e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = 2.9999971463877179684252347125936
y[1] (numeric) = 2.999997146387717968425234712594
absolute error = 4e-31
relative error = 1.3333346016066650674853655773020e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = 2.9999710363300244584322978879616
y[1] (numeric) = 2.9999710363300244584322978879621
absolute error = 5e-31
relative error = 1.6666827577497831300712528235234e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.007329
Order of pole (three term test) = -0.8902
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = 2.9998449300020043652428419115577
y[1] (numeric) = 2.9998449300020043652428419115581
absolute error = 4e-31
relative error = 1.3334022568951013660767966753570e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01696
Order of pole (three term test) = -0.8961
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = 2.9996188400141854026097970480728
y[1] (numeric) = 2.9996188400141854026097970480732
absolute error = 4e-31
relative error = 1.3335027592976058673101573721673e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02657
Order of pole (three term test) = -0.9066
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = 2.9992927889753779447342707555971
y[1] (numeric) = 2.9992927889753779447342707555975
absolute error = 4e-31
relative error = 1.3336477234576637886058641105307e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03618
Order of pole (three term test) = -0.9217
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = 2.9988668094904141640687400845694
y[1] (numeric) = 2.9988668094904141640687400845699
absolute error = 5e-31
relative error = 1.6672964548397635097654593852597e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04578
Order of pole (three term test) = -0.9414
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = 2.9983409441568875752704093382995
y[1] (numeric) = 2.9983409441568875752704093382999
absolute error = 4e-31
relative error = 1.3340710994842422496577788117890e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05535
Order of pole (three term test) = -0.9658
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = 2.9977152455608933113476206216477
y[1] (numeric) = 2.9977152455608933113476206216481
absolute error = 4e-31
relative error = 1.3343495536887034313148457327087e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06491
Order of pole (three term test) = -0.9947
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = 2.9969897762717695579681528787627
y[1] (numeric) = 2.9969897762717695579681528787632
absolute error = 5e-31
relative error = 1.6683406929135269053205501856314e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07444
Order of pole (three term test) = -1.028
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = 2.9961646088358406717815964665036
y[1] (numeric) = 2.9961646088358406717815964665041
absolute error = 5e-31
relative error = 1.6688001671385969950118423612841e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08393
Order of pole (three term test) = -1.066
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = 2.995239825769162608438756975404
y[1] (numeric) = 2.9952398257691626084387569754045
absolute error = 5e-31
relative error = 1.6693154107337715451125845337197e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0934
Order of pole (three term test) = -1.109
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = 2.9942155195492713857592409012983
y[1] (numeric) = 2.9942155195492713857592409012988
absolute error = 5e-31
relative error = 1.6698864752236223853775659477343e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1028
Order of pole (three term test) = -1.156
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = 2.9930917926059354071940301512694
y[1] (numeric) = 2.9930917926059354071940301512699
absolute error = 5e-31
relative error = 1.6705134177147136328166256298611e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1122
Order of pole (three term test) = -1.208
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = 2.9918687573109125703429927550405
y[1] (numeric) = 2.991868757310912570342992755041
absolute error = 5e-31
relative error = 1.6711963009012443999190745799026e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1216
Order of pole (three term test) = -1.264
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = 2.9905465359667131848079423162912
y[1] (numeric) = 2.9905465359667131848079423162917
absolute error = 5e-31
relative error = 1.6719351930712284350772126768315e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1308
Order of pole (three term test) = -1.325
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = 2.9891252607943698230800966940429
y[1] (numeric) = 2.9891252607943698230800966940434
absolute error = 5e-31
relative error = 1.6727301681132070163881895474456e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1401
Order of pole (three term test) = -1.39
NO COMPLEX POLE (six term test) for Equation 1
bytes used=100037224, alloc=4521156, time=3.77
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = 2.9876050739202153274666554112925
y[1] (numeric) = 2.987605073920215327466655411293
absolute error = 5e-31
relative error = 1.6735813055234910664832801311869e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1493
Order of pole (three term test) = -1.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = 2.9859861273616702952447848423184
y[1] (numeric) = 2.9859861273616702952447848423189
absolute error = 5e-31
relative error = 1.6744886904139280955721404473621e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1584
Order of pole (three term test) = -1.534
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = 2.9842685830120414632826520572489
y[1] (numeric) = 2.9842685830120414632826520572494
absolute error = 5e-31
relative error = 1.6754524135201892118973414365592e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1675
Order of pole (three term test) = -1.613
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = 2.9824526126243325122763772499183
y[1] (numeric) = 2.9824526126243325122763772499188
absolute error = 5e-31
relative error = 1.6764725712105710626639342589152e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1764
Order of pole (three term test) = -1.695
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = 2.9805383977940689095089901022697
y[1] (numeric) = 2.9805383977940689095089901022702
absolute error = 5e-31
relative error = 1.6775492654953071836237559156240e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1854
Order of pole (three term test) = -1.782
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = 2.9785261299411385076328016063411
y[1] (numeric) = 2.9785261299411385076328016063416
absolute error = 5e-31
relative error = 1.6786826040363828412290733444005e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1942
Order of pole (three term test) = -1.874
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = 2.9764160102906497154001803227491
y[1] (numeric) = 2.9764160102906497154001803227496
absolute error = 5e-31
relative error = 1.6798727001578470469894392556544e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.203
Order of pole (three term test) = -1.969
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = 2.9742082498528091545097085268232
y[1] (numeric) = 2.9742082498528091545097085268236
absolute error = 4e-31
relative error = 1.3448957382852920069784965105829e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2117
Order of pole (three term test) = -2.069
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = 2.9719030694018208147852650633774
y[1] (numeric) = 2.9719030694018208147852650633778
absolute error = 4e-31
relative error = 1.3459389174510030857061712350453e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2203
Order of pole (three term test) = -2.173
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = 2.9695006994538088177549330230967
y[1] (numeric) = 2.9695006994538088177549330230972
absolute error = 5e-31
relative error = 1.6837847524062440478842061965914e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2288
Order of pole (three term test) = -2.281
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = 2.9670013802437659963349767140779
y[1] (numeric) = 2.9670013802437659963349767140784
absolute error = 5e-31
relative error = 1.6852031257192083884478139829012e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2372
Order of pole (three term test) = -2.394
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = 2.9644053617015305957417100779289
y[1] (numeric) = 2.9644053617015305957417100779294
absolute error = 5e-31
relative error = 1.6866789085586001746722343356291e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2455
Order of pole (three term test) = -2.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = 2.9617129034267934979411460144111
y[1] (numeric) = 2.9617129034267934979411460144116
absolute error = 5e-31
relative error = 1.6882122484643414437023224888581e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2538
Order of pole (three term test) = -2.63
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 2 ) = sin(x);
Iterations = 490
Total Elapsed Time = 3 Seconds
Elapsed Time(since restart) = 3 Seconds
Time to Timeout = 2 Minutes 56 Seconds
Percent Done = 100.2 %
> quit
bytes used=102774528, alloc=4521156, time=3.87