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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_large_float, array_pole,
glob_type_given_pole, array_given_rad_poles, array_given_ord_poles,
array_complex_poles, array_poles, array_real_poles, array_x;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_x[1] - array_given_rad_poles[1, 1], 2.0)
+ expt(array_given_rad_poles[1, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_poles[1, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if 0. < array_real_poles[1, 1] and
array_real_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_real_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if 0. < array_complex_poles[1, 1] and
array_complex_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 2
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 2;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 4
> # Begin Function number 5
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4_c1,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 2
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> if (min_size < 1.0) then # if number 2
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2,
array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4_c1,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 2
> max_estimated_step_error := est_tmp;
> fi;# end if 2;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2,
array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
max_estimated_step_error := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4_c1,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2
> ret := true;
> else
> ret := false;
> fi;# end if 2;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2,
array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4_c1,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 2
> if (iter >= 0) then # if number 3
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 4
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 5
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 5;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 4;
> if (glob_iter = 1) then # if number 4
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 4;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 3;
> #BOTTOM DISPLAY ALOT
> fi;# end if 2;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2,
array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4_c1,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 3
> glob_normmax := tmp;
> fi;# end if 3
> fi;# end if 2;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 3
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 3
> fi;# end if 2;
> if ( not glob_reached_optimal_h) then # if number 2
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 2;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2,
array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 9
> # Begin Function number 10
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4_c1,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 2
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 2;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2,
array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4_c1,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3
> if (tmp_rad < rad_c) then # if number 4
> rad_c := tmp_rad;
> fi;# end if 4;
> elif
> (cnt = 0) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5
> fi;# end if 4;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 4
> if (rad_c < array_pole[1]) then # if number 5
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 5;
> fi;# end if 4;
> #BOTTOM radius ratio test in Henrici1
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 4
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 5
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 5
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 4;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 4;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 4
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) <> 0.0) then # if number 7
> if (rcs > 0.0) then # if number 8
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 8
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> fi;# end if 5;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 4;
> #BOTTOM RADII COMPLEX EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 4;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 4
> display_poles();
> fi;# end if 4
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2,
array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y_higher[1, n]) = 0. or
omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or
omniabs(array_y_higher[1, m - 1]) = 0. or
omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4_c1,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 4
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 5;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 4;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2,
array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4_c1,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D2[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D3[1];
> #emit pre sin 1 $eq_no = 1
> array_tmp3[1] := sin(array_x[1]);
> array_tmp3_g[1] := cos(array_x[1]);
> #emit pre expt LINEAR - FULL $eq_no = 1 i = 1
> array_tmp4[1] := expt(array_tmp2[1] , array_tmp3[1] ) ;
> array_tmp4_a1[1] := ln(array_tmp2[1] ) ;
> array_tmp4_a1[2] := array_tmp2[2] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D2[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp3[2] := array_tmp3_g[1] * array_x[2] / 1;
> array_tmp3_g[2] := -array_tmp3[1] * array_x[2] / 1;
> #emit pre expt LINEAR - FULL $eq_no = 1 i = 2
> array_tmp4_a2[1] := (array_tmp4_a1[1] * array_tmp3[2] + array_tmp4_a1[2] * array_tmp3[1]) / glob_h;
> array_tmp4[2] := array_tmp4[1] * array_tmp4_a2[1] * glob_h;
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := array_tmp3_g[2] * array_x[2] / 2;
> array_tmp3_g[3] := -array_tmp3[2] * array_x[2] / 2;
> #emit pre expt LINEAR - FULL $eq_no = 1 i = 3
> array_tmp4_a1[3] := -array_tmp4_a1[2] * array_tmp2[2] * 1 / array_tmp2[1] / 2;
> array_tmp4_a2[2] := ats(3,array_tmp3,array_tmp4_a1,1)*2 / glob_h;
> array_tmp4[3] := ats(2,array_tmp4,array_tmp4_a2,1)*glob_h/2;
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := array_tmp3_g[3] * array_x[2] / 3;
> array_tmp3_g[4] := -array_tmp3[3] * array_x[2] / 3;
> #emit pre expt LINEAR - FULL $eq_no = 1 i = 4
> array_tmp4_a1[4] := -array_tmp4_a1[3] * array_tmp2[2] * 2 / array_tmp2[1] / 3;
> array_tmp4_a2[3] := ats(4,array_tmp3,array_tmp4_a1,1)*3 / glob_h;
> array_tmp4[4] := ats(3,array_tmp4,array_tmp4_a2,1)*glob_h/3;
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := array_tmp3_g[4] * array_x[2] / 4;
> array_tmp3_g[5] := -array_tmp3[4] * array_x[2] / 4;
> #emit pre expt LINEAR - FULL $eq_no = 1 i = 5
> array_tmp4_a1[5] := -array_tmp4_a1[4] * array_tmp2[2] * 3 / array_tmp2[1] / 4;
> array_tmp4_a2[4] := ats(5,array_tmp3,array_tmp4_a1,1)*4 / glob_h;
> array_tmp4[5] := ats(4,array_tmp4,array_tmp4_a2,1)*glob_h/4;
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin LINEAR $eq_no = 1
> array_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp3_g[kkk] := -array_tmp3[kkk - 1] * array_x[2] / (kkk - 1);
> #emit expt LINEAR FULL $eq_no = 1 i = 1
> array_tmp4_a1[kkk] := -array_tmp4_a1[kkk-1] * array_tmp2[2] * (kkk-2) / array_tmp2[1] / (kkk - 1);
> array_tmp4_a2[kkk-1] := ats(kkk,array_tmp3,array_tmp4_a1,1) * (kkk-1) / glob_h;
> array_tmp4[kkk] := ats(kkk-1,array_tmp4,array_tmp4_a2,1) * glob_h/(kkk-1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2,
array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_tmp1[1] := array_const_0D2[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D3[1];
array_tmp3[1] := sin(array_x[1]);
array_tmp3_g[1] := cos(array_x[1]);
array_tmp4[1] := expt(array_tmp2[1], array_tmp3[1]);
array_tmp4_a1[1] := ln(array_tmp2[1]);
array_tmp4_a1[2] := array_tmp2[2]/array_tmp2[1];
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D2[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp3_g[1]*array_x[2];
array_tmp3_g[2] := -array_tmp3[1]*array_x[2];
array_tmp4_a2[1] := (
array_tmp4_a1[1]*array_tmp3[2] + array_tmp4_a1[2]*array_tmp3[1])/
glob_h;
array_tmp4[2] := array_tmp4[1]*array_tmp4_a2[1]*glob_h;
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp3[3] := 1/2*array_tmp3_g[2]*array_x[2];
array_tmp3_g[3] := -1/2*array_tmp3[2]*array_x[2];
array_tmp4_a1[3] := -1/2*array_tmp4_a1[2]*array_tmp2[2]/array_tmp2[1];
array_tmp4_a2[2] := 2*ats(3, array_tmp3, array_tmp4_a1, 1)/glob_h;
array_tmp4[3] := 1/2*ats(2, array_tmp4, array_tmp4_a2, 1)*glob_h;
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp3[4] := 1/3*array_tmp3_g[3]*array_x[2];
array_tmp3_g[4] := -1/3*array_tmp3[3]*array_x[2];
array_tmp4_a1[4] := -2/3*array_tmp4_a1[3]*array_tmp2[2]/array_tmp2[1];
array_tmp4_a2[3] := 3*ats(4, array_tmp3, array_tmp4_a1, 1)/glob_h;
array_tmp4[4] := 1/3*ats(3, array_tmp4, array_tmp4_a2, 1)*glob_h;
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp3[5] := 1/4*array_tmp3_g[4]*array_x[2];
array_tmp3_g[5] := -1/4*array_tmp3[4]*array_x[2];
array_tmp4_a1[5] := -3/4*array_tmp4_a1[4]*array_tmp2[2]/array_tmp2[1];
array_tmp4_a2[4] := 4*ats(5, array_tmp3, array_tmp4_a1, 1)/glob_h;
array_tmp4[5] := 1/4*ats(4, array_tmp4, array_tmp4_a2, 1)*glob_h;
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp3[kkk] := array_tmp3_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp3_g[kkk] := -array_tmp3[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp4_a1[kkk] := -array_tmp4_a1[kkk - 1]*array_tmp2[2]*
(kkk - 2)/(array_tmp2[1]*(kkk - 1));
array_tmp4_a2[kkk - 1] :=
ats(kkk, array_tmp3, array_tmp4_a1, 1)*(kkk - 1)/glob_h;
array_tmp4[kkk] :=
ats(kkk - 1, array_tmp4, array_tmp4_a2, 1)*glob_h/(kkk - 1);
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 13
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s
", str)
end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-42.4g %s
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then printf("%-30s = %-32d %s
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " |
")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,m,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_int(ALWAYS,"m",4, m ,4," ");
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, m, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_int(ALWAYS, "m", 4, m, 4, " ");
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file)
fprintf(file, "
")
end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(0.0);
> end;
exact_soln_y := proc(x) return 0. end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4_c1,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_estimated_step_error := 0.0;
> glob_ratio_of_radius := 0.1;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_min_h := 0.000001;
> glob_type_given_pole := 0;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/expt_lin_sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 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,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(0.0);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(2 + 1),[]);
> array_last_rel_error:= Array(0..(2 + 1),[]);
> array_type_pole:= Array(0..(2 + 1),[]);
> array_type_real_pole:= Array(0..(2 + 1),[]);
> array_type_complex_pole:= Array(0..(2 + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3_g:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4_c1:= Array(0..(max_terms + 1),[]);
> array_tmp4_a1:= Array(0..(max_terms + 1),[]);
> array_tmp4_a2:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4_c1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4_c1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4_c1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4_a1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4_a2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_const_0D2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D2[1] := 0.2;
> array_const_0D3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D3[1] := 0.3;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> found_h := false;
> glob_h := glob_min_h;
> if (glob_max_h < glob_h) then # if number 4
> glob_h := glob_max_h;
> fi;# end if 4;
> if (glob_display_interval < glob_h) then # if number 4
> glob_h := glob_display_interval;
> fi;# end if 4;
> best_h := glob_h;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := 0.0;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4
> found_h := true;
> glob_h := glob_max_h;
> best_h := glob_h;
> elif
> ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5
> glob_h := glob_h/2.0;
> best_h := glob_h;
> found_h := true;
> else
> glob_h := glob_h*2.0;
> best_h := glob_h;
> fi;# end if 5;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 5
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 5;
> if (opt_iter > 100) then # if number 5
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 5;
> if (glob_display_interval < glob_h) then # if number 5
> glob_h := glob_display_interval;
> fi;# end if 5;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 5
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 5;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 5
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 6
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 6;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 6
> #left paren 0004C
> check_for_pole();
> fi;# end if 6;#was right paren 0004C
> if (reached_interval()) then # if number 6
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 6;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 6
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 6;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 6;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 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,"2013-05-26T01:42:47-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"expt_lin_sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 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,"expt_lin_sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"expt_lin_sin maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2,
array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_estimated_step_error := 0.;
glob_ratio_of_radius := 0.1;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_min_h := 0.1*10^(-5);
glob_type_given_pole := 0;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/expt_lin_sinpostode.ode#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 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, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(0.0);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3_g := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4_c1 := Array(0 .. max_terms + 1, []);
array_tmp4_a1 := Array(0 .. max_terms + 1, []);
array_tmp4_a2 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4_c1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4_a1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4_a2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp3_g[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4_c1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_c1[term] := 0.; term := term + 1
end do;
array_tmp4_a1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_a1[term] := 0.; term := term + 1
end do;
array_tmp4_a2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_a2[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_0D2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D2[term] := 0.; term := term + 1
end do;
array_const_0D2[1] := 0.2;
array_const_0D3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D3[term] := 0.; term := term + 1
end do;
array_const_0D3[1] := 0.3;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
found_h := false;
glob_h := glob_min_h;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
best_h := glob_h;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err,
16, "");
estimated_step_error := 0.;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if est_needed_step_err < estimated_step_error and opt_iter = 1 or
glob_max_h <= glob_h then
found_h := true; glob_h := glob_max_h; best_h := glob_h
elif est_needed_step_err < estimated_step_error and not found_h
then glob_h := glob_h/2.0; best_h := glob_h; found_h := true
else glob_h := glob_h*2.0; best_h := glob_h
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,
"diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 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, "2013-05-26T01:42:47-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"expt_lin_sin");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 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, "expt_lin_sin diffeq.mxt");
logitem_str(html_log_file, "expt_lin_sin 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/expt_lin_sinpostode.ode#################
diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , 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);
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(0.0);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 4.9
estimated_steps = 4900000
step_error = 2.0408163265306122448979591836735e-17
est_needed_step_err = 2.0408163265306122448979591836735e-17
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.0008294884127150148088176447894e-167
estimated_step_error = 1.0008294884127150148088176447894e-167
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.0942333894510672736633599509993e-156
estimated_step_error = 7.0942333894510672736633599509993e-156
best_h = 4.00e-06
opt_iter = 3
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.7608566268903953927523182564398e-148
estimated_step_error = 4.7608566268903953927523182564398e-148
best_h = 8.000e-06
opt_iter = 4
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.1949530270890506377146090033458e-140
estimated_step_error = 3.1949530270890506377146090033458e-140
best_h = 1.60000e-05
opt_iter = 5
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.1440916192916019380974309587992e-132
estimated_step_error = 2.1440916192916019380974309587992e-132
best_h = 3.200000e-05
opt_iter = 6
bytes used=4000072, alloc=2948580, time=0.12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.4388687340727311318801609253558e-124
estimated_step_error = 1.4388687340727311318801609253558e-124
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 = 9.6559934225367110972574084712419e-117
estimated_step_error = 9.6559934225367110972574084712419e-117
best_h = 0.000128
opt_iter = 8
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.4799050956027651315595944554010e-109
estimated_step_error = 6.4799050956027651315595944554010e-109
best_h = 0.000256
opt_iter = 9
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.3484264272151058581295739979561e-101
estimated_step_error = 4.3484264272151058581295739979561e-101
best_h = 0.000512
opt_iter = 10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.9179591217923263957328961384620e-93
estimated_step_error = 2.9179591217923263957328961384620e-93
best_h = 0.001024
opt_iter = 11
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.9579133956320613116579393809685e-85
estimated_step_error = 1.9579133956320613116579393809685e-85
best_h = 0.002048
opt_iter = 12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.3135365714766194580399836454034e-77
estimated_step_error = 1.3135365714766194580399836454034e-77
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 = 8.8096729063793952532300648663700e-70
estimated_step_error = 8.8096729063793952532300648663700e-70
best_h = 0.008192
opt_iter = 14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.9049416043332866942455237977617e-62
estimated_step_error = 5.9049416043332866942455237977617e-62
best_h = 0.016384
opt_iter = 15
bytes used=8001020, alloc=3996964, time=0.24
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.9532046732466681128306260585952e-54
estimated_step_error = 3.9532046732466681128306260585952e-54
best_h = 0.032768
opt_iter = 16
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.6402473799503613584883129182483e-46
estimated_step_error = 2.6402473799503613584883129182483e-46
best_h = 0.065536
opt_iter = 17
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.7550413712172457277811286488202e-38
estimated_step_error = 1.7550413712172457277811286488202e-38
best_h = 0.131072
opt_iter = 18
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.1559167249811110859520527040060e-30
estimated_step_error = 1.1559167249811110859520527040060e-30
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 0
y[1] (numeric) = 0
absolute error = 0
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.9391
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 0
y[1] (numeric) = 0.0089130508616163470711550620085135
absolute error = 0.0089130508616163470711550620085135
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.683
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.721
Order of pole (six term test) = 0.4029
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 0
y[1] (numeric) = 0.01769694305689905545082257152429
absolute error = 0.01769694305689905545082257152429
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.694
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.659
Order of pole (six term test) = 0.437
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 0
y[1] (numeric) = 0.026389519476849601120977063764858
absolute error = 0.026389519476849601120977063764858
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.704
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.593
Order of pole (six term test) = 0.4771
TOP MAIN SOLVE Loop
bytes used=12002232, alloc=4193536, time=0.37
x[1] = 0.14
y[1] (analytic) = 0
y[1] (numeric) = 0.034992859903445018880788140848454
absolute error = 0.034992859903445018880788140848454
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.715
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.52
Order of pole (six term test) = 0.5243
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 0
y[1] (numeric) = 0.043508997842014165853690800683198
absolute error = 0.043508997842014165853690800683198
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.725
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.438
Order of pole (six term test) = 0.58
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 0
y[1] (numeric) = 0.051939921790838600501225794541086
absolute error = 0.051939921790838600501225794541086
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.736
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.344
Order of pole (six term test) = 0.6457
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 0
y[1] (numeric) = 0.060287576472853039115352214767412
absolute error = 0.060287576472853039115352214767412
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.746
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.233
Order of pole (six term test) = 0.7237
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 0
y[1] (numeric) = 0.068553864030719146750288990016854
absolute error = 0.068553864030719146750288990016854
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.757
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.099
Order of pole (six term test) = 0.8167
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 0
y[1] (numeric) = 0.076740645186497361554584344315844
absolute error = 0.076740645186497361554584344315844
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.767
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9254
Order of pole (six term test) = 0.9286
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 0
y[1] (numeric) = 0.084849740367094562651464351960624
absolute error = 0.084849740367094562651464351960624
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.777
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6765
Order of pole (six term test) = 1.064
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 0
y[1] (numeric) = 0.092882930796620561069345146658184
absolute error = 0.092882930796620561069345146658184
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.788
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 0
y[1] (numeric) = 0.10084195955674351616515722444398
absolute error = 0.10084195955674351616515722444398
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.798
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=16003488, alloc=4324584, time=0.51
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 0
y[1] (numeric) = 0.10872853261609335795903141148132
absolute error = 0.10872853261609335795903141148132
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.809
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 0
y[1] (numeric) = 0.11654431982972303590088994824121
absolute error = 0.11654431982972303590088994824121
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.819
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 0
y[1] (numeric) = 0.12429095590959982919301204880663
absolute error = 0.12429095590959982919301204880663
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.83
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 0
y[1] (numeric) = 0.13197004136706296022410989659297
absolute error = 0.13197004136706296022410989659297
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 0
y[1] (numeric) = 0.13958314342814927289663746932678
absolute error = 0.13958314342814927289663746932678
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.851
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 0
y[1] (numeric) = 0.14713179692265569796773699247089
absolute error = 0.14713179692265569796773699247089
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.861
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 0
y[1] (numeric) = 0.15461750514777555837447427712518
absolute error = 0.15461750514777555837447427712518
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.871
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 0
y[1] (numeric) = 0.16204174070711540310471268808454
absolute error = 0.16204174070711540310471268808454
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.882
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=20004272, alloc=4390108, time=0.64
x[1] = 0.31
y[1] (analytic) = 0
y[1] (numeric) = 0.16940594632586993633027129237191
absolute error = 0.16940594632586993633027129237191
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.892
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 0
y[1] (numeric) = 0.17671153564290467043943404877286
absolute error = 0.17671153564290467043943404877286
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.903
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.94
Order of pole (six term test) = -31.57
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 0
y[1] (numeric) = 0.18395989398046912166402145692739
absolute error = 0.18395989398046912166402145692739
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.913
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.303
Order of pole (six term test) = -13.94
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 0
y[1] (numeric) = 0.19115237909223763254597801470173
absolute error = 0.19115237909223763254597801470173
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.924
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.33
Order of pole (six term test) = -9.275
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 0
y[1] (numeric) = 0.19829032189035019668668412272878
absolute error = 0.19829032189035019668668412272878
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.934
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.785
Order of pole (six term test) = -7.132
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 0
y[1] (numeric) = 0.20537502715210193086236306747911
absolute error = 0.20537502715210193086236306747911
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.945
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.422
Order of pole (six term test) = -5.908
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 0
y[1] (numeric) = 0.21240777420690704294517699179896
absolute error = 0.21240777420690704294517699179896
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.955
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.154
Order of pole (six term test) = -5.125
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 0
y[1] (numeric) = 0.2193898176041412387511784748081
absolute error = 0.2193898176041412387511784748081
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.966
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.941
Order of pole (six term test) = -4.588
TOP MAIN SOLVE Loop
bytes used=24005248, alloc=4390108, time=0.78
x[1] = 0.39
y[1] (analytic) = 0
y[1] (numeric) = 0.2263223877624454567513857708958
absolute error = 0.2263223877624454567513857708958
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.976
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.763
Order of pole (six term test) = -4.204
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 0
y[1] (numeric) = 0.2332066916010535784104421492584
absolute error = 0.2332066916010535784104421492584
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.986
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.607
Order of pole (six term test) = -3.923
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 0
y[1] (numeric) = 0.24004391315368729759017164120707
absolute error = 0.24004391315368729759017164120707
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.997
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.466
Order of pole (six term test) = -3.718
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 0
y[1] (numeric) = 0.24683521416554261064462588279101
absolute error = 0.24683521416554261064462588279101
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.007
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.335
Order of pole (six term test) = -3.571
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 0
y[1] (numeric) = 0.25358173467387437694615486698711
absolute error = 0.25358173467387437694615486698711
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.018
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.209
Order of pole (six term test) = -3.472
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 0
y[1] (numeric) = 0.26028459357266806666313489672096
absolute error = 0.26028459357266806666313489672096
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.028
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.086
Order of pole (six term test) = -3.416
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 0
y[1] (numeric) = 0.26694488916187112924899545697763
absolute error = 0.26694488916187112924899545697763
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.039
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.963
Order of pole (six term test) = -3.397
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 0
y[1] (numeric) = 0.27356369968164035434776280569276
absolute error = 0.27356369968164035434776280569276
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.049
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.838
Order of pole (six term test) = -3.415
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 0
y[1] (numeric) = 0.28014208383204613010006492398463
absolute error = 0.28014208383204613010006492398463
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.06
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.709
Order of pole (six term test) = -3.468
bytes used=28006568, alloc=4455632, time=0.90
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 0
y[1] (numeric) = 0.2866810812786596068739141545456
absolute error = 0.2866810812786596068739141545456
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.07
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.575
Order of pole (six term test) = -3.556
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 0
y[1] (numeric) = 0.29318171314443442320564075270416
absolute error = 0.29318171314443442320564075270416
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.081
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.433
Order of pole (six term test) = -3.68
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 0
y[1] (numeric) = 0.29964498248828082234065513431963
absolute error = 0.29964498248828082234065513431963
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.091
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.28
Order of pole (six term test) = -3.838
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 0
y[1] (numeric) = 0.30607187477071666043438421854034
absolute error = 0.30607187477071666043438421854034
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.101
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.113
Order of pole (six term test) = -4.032
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 0
y[1] (numeric) = 0.31246335830696696047524661298862
absolute error = 0.31246335830696696047524661298862
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.112
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9236
Order of pole (six term test) = -4.259
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 0
y[1] (numeric) = 0.3188203847078712795741273697958
absolute error = 0.3188203847078712795741273697958
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.122
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6974
Order of pole (six term test) = -4.519
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 0
y[1] (numeric) = 0.32514388930894621261212246086078
absolute error = 0.32514388930894621261212246086078
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.133
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3739
Order of pole (six term test) = -4.81
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 0
y[1] (numeric) = 0.33143479158793883441816927883249
absolute error = 0.33143479158793883441816927883249
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.143
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=32007520, alloc=4455632, time=1.04
x[1] = 0.56
y[1] (analytic) = 0
y[1] (numeric) = 0.33769399557119576856624645336748
absolute error = 0.33769399557119576856624645336748
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.154
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = 0
y[1] (numeric) = 0.34392239022916184723804745575013
absolute error = 0.34392239022916184723804745575013
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.164
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 0
y[1] (numeric) = 0.35012084986131197784452036478501
absolute error = 0.35012084986131197784452036478501
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.175
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 0
y[1] (numeric) = 0.35629023447080984340602252617478
absolute error = 0.35629023447080984340602252617478
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.185
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 0
y[1] (numeric) = 0.36243139012917742090169472777591
absolute error = 0.36243139012917742090169472777591
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.196
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 0
y[1] (numeric) = 0.36854514933124999140330533564397
absolute error = 0.36854514933124999140330533564397
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.206
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 0
y[1] (numeric) = 0.37463233134068232490778949842663
absolute error = 0.37463233134068232490778949842663
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.217
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 0
y[1] (numeric) = 0.38069374252626303905722578545102
absolute error = 0.38069374252626303905722578545102
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.227
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 0
y[1] (numeric) = 0.38673017668928574261809067315143
absolute error = 0.38673017668928574261809067315143
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.238
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=36010872, alloc=4455632, time=1.17
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 0
y[1] (numeric) = 0.3927424153822174704409392348893
absolute error = 0.3927424153822174704409392348893
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.248
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 0
y[1] (numeric) = 0.39873122821889708589368216398932
absolute error = 0.39873122821889708589368216398932
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.259
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 0
y[1] (numeric) = 0.40469737317648875918745219163572
absolute error = 0.40469737317648875918745219163572
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.269
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 0
y[1] (numeric) = 0.41064159688940831577639405192662
absolute error = 0.41064159688940831577639405192662
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.28
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] = 0.69
y[1] (analytic) = 0
y[1] (numeric) = 0.41656463493543317872422094015821
absolute error = 0.41656463493543317872422094015821
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.29
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 0
y[1] (numeric) = 0.42246721211419979361312246237109
absolute error = 0.42246721211419979361312246237109
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.301
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 0
y[1] (numeric) = 0.42835004271828581563665894457166
absolute error = 0.42835004271828581563665894457166
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.311
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 0
y[1] (numeric) = 0.43421383079706794775135421094842
absolute error = 0.43421383079706794775135421094842
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.322
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=40011592, alloc=4521156, time=1.31
x[1] = 0.73
y[1] (analytic) = 0
y[1] (numeric) = 0.44005927041354013829978477532193
absolute error = 0.44005927041354013829978477532193
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.332
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 0
y[1] (numeric) = 0.44588704589427086883683973256774
absolute error = 0.44588704589427086883683973256774
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.343
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 0
y[1] (numeric) = 0.45169783207267248078848177315606
absolute error = 0.45169783207267248078848177315606
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.353
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 0
y[1] (numeric) = 0.45749229452574989615419543469559
absolute error = 0.45749229452574989615419543469559
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.363
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 0
y[1] (numeric) = 0.46327108980449067612920565809117
absolute error = 0.46327108980449067612920565809117
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.374
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 0
y[1] (numeric) = 0.46903486565805312594946637541551
absolute error = 0.46903486565805312594946637541551
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.384
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 0
y[1] (numeric) = 0.47478426125190408839786622174907
absolute error = 0.47478426125190408839786622174907
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.394
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 0
y[1] (numeric) = 0.48051990738005316645615727726065
absolute error = 0.48051990738005316645615727726065
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.404
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 0
y[1] (numeric) = 0.48624242667152537199007480001697
absolute error = 0.48624242667152537199007480001697
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.414
Order of pole (ratio test) 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=44012664, alloc=4521156, time=1.44
x[1] = 0.82
y[1] (analytic) = 0
y[1] (numeric) = 0.49195243379120960679469449199405
absolute error = 0.49195243379120960679469449199405
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.424
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 0
y[1] (numeric) = 0.4976505356352159397061504710195
absolute error = 0.4976505356352159397061504710195
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.434
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = 0
y[1] (numeric) = 0.50333733152087034392071370626457
absolute error = 0.50333733152087034392071370626457
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.444
Order of pole (ratio test) Not computed
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) = 0
y[1] (numeric) = 0.50901341337147139747335805715844
absolute error = 0.50901341337147139747335805715844
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.454
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 0
y[1] (numeric) = 0.51467936589592942253109667776973
absolute error = 0.51467936589592942253109667776973
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.464
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 0
y[1] (numeric) = 0.52033576676340464145426056747126
absolute error = 0.52033576676340464145426056747126
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.473
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 0
y[1] (numeric) = 0.52598318677305715535314675680255
absolute error = 0.52598318677305715535314675680255
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.482
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 0
y[1] (numeric) = 0.53162219001901790017102445221964
absolute error = 0.53162219001901790017102445221964
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.489
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=48013608, alloc=4521156, time=1.58
x[1] = 0.9
y[1] (analytic) = 0
y[1] (numeric) = 0.5372533340506862023743292134435
absolute error = 0.5372533340506862023743292134435
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.496
Order of pole (ratio test) Not computed
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) = 0
y[1] (numeric) = 0.54287717002845613750107830676704
absolute error = 0.54287717002845613750107830676704
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.502
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 0
y[1] (numeric) = 0.54849424287497058663367314024166
absolute error = 0.54849424287497058663367314024166
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.508
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 0
y[1] (numeric) = 0.55410509142199868499105505434248
absolute error = 0.55410509142199868499105505434248
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.514
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 0
y[1] (numeric) = 0.55971024855302926008451911110968
absolute error = 0.55971024855302926008451911110968
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.519
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 0
y[1] (numeric) = 0.56531024134166986119059822345939
absolute error = 0.56531024134166986119059822345939
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.525
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 0
y[1] (numeric) = 0.57090559118593808432937823442441
absolute error = 0.57090559118593808432937823442441
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.53
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 0
y[1] (numeric) = 0.57649681393852909468501994987527
absolute error = 0.57649681393852909468501994987527
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.535
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 0
y[1] (numeric) = 0.58208442003314053877126703612224
absolute error = 0.58208442003314053877126703612224
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.54
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=52015728, alloc=4521156, time=1.72
x[1] = 0.99
y[1] (analytic) = 0
y[1] (numeric) = 0.58766891460693341904407240806311
absolute error = 0.58766891460693341904407240806311
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.545
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 0
y[1] (numeric) = 0.59325079761920497161893423373692
absolute error = 0.59325079761920497161893423373692
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.55
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] = 1.01
y[1] (analytic) = 0
y[1] (numeric) = 0.59883056396634714088737595195358
absolute error = 0.59883056396634714088737595195358
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.555
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 0
y[1] (numeric) = 0.60440870359316188086875103800265
absolute error = 0.60440870359316188086875103800265
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.56
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 0
y[1] (numeric) = 0.60998570160060222989783861219663
absolute error = 0.60998570160060222989783861219663
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.566
Order of pole (ratio test) Not computed
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) = 0
y[1] (numeric) = 0.61556203835000590064331097011654
absolute error = 0.61556203835000590064331097011654
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.572
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1464
Order of pole (six term test) = -11.99
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 0
y[1] (numeric) = 0.62113818956388599947122975256732
absolute error = 0.62113818956388599947122975256732
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.579
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2074
Order of pole (six term test) = -11.98
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 0
y[1] (numeric) = 0.62671462642334143588806143097638
absolute error = 0.62671462642334143588806143097638
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.588
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2497
Order of pole (six term test) = -11.96
TOP MAIN SOLVE Loop
bytes used=56016732, alloc=4521156, time=1.85
x[1] = 1.07
y[1] (analytic) = 0
y[1] (numeric) = 0.63229181566214760237521810170639
absolute error = 0.63229181566214760237521810170639
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.591
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2811
Order of pole (six term test) = -11.93
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 0
y[1] (numeric) = 0.63787021965758599559345852598212
absolute error = 0.63787021965758599559345852598212
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.58
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3043
Order of pole (six term test) = -11.91
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 0
y[1] (numeric) = 0.64345029651806960999467034371366
absolute error = 0.64345029651806960999467034371366
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.565
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3207
Order of pole (six term test) = -11.87
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 0
y[1] (numeric) = 0.64903250016761916270386541858298
absolute error = 0.64903250016761916270386541858298
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.547
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3308
Order of pole (six term test) = -11.84
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 0
y[1] (numeric) = 0.65461728042724350256506754869351
absolute error = 0.65461728042724350256506754869351
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.525
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3349
Order of pole (six term test) = -11.8
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 0
y[1] (numeric) = 0.66020508309327591498372776763479
absolute error = 0.66020508309327591498372776763479
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.5
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.333
Order of pole (six term test) = -11.76
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 0
y[1] (numeric) = 0.66579635001271645620821277809442
absolute error = 0.66579635001271645620821277809442
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.472
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3247
Order of pole (six term test) = -11.71
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 0
y[1] (numeric) = 0.67139151915562893459409602097286
absolute error = 0.67139151915562893459409602097286
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.439
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3095
Order of pole (six term test) = -11.67
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 0
y[1] (numeric) = 0.67699102468463970086251584838654
absolute error = 0.67699102468463970086251584838654
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.402
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2865
Order of pole (six term test) = -11.62
TOP MAIN SOLVE Loop
bytes used=60017672, alloc=4586680, time=1.99
x[1] = 1.16
y[1] (analytic) = 0
y[1] (numeric) = 0.68259529702158401312495018715209
absolute error = 0.68259529702158401312495018715209
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.36
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2535
Order of pole (six term test) = -11.58
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 0
y[1] (numeric) = 0.68820476291134440427815093390914
absolute error = 0.68820476291134440427815093390914
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.314
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2063
Order of pole (six term test) = -11.53
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 0
y[1] (numeric) = 0.69381984548292419809851246216703
absolute error = 0.69381984548292419809851246216703
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.263
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.131
Order of pole (six term test) = -11.48
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 0
y[1] (numeric) = 0.69944096430779809485329120428963
absolute error = 0.69944096430779809485329120428963
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.208
Order of pole (ratio test) Not computed
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) = 0
y[1] (numeric) = 0.70506853545558057640760731651835
absolute error = 0.70506853545558057640760731651835
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.147
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 0
y[1] (numeric) = 0.71070297154705176359179119761789
absolute error = 0.71070297154705176359179119761789
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.081
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 0
y[1] (numeric) = 0.71634468180457929399187726192978
absolute error = 0.71634468180457929399187726192978
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.011
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 0
y[1] (numeric) = 0.72199407209997377536094102796797
absolute error = 0.72199407209997377536094102796797
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.935
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=64018620, alloc=4586680, time=2.13
x[1] = 1.24
y[1] (analytic) = 0
y[1] (numeric) = 0.72765154499981440757798941112871
absolute error = 0.72765154499981440757798941112871
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.733317499808280453593047615029
absolute error = 0.733317499808280453593047615029
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.73899233260752337621003271276751
absolute error = 0.73899233260752337621003271276751
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.74467643629561364201835724191472
absolute error = 0.74467643629561364201835724191472
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.75037020062209542546070828152473
absolute error = 0.75037020062209542546070828152473
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.75607401222118172411228084825763
absolute error = 0.75607401222118172411228084825763
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.76178825464262171996166241076355
absolute error = 0.76178825464262171996166241076355
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.76751330838027159006106231370625
absolute error = 0.76751330838027159006106231370625
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.77324955089839938260709916706609
absolute error = 0.77324955089839938260709916706609
relative error = -1 %
Correct digits = -1
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=68019676, alloc=4586680, time=2.27
x[1] = 1.33
y[1] (analytic) = 0
y[1] (numeric) = 0.77899735665575403059253729174543
absolute error = 0.77899735665575403059253729174543
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.78475709712742807391831018191323
absolute error = 0.78475709712742807391831018191323
relative error = -1 %
Correct digits = -1
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] = 1.35
y[1] (analytic) = 0
y[1] (numeric) = 0.79052914082454320157078371960975
absolute error = 0.79052914082454320157078371960975
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.79631385331178730745953264548259
absolute error = 0.79631385331178730745953264548259
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.80211159722283137609349178377737
absolute error = 0.80211159722283137609349178377737
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.80792273227365417677370105903818
absolute error = 0.80792273227365417677370105903818
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.8137476152738024467308854032061
absolute error = 0.8137476152738024467308854032061
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.81958660013561398397257000954913
absolute error = 0.81958660013561398397257000954913
relative error = -1 %
Correct digits = -1
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) = 0
y[1] (numeric) = 0.82544003788143084886749738306196
absolute error = 0.82544003788143084886749738306196
relative error = -1 %
Correct digits = -1
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=72021032, alloc=4586680, time=2.40
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 0
y[1] (numeric) = 0.83130827664882968902690373288476
absolute error = 0.83130827664882968902690373288476
relative error = -1 %
Correct digits = -1
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 = 1.538
Order of pole (three term test) = -147.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 0
y[1] (numeric) = 0.83719166169389605418538268809691
absolute error = 0.83719166169389605418538268809691
relative error = -1 %
Correct digits = -1
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 = 0.4756
Order of pole (three term test) = -46.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 0
y[1] (numeric) = 0.84309053539256945588042520569382
absolute error = 0.84309053539256945588042520569382
relative error = -1 %
Correct digits = -1
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 = 0.2793
Order of pole (three term test) = -28.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 0
y[1] (numeric) = 0.84900523724008585011889991838466
absolute error = 0.84900523724008585011889991838466
relative error = -1 %
Correct digits = -1
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 = 0.1986
Order of pole (three term test) = -21.46
Radius of convergence (six term test) for eq 1 = 0.2679
Order of pole (six term test) = -11.56
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 0
y[1] (numeric) = 0.85493610384854417923685659204746
absolute error = 0.85493610384854417923685659204746
relative error = -1 %
Correct digits = -1
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 = 0.1556
Order of pole (three term test) = -17.92
Radius of convergence (six term test) for eq 1 = 0.4153
Order of pole (six term test) = -11.53
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 0
y[1] (numeric) = 0.86088346894262360113745768133954
absolute error = 0.86088346894262360113745768133954
relative error = -1 %
Correct digits = -1
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 = 0.1293
Order of pole (three term test) = -16.04
Radius of convergence (six term test) for eq 1 = 0.5053
Order of pole (six term test) = -11.49
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 0
y[1] (numeric) = 0.86684766335347805935592709555379
absolute error = 0.86684766335347805935592709555379
relative error = -1 %
Correct digits = -1
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 = 0.1117
Order of pole (three term test) = -15.08
Radius of convergence (six term test) for eq 1 = 0.5655
Order of pole (six term test) = -11.45
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 0
y[1] (numeric) = 0.87282901501083490526830874220962
absolute error = 0.87282901501083490526830874220962
relative error = -1 %
Correct digits = -1
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 = 0.09912
Order of pole (three term test) = -14.69
Radius of convergence (six term test) for eq 1 = 0.6065
Order of pole (six term test) = -11.41
TOP MAIN SOLVE Loop
bytes used=76024956, alloc=4586680, time=2.54
x[1] = 1.5
y[1] (analytic) = 0
y[1] (numeric) = 0.87882784893332437354234864123791
absolute error = 0.87882784893332437354234864123791
relative error = -1 %
Correct digits = -1
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 = 0.0895
Order of pole (three term test) = -14.69
Radius of convergence (six term test) for eq 1 = 0.6344
Order of pole (six term test) = -11.37
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 0
y[1] (numeric) = 0.88484448721706683292427376414128
absolute error = 0.88484448721706683292427376414128
relative error = -1 %
Correct digits = -1
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 = 0.08168
Order of pole (three term test) = -14.99
Radius of convergence (six term test) for eq 1 = 0.6534
Order of pole (six term test) = -11.33
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = 0
y[1] (numeric) = 0.89087924902254488595440234685864
absolute error = 0.89087924902254488595440234685864
relative error = -1 %
Correct digits = -1
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 = 0.07489
Order of pole (three term test) = -15.52
Radius of convergence (six term test) for eq 1 = 0.6666
Order of pole (six term test) = -11.3
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 0
y[1] (numeric) = 0.89693245055978757248555579243636
absolute error = 0.89693245055978757248555579243636
relative error = -1 %
Correct digits = -1
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 = 0.06862
Order of pole (three term test) = -16.22
Radius of convergence (six term test) for eq 1 = 0.6764
Order of pole (six term test) = -11.27
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 0
y[1] (numeric) = 0.90300440507189414220673720976515
absolute error = 0.90300440507189414220673720976515
relative error = -1 %
Correct digits = -1
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 = 0.06251
Order of pole (three term test) = -17.07
Radius of convergence (six term test) for eq 1 = 0.6843
Order of pole (six term test) = -11.24
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 0
y[1] (numeric) = 0.9090954228169251000025473006877
absolute error = 0.9090954228169251000025473006877
relative error = -1 %
Correct digits = -1
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 = 0.05629
Order of pole (three term test) = -18.02
Radius of convergence (six term test) for eq 1 = 0.6918
Order of pole (six term test) = -11.22
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = 0
y[1] (numeric) = 0.91520581104818849414393800936634
absolute error = 0.91520581104818849414393800936634
relative error = -1 %
Correct digits = -1
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 = 0.04977
Order of pole (three term test) = -19.06
Radius of convergence (six term test) for eq 1 = 0.6998
Order of pole (six term test) = -11.19
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 0
y[1] (numeric) = 0.92133587399294971023047718657662
absolute error = 0.92133587399294971023047718657662
relative error = -1 %
Correct digits = -1
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 = 0.04282
Order of pole (three term test) = -20.14
Radius of convergence (six term test) for eq 1 = 0.7091
Order of pole (six term test) = -11.16
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 0
y[1] (numeric) = 0.92748591282959335269453036736189
absolute error = 0.92748591282959335269453036736189
relative error = -1 %
Correct digits = -1
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 = 0.03535
Order of pole (three term test) = -21.24
Radius of convergence (six term test) for eq 1 = 0.7201
Order of pole (six term test) = -11.14
TOP MAIN SOLVE Loop
bytes used=80026000, alloc=4586680, time=2.67
x[1] = 1.59
y[1] (analytic) = 0
y[1] (numeric) = 0.93365622566326613972301489603156
absolute error = 0.93365622566326613972301489603156
relative error = -1 %
Correct digits = -1
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 = 0.02734
Order of pole (three term test) = -22.31
Radius of convergence (six term test) for eq 1 = 0.7333
Order of pole (six term test) = -11.11
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 0
y[1] (numeric) = 0.93984710750003010582443548878382
absolute error = 0.93984710750003010582443548878382
relative error = -1 %
Correct digits = -1
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 = 0.01878
Order of pole (three term test) = -23.32
Radius of convergence (six term test) for eq 1 = 0.749
Order of pole (six term test) = -11.07
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = 0
y[1] (numeric) = 0.94605885021955579812133473512838
absolute error = 0.94605885021955579812133473512838
relative error = -1 %
Correct digits = -1
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 = 0.009728
Order of pole (three term test) = -24.24
Radius of convergence (six term test) for eq 1 = 0.7675
Order of pole (six term test) = -11.03
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 0
y[1] (numeric) = 0.95229174254638556691582945600128
absolute error = 0.95229174254638556691582945600128
relative error = -1 %
Correct digits = -1
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 = 0.0002695
Order of pole (three term test) = -25.02
Radius of convergence (six term test) for eq 1 = 0.789
Order of pole (six term test) = -10.99
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 0
y[1] (numeric) = 0.95854607001979748727392794704939
absolute error = 0.95854607001979748727392794704939
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 0.8137
Order of pole (six term test) = -10.94
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 0
y[1] (numeric) = 0.96482211496230090539835033265986
absolute error = 0.96482211496230090539835033265986
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 0.8419
Order of pole (six term test) = -10.89
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 0
y[1] (numeric) = 0.97112015644679508048483338828657
absolute error = 0.97112015644679508048483338828657
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 0.8735
Order of pole (six term test) = -10.82
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 0
y[1] (numeric) = 0.97744047026242288863796301396573
absolute error = 0.97744047026242288863796301396573
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 0.909
Order of pole (six term test) = -10.75
TOP MAIN SOLVE Loop
bytes used=84027016, alloc=4586680, time=2.81
x[1] = 1.67
y[1] (analytic) = 0
y[1] (numeric) = 0.98378332887915206929304528484773
absolute error = 0.98378332887915206929304528484773
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 0.9485
Order of pole (six term test) = -10.67
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 0
y[1] (numeric) = 0.99014900141111702546278938102279
absolute error = 0.99014900141111702546278938102279
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 0.9923
Order of pole (six term test) = -10.57
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 0
y[1] (numeric) = 0.99653775357875473599262374598076
absolute error = 0.99653775357875473599262374598076
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.041
Order of pole (six term test) = -10.46
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 0
y[1] (numeric) = 1.0029498476697688998357758222879
absolute error = 1.0029498476697688998357758222879
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.094
Order of pole (six term test) = -10.33
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 0
y[1] (numeric) = 1.009385542498957008096723447878
absolute error = 1.009385542498957008096723447878
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.152
Order of pole (six term test) = -10.18
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 0
y[1] (numeric) = 1.0158450933669356281656285264113
absolute error = 1.0158450933669356281656285264113
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.216
Order of pole (six term test) = -10
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 0
y[1] (numeric) = 1.0223287520177997845817796566606
absolute error = 1.0223287520177997845817796566606
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.286
Order of pole (six term test) = -9.801
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 0
y[1] (numeric) = 1.028836766595752932204475544852
absolute error = 1.028836766595752932204475544852
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.363
Order of pole (six term test) = -9.567
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 0
y[1] (numeric) = 1.0353693816007446376976622809535
absolute error = 1.0353693816007446376976622809535
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.446
Order of pole (six term test) = -9.295
TOP MAIN SOLVE Loop
bytes used=88028400, alloc=4586680, time=2.94
x[1] = 1.76
y[1] (analytic) = 0
y[1] (numeric) = 1.0419268378431537140916897894694
absolute error = 1.0419268378431537140916897894694
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.538
Order of pole (six term test) = -8.978
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 0
y[1] (numeric) = 1.0485093723975551890930472290174
absolute error = 1.0485093723975551890930472290174
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.638
Order of pole (six term test) = -8.609
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 0
y[1] (numeric) = 1.055117218555610129672163099696
absolute error = 1.055117218555610129672163099696
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.747
Order of pole (six term test) = -8.178
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = 0
y[1] (numeric) = 1.0617506057781179920521358510813
absolute error = 1.0617506057781179920521358510813
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.866
Order of pole (six term test) = -7.675
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 0
y[1] (numeric) = 1.068409759646271816310539920028
absolute error = 1.068409759646271816310539920028
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 1.996
Order of pole (six term test) = -7.087
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 0
y[1] (numeric) = 1.0750949018121572371369616473371
absolute error = 1.0750949018121572371369616473371
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.138
Order of pole (six term test) = -6.4
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 0
y[1] (numeric) = 1.081806249948536935587915278428
absolute error = 1.081806249948536935587915278428
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.292
Order of pole (six term test) = -5.598
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 0
y[1] (numeric) = 1.0885440176979628096588647461666
absolute error = 1.0885440176979628096588647461666
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.459
Order of pole (six term test) = -4.663
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = 0
y[1] (numeric) = 1.0953084146212587928450510737056
absolute error = 1.0953084146212587928450510737056
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.639
Order of pole (six term test) = -3.578
TOP MAIN SOLVE Loop
bytes used=92029840, alloc=4586680, time=3.08
x[1] = 1.85
y[1] (analytic) = 0
y[1] (numeric) = 1.1020996461454178982687045930063
absolute error = 1.1020996461454178982687045930063
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.833
Order of pole (six term test) = -2.324
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 0
y[1] (numeric) = 1.1089179135109577100762363852674
absolute error = 1.1089179135109577100762363852674
relative error = -1 %
Correct digits = -1
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 = 0.006749
Order of pole (three term test) = -0.9734
Radius of convergence (six term test) for eq 1 = 3.04
Order of pole (six term test) = -0.8847
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 0
y[1] (numeric) = 1.1157634137187791823087191626422
absolute error = 1.1157634137187791823087191626422
relative error = -1 %
Correct digits = -1
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 = 0.01573
Order of pole (three term test) = -1.356
Radius of convergence (six term test) for eq 1 = 3.258
Order of pole (six term test) = 0.7499
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 0
y[1] (numeric) = 1.1226363394765742369644661352532
absolute error = 1.1226363394765742369644661352532
relative error = -1 %
Correct digits = -1
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 = 0.02392
Order of pole (three term test) = -2.045
Radius of convergence (six term test) for eq 1 = 3.487
Order of pole (six term test) = 2.582
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 0
y[1] (numeric) = 1.1295368791448282761356515231701
absolute error = 1.1295368791448282761356515231701
relative error = -1 %
Correct digits = -1
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 = 0.03114
Order of pole (three term test) = -3.024
Radius of convergence (six term test) for eq 1 = 3.721
Order of pole (six term test) = 4.598
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = 0
y[1] (numeric) = 1.1364652166824643365346413163976
absolute error = 1.1364652166824643365346413163976
relative error = -1 %
Correct digits = -1
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 = 0.03722
Order of pole (three term test) = -4.27
Radius of convergence (six term test) for eq 1 = 3.958
Order of pole (six term test) = 6.767
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 0
y[1] (numeric) = 1.1434215315921762170454658457335
absolute error = 1.1434215315921762170454658457335
relative error = -1 %
Correct digits = -1
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 = 0.042
Order of pole (three term test) = -5.752
Radius of convergence (six term test) for eq 1 = 4.19
Order of pole (six term test) = 9.033
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 0
y[1] (numeric) = 1.1504059988654984997510751047086
absolute error = 1.1504059988654984997510751047086
relative error = -1 %
Correct digits = -1
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 = 0.04537
Order of pole (three term test) = -7.435
Radius of convergence (six term test) for eq 1 = 4.411
Order of pole (six term test) = 11.32
TOP MAIN SOLVE Loop
bytes used=96030672, alloc=4586680, time=3.22
x[1] = 1.93
y[1] (analytic) = 0
y[1] (numeric) = 1.1574187889276619608025743742933
absolute error = 1.1574187889276619608025743742933
relative error = -1 %
Correct digits = -1
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 = 0.04725
Order of pole (three term test) = -9.277
Radius of convergence (six term test) for eq 1 = 4.614
Order of pole (six term test) = 13.52
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 0
y[1] (numeric) = 1.164460067582283428114532420716
absolute error = 1.164460067582283428114532420716
relative error = -1 %
Correct digits = -1
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 = 0.04758
Order of pole (three term test) = -11.23
Radius of convergence (six term test) for eq 1 = 4.791
Order of pole (six term test) = 15.53
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 0
y[1] (numeric) = 1.1715299959559396867914294815427
absolute error = 1.1715299959559396867914294815427
relative error = -1 %
Correct digits = -1
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 = 0.04635
Order of pole (three term test) = -13.25
Radius of convergence (six term test) for eq 1 = 4.937
Order of pole (six term test) = 17.25
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 0
y[1] (numeric) = 1.1786287304426755590155834536347
absolute error = 1.1786287304426755590155834536347
relative error = -1 %
Correct digits = -1
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 = 0.04359
Order of pole (three term test) = -15.29
Radius of convergence (six term test) for eq 1 = 5.048
Order of pole (six term test) = 18.6
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 0
y[1] (numeric) = 1.1857564226484967914599319582201
absolute error = 1.1857564226484967914599319582201
relative error = -1 %
Correct digits = -1
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 = 0.03936
Order of pole (three term test) = -17.28
Radius of convergence (six term test) for eq 1 = 5.122
Order of pole (six term test) = 19.54
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = 0
y[1] (numeric) = 1.1929132193358988687374215088309
absolute error = 1.1929132193358988687374215088309
relative error = -1 %
Correct digits = -1
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 = 0.03377
Order of pole (three term test) = -19.19
Radius of convergence (six term test) for eq 1 = 5.162
Order of pole (six term test) = 20.07
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 0
y[1] (numeric) = 1.2000992623684833345760162467687
absolute error = 1.2000992623684833345760162467687
relative error = -1 %
Correct digits = -1
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 = 0.02695
Order of pole (three term test) = -20.95
Radius of convergence (six term test) for eq 1 = 5.171
Order of pole (six term test) = 20.22
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 0
y[1] (numeric) = 1.2073146886557136419359722654635
absolute error = 1.2073146886557136419359722654635
relative error = -1 %
Correct digits = -1
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 = 0.01907
Order of pole (three term test) = -22.52
Radius of convergence (six term test) for eq 1 = 5.154
Order of pole (six term test) = 20.05
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 0
y[1] (numeric) = 1.2145596300978629677954376232748
absolute error = 1.2145596300978629677954376232748
relative error = -1 %
Correct digits = -1
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 = 0.01034
Order of pole (three term test) = -23.87
Radius of convergence (six term test) for eq 1 = 5.117
Order of pole (six term test) = 19.62
TOP MAIN SOLVE Loop
bytes used=100031748, alloc=4586680, time=3.36
x[1] = 2.02
y[1] (analytic) = 0
y[1] (numeric) = 1.2218342135312068164650019600829
absolute error = 1.2218342135312068164650019600829
relative error = -1 %
Correct digits = -1
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 = 0.0009821
Order of pole (three term test) = -24.94
Radius of convergence (six term test) for eq 1 = 5.064
Order of pole (six term test) = 19.01
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 0
y[1] (numeric) = 1.229138560673513595708942570805
absolute error = 1.229138560673513595708942570805
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 5.001
Order of pole (six term test) = 18.28
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 0
y[1] (numeric) = 1.236472788069886681324162720082
absolute error = 1.236472788069886681324162720082
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.932
Order of pole (six term test) = 17.48
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 0
y[1] (numeric) = 1.2438370070390117868490690170427
absolute error = 1.2438370070390117868490690170427
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.859
Order of pole (six term test) = 16.66
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 0
y[1] (numeric) = 1.2512313236198637244562554411994
absolute error = 1.2512313236198637244562554411994
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.786
Order of pole (six term test) = 15.84
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 0
y[1] (numeric) = 1.2586558385189268795599200294246
absolute error = 1.2586558385189268795599200294246
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.715
Order of pole (six term test) = 15.04
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 0
y[1] (numeric) = 1.2661106470579839240014354765358
absolute error = 1.2661106470579839240014354765358
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.645
Order of pole (six term test) = 14.28
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 0
y[1] (numeric) = 1.2735958391225274596516062659079
absolute error = 1.2735958391225274596516062659079
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.579
Order of pole (six term test) = 13.57
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 0
y[1] (numeric) = 1.28111149911084941470249403693
absolute error = 1.28111149911084941470249403693
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.517
Order of pole (six term test) = 12.91
TOP MAIN SOLVE Loop
bytes used=104032808, alloc=4586680, time=3.50
x[1] = 2.11
y[1] (analytic) = 0
y[1] (numeric) = 1.288657705883863107663614480208
absolute error = 1.288657705883863107663614480208
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.459
Order of pole (six term test) = 12.3
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 0
y[1] (numeric) = 1.2962345327157129480091257828125
absolute error = 1.2962345327157129480091257828125
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.406
Order of pole (six term test) = 11.74
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 0
y[1] (numeric) = 1.3038420472452267564629247394766
absolute error = 1.3038420472452267564629247394766
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.356
Order of pole (six term test) = 11.23
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 0
y[1] (numeric) = 1.311480311428265661014455469918
absolute error = 1.311480311428265661014455469918
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.311
Order of pole (six term test) = 10.77
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 0
y[1] (numeric) = 1.3191493814910264559274161337042
absolute error = 1.3191493814910264559274161337042
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.269
Order of pole (six term test) = 10.35
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 0
y[1] (numeric) = 1.3268493078843511992773454649006
absolute error = 1.3268493078843511992773454649006
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.231
Order of pole (six term test) = 9.977
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 0
y[1] (numeric) = 1.3345801352390986690184513416989
absolute error = 1.3345801352390986690184513416989
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.196
Order of pole (six term test) = 9.636
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 0
y[1] (numeric) = 1.3423419023226320973686106147625
absolute error = 1.3423419023226320973686106147625
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.164
Order of pole (six term test) = 9.328
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 0
y[1] (numeric) = 1.3501346419964773575974188393902
absolute error = 1.3501346419964773575974188393902
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.136
Order of pole (six term test) = 9.05
TOP MAIN SOLVE Loop
bytes used=108033808, alloc=4586680, time=3.64
x[1] = 2.2
y[1] (analytic) = 0
y[1] (numeric) = 1.3579583811752054853404097575992
absolute error = 1.3579583811752054853404097575992
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.109
Order of pole (six term test) = 8.801
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 0
y[1] (numeric) = 1.3658131407865930776317971614205
absolute error = 1.3658131407865930776317971614205
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.086
Order of pole (six term test) = 8.575
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 0
y[1] (numeric) = 1.3736989357331137262928341635907
absolute error = 1.3736989357331137262928341635907
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.064
Order of pole (six term test) = 8.373
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 0
y[1] (numeric) = 1.3816157748548132075354463202005
absolute error = 1.3816157748548132075354463202005
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.044
Order of pole (six term test) = 8.19
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 0
y[1] (numeric) = 1.389563660893620666103189325855
absolute error = 1.389563660893620666103189325855
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.026
Order of pole (six term test) = 8.025
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 0
y[1] (numeric) = 1.3975425904591474994973747932857
absolute error = 1.3975425904591474994973747932857
relative error = -1 %
Correct digits = -1
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 = 0.005078
Order of pole (three term test) = -0.9378
Radius of convergence (six term test) for eq 1 = 4.01
Order of pole (six term test) = 7.877
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 0
y[1] (numeric) = 1.4055525539960250654122927397116
absolute error = 1.4055525539960250654122927397116
relative error = -1 %
Correct digits = -1
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 = 0.0143
Order of pole (three term test) = -1.264
Radius of convergence (six term test) for eq 1 = 3.996
Order of pole (six term test) = 7.744
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 0
y[1] (numeric) = 1.4135935357528317030817586260468
absolute error = 1.4135935357528317030817586260468
relative error = -1 %
Correct digits = -1
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 = 0.02291
Order of pole (three term test) = -1.9
Radius of convergence (six term test) for eq 1 = 3.982
Order of pole (six term test) = 7.624
TOP MAIN SOLVE Loop
bytes used=112034924, alloc=4586680, time=3.78
x[1] = 2.28
y[1] (analytic) = 0
y[1] (numeric) = 1.4216655137526588765382939616651
absolute error = 1.4216655137526588765382939616651
relative error = -1 %
Correct digits = -1
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 = 0.0307
Order of pole (three term test) = -2.829
Radius of convergence (six term test) for eq 1 = 3.97
Order of pole (six term test) = 7.516
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 0
y[1] (numeric) = 1.4297684597653655145928574674948
absolute error = 1.4297684597653655145928574674948
relative error = -1 %
Correct digits = -1
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 = 0.03746
Order of pole (three term test) = -4.029
Radius of convergence (six term test) for eq 1 = 3.959
Order of pole (six term test) = 7.42
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 0
y[1] (numeric) = 1.4379023392815688385135393314096
absolute error = 1.4379023392815688385135393314096
relative error = -1 %
Correct digits = -1
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 = 0.04304
Order of pole (three term test) = -5.47
Radius of convergence (six term test) for eq 1 = 3.949
Order of pole (six term test) = 7.335
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 0
y[1] (numeric) = 1.4460671114884191338433324679728
absolute error = 1.4460671114884191338433324679728
relative error = -1 %
Correct digits = -1
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) = -7.117
Radius of convergence (six term test) for eq 1 = 3.94
Order of pole (six term test) = 7.259
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 0
y[1] (numeric) = 1.4542627292472050375495173009382
absolute error = 1.4542627292472050375495173009382
relative error = -1 %
Correct digits = -1
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 = 0.05011
Order of pole (three term test) = -8.927
Radius of convergence (six term test) for eq 1 = 3.933
Order of pole (six term test) = 7.192
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 0
y[1] (numeric) = 1.4624891390728349758131857240923
absolute error = 1.4624891390728349758131857240923
relative error = -1 %
Correct digits = -1
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 = 0.05141
Order of pole (three term test) = -10.85
Radius of convergence (six term test) for eq 1 = 3.926
Order of pole (six term test) = 7.134
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 0
y[1] (numeric) = 1.4707462811152394013941822198604
absolute error = 1.4707462811152394013941822198604
relative error = -1 %
Correct digits = -1
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 = 0.05115
Order of pole (three term test) = -12.85
Radius of convergence (six term test) for eq 1 = 3.919
Order of pole (six term test) = 7.084
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 0
y[1] (numeric) = 1.4790340891427374428667093431584
absolute error = 1.4790340891427374428667093431584
relative error = -1 %
Correct digits = -1
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 = 0.04934
Order of pole (three term test) = -14.85
Radius of convergence (six term test) for eq 1 = 3.914
Order of pole (six term test) = 7.043
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 0
y[1] (numeric) = 1.4873524905274104914125274819709
absolute error = 1.4873524905274104914125274819709
relative error = -1 %
Correct digits = -1
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 = 0.04601
Order of pole (three term test) = -16.82
Radius of convergence (six term test) for eq 1 = 3.91
Order of pole (six term test) = 7.009
TOP MAIN SOLVE Loop
bytes used=116035720, alloc=4652204, time=3.92
x[1] = 2.37
y[1] (analytic) = 0
y[1] (numeric) = 1.4957014062325241146572763177802
absolute error = 1.4957014062325241146572763177802
relative error = -1 %
Correct digits = -1
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 = 0.04125
Order of pole (three term test) = -18.69
Radius of convergence (six term test) for eq 1 = 3.906
Order of pole (six term test) = 6.982
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 0
y[1] (numeric) = 1.5040807508020385016933980959159
absolute error = 1.5040807508020385016933980959159
relative error = -1 %
Correct digits = -1
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 = 0.03517
Order of pole (three term test) = -20.42
Radius of convergence (six term test) for eq 1 = 3.903
Order of pole (six term test) = 6.963
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 0
y[1] (numeric) = 1.5124904323522464094805332256123
absolute error = 1.5124904323522464094805332256123
relative error = -1 %
Correct digits = -1
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 = 0.02793
Order of pole (three term test) = -21.95
Radius of convergence (six term test) for eq 1 = 3.901
Order of pole (six term test) = 6.95
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 0
y[1] (numeric) = 1.5209303525655762988590803542118
absolute error = 1.5209303525655762988590803542118
relative error = -1 %
Correct digits = -1
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 = 0.01974
Order of pole (three term test) = -23.24
Radius of convergence (six term test) for eq 1 = 3.9
Order of pole (six term test) = 6.944
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 0
y[1] (numeric) = 1.5294004066865970191409017438932
absolute error = 1.5294004066865970191409017438932
relative error = -1 %
Correct digits = -1
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 = 0.0108
Order of pole (three term test) = -24.26
Radius of convergence (six term test) for eq 1 = 3.899
Order of pole (six term test) = 6.945
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 0
y[1] (numeric) = 1.5379004835202590244169800722717
absolute error = 1.5379004835202590244169800722717
relative error = -1 %
Correct digits = -1
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 = 0.00136
Order of pole (three term test) = -24.96
Radius of convergence (six term test) for eq 1 = 3.899
Order of pole (six term test) = 6.951
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 0
y[1] (numeric) = 1.5464304654324056831871468309762
absolute error = 1.5464304654324056831871468309762
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.899
Order of pole (six term test) = 6.964
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 0
y[1] (numeric) = 1.5549902283525867765913444008162
absolute error = 1.5549902283525867765913444008162
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.9
Order of pole (six term test) = 6.981
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 0
y[1] (numeric) = 1.5635796417792047704019376744535
absolute error = 1.5635796417792047704019376744535
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.902
Order of pole (six term test) = 7.004
TOP MAIN SOLVE Loop
bytes used=120036860, alloc=4652204, time=4.05
x[1] = 2.46
y[1] (analytic) = 0
y[1] (numeric) = 1.5721985687870228930955959680842
absolute error = 1.5721985687870228930955959680842
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.904
Order of pole (six term test) = 7.03
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 0
y[1] (numeric) = 1.5808468660370624579102775554215
absolute error = 1.5808468660370624579102775554215
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.907
Order of pole (six term test) = 7.061
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 0
y[1] (numeric) = 1.5895243837889152320318511759073
absolute error = 1.5895243837889152320318511759073
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.909
Order of pole (six term test) = 7.094
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 0
y[1] (numeric) = 1.598230965915494982243754581872
absolute error = 1.598230965915494982243754581872
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.912
Order of pole (six term test) = 7.13
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 0
y[1] (numeric) = 1.6069664499202506148823937477615
absolute error = 1.6069664499202506148823937477615
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.916
Order of pole (six term test) = 7.168
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 0
y[1] (numeric) = 1.6157306669568615802126642494287
absolute error = 1.6157306669568615802126642494287
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.919
Order of pole (six term test) = 7.207
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 0
y[1] (numeric) = 1.6245234418514344288838395792618
absolute error = 1.6245234418514344288838395792618
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.923
Order of pole (six term test) = 7.246
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 0
y[1] (numeric) = 1.6333445931272175925261694734761
absolute error = 1.6333445931272175925261694734761
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.926
Order of pole (six term test) = 7.285
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 0
y[1] (numeric) = 1.6421939330318496134493703203516
absolute error = 1.6421939330318496134493703203516
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.929
Order of pole (six term test) = 7.323
TOP MAIN SOLVE Loop
bytes used=124038648, alloc=4652204, time=4.20
x[1] = 2.55
y[1] (analytic) = 0
y[1] (numeric) = 1.6510712675671541715168033274756
absolute error = 1.6510712675671541715168033274756
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.933
Order of pole (six term test) = 7.359
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 0
y[1] (numeric) = 1.6599763965214933513670161605053
absolute error = 1.6599763965214933513670161605053
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.936
Order of pole (six term test) = 7.393
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 0
y[1] (numeric) = 1.6689091135046886620712092327471
absolute error = 1.6689091135046886620712092327471
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.938
Order of pole (six term test) = 7.425
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 0
y[1] (numeric) = 1.6778692059855173659427169344792
absolute error = 1.6778692059855173659427169344792
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.941
Order of pole (six term test) = 7.453
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 0
y[1] (numeric) = 1.6868564553317896954998222342324
absolute error = 1.6868564553317896954998222342324
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.943
Order of pole (six term test) = 7.477
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 0
y[1] (numeric) = 1.6958706368530105395260104421455
absolute error = 1.6958706368530105395260104421455
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.944
Order of pole (six term test) = 7.497
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 0
y[1] (numeric) = 1.7049115198456271628220407348329
absolute error = 1.7049115198456271628220407348329
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.945
Order of pole (six term test) = 7.513
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 0
y[1] (numeric) = 1.7139788676408624916991038945711
absolute error = 1.7139788676408624916991038945711
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.946
Order of pole (six term test) = 7.524
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 0
y[1] (numeric) = 1.7230724376551314506632006224266
absolute error = 1.7230724376551314506632006224266
relative error = -1 %
Correct digits = -1
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 = 0.002866
Order of pole (three term test) = -0.9072
Radius of convergence (six term test) for eq 1 = 3.947
Order of pole (six term test) = 7.531
bytes used=128040372, alloc=4652204, time=4.34
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 0
y[1] (numeric) = 1.732191981443035777270213059022
absolute error = 1.732191981443035777270213059022
relative error = -1 %
Correct digits = -1
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 = 0.01233
Order of pole (three term test) = -1.164
Radius of convergence (six term test) for eq 1 = 3.947
Order of pole (six term test) = 7.534
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 0
y[1] (numeric) = 1.7413372447529306740093895158048
absolute error = 1.7413372447529306740093895158048
relative error = -1 %
Correct digits = -1
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 = 0.02136
Order of pole (three term test) = -1.737
Radius of convergence (six term test) for eq 1 = 3.946
Order of pole (six term test) = 7.533
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 0
y[1] (numeric) = 1.7505079675850545805551980708208
absolute error = 1.7505079675850545805551980708208
relative error = -1 %
Correct digits = -1
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 = 0.02975
Order of pole (three term test) = -2.612
Radius of convergence (six term test) for eq 1 = 3.945
Order of pole (six term test) = 7.527
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 0
y[1] (numeric) = 1.7597038842522112691000572621774
absolute error = 1.7597038842522112691000572621774
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.133
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.03727
Order of pole (three term test) = -3.765
Radius of convergence (six term test) for eq 1 = 3.944
Order of pole (six term test) = 7.519
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 0
y[1] (numeric) = 1.7689247234429913820574179928555
absolute error = 1.7689247234429913820574179928555
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.466
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.04373
Order of pole (three term test) = -5.169
Radius of convergence (six term test) for eq 1 = 3.943
Order of pole (six term test) = 7.507
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 0
y[1] (numeric) = 1.7781702082875184475443501700997
absolute error = 1.7781702082875184475443501700997
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.332
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.04896
Order of pole (three term test) = -6.787
Radius of convergence (six term test) for eq 1 = 3.941
Order of pole (six term test) = 7.492
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 0
y[1] (numeric) = 1.787440056425702326074045465559
absolute error = 1.787440056425702326074045465559
relative error = -1 %
Correct digits = -1
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 = 0.05283
Order of pole (three term test) = -8.576
Radius of convergence (six term test) for eq 1 = 3.939
Order of pole (six term test) = 7.476
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 0
y[1] (numeric) = 1.7967339800779809641872061786121
absolute error = 1.7967339800779809641872061786121
relative error = -1 %
Correct digits = -1
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 = 0.05523
Order of pole (three term test) = -10.49
Radius of convergence (six term test) for eq 1 = 3.937
Order of pole (six term test) = 7.458
TOP MAIN SOLVE Loop
bytes used=132041176, alloc=4652204, time=4.48
x[1] = 2.72
y[1] (analytic) = 0
y[1] (numeric) = 1.8060516861185292597159609600447
absolute error = 1.8060516861185292597159609600447
relative error = -1 %
Correct digits = -1
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 = 0.05608
Order of pole (three term test) = -12.48
Radius of convergence (six term test) for eq 1 = 3.935
Order of pole (six term test) = 7.439
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 0
y[1] (numeric) = 1.8153928761509117814028102224579
absolute error = 1.8153928761509117814028102224579
relative error = -1 %
Correct digits = -1
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 = 0.05537
Order of pole (three term test) = -14.48
Radius of convergence (six term test) for eq 1 = 3.933
Order of pole (six term test) = 7.42
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 0
y[1] (numeric) = 1.8247572465861540350936371555688
absolute error = 1.8247572465861540350936371555688
relative error = -1 %
Correct digits = -1
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 = 0.05309
Order of pole (three term test) = -16.45
Radius of convergence (six term test) for eq 1 = 3.93
Order of pole (six term test) = 7.402
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 0
y[1] (numeric) = 1.8341444887232049320930000098996
absolute error = 1.8341444887232049320930000098996
relative error = -1 %
Correct digits = -1
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 = 0.0493
Order of pole (three term test) = -18.32
Radius of convergence (six term test) for eq 1 = 3.929
Order of pole (six term test) = 7.384
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 0
y[1] (numeric) = 1.8435542888317610949142849536628
absolute error = 1.8435542888317610949142849536628
relative error = -1 %
Correct digits = -1
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 = 0.04411
Order of pole (three term test) = -20.05
Radius of convergence (six term test) for eq 1 = 3.927
Order of pole (six term test) = 7.368
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 0
y[1] (numeric) = 1.8529863282374216339729895267233
absolute error = 1.8529863282374216339729895267233
relative error = -1 %
Correct digits = -1
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 = 0.03765
Order of pole (three term test) = -21.59
Radius of convergence (six term test) for eq 1 = 3.925
Order of pole (six term test) = 7.355
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 0
y[1] (numeric) = 1.8624402834091400481442048946366
absolute error = 1.8624402834091400481442048946366
relative error = -1 %
Correct digits = -1
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 = 0.03008
Order of pole (three term test) = -22.88
Radius of convergence (six term test) for eq 1 = 3.924
Order of pole (six term test) = 7.343
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 0
y[1] (numeric) = 1.8719158260489379449067149260755
absolute error = 1.8719158260489379449067149260755
relative error = -1 %
Correct digits = -1
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 = 0.02164
Order of pole (three term test) = -23.9
Radius of convergence (six term test) for eq 1 = 3.923
Order of pole (six term test) = 7.335
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 0
y[1] (numeric) = 1.8814126231838433443791699661568
absolute error = 1.8814126231838433443791699661568
relative error = -1 %
Correct digits = -1
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 = 0.01254
Order of pole (three term test) = -24.61
Radius of convergence (six term test) for eq 1 = 3.923
Order of pole (six term test) = 7.33
TOP MAIN SOLVE Loop
bytes used=136042336, alloc=4652204, time=4.61
x[1] = 2.81
y[1] (analytic) = 0
y[1] (numeric) = 1.8909303372600144282493983849743
absolute error = 1.8909303372600144282493983849743
relative error = -1 %
Correct digits = -1
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 = 0.003042
Order of pole (three term test) = -24.99
Radius of convergence (six term test) for eq 1 = 3.922
Order of pole (six term test) = 7.329
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 0
y[1] (numeric) = 1.9004686262390077217107654159021
absolute error = 1.9004686262390077217107654159021
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.923
Order of pole (six term test) = 7.331
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = 0
y[1] (numeric) = 1.9100271436961478563241458820429
absolute error = 1.9100271436961478563241458820429
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.923
Order of pole (six term test) = 7.336
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 0
y[1] (numeric) = 1.9196055389209542564611390392089
absolute error = 1.9196055389209542564611390392089
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.924
Order of pole (six term test) = 7.345
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 0
y[1] (numeric) = 1.9292034570195783238564156328044
absolute error = 1.9292034570195783238564156328044
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.925
Order of pole (six term test) = 7.357
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 0
y[1] (numeric) = 1.9388205390192029659657789662691
absolute error = 1.9388205390192029659657789662691
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.927
Order of pole (six term test) = 7.372
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 0
y[1] (numeric) = 1.9484564219743546264076019971462
absolute error = 1.9484564219743546264076019971462
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.929
Order of pole (six term test) = 7.39
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = 0
y[1] (numeric) = 1.9581107390750763318258254671118
absolute error = 1.9581107390750763318258254671118
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.931
Order of pole (six term test) = 7.41
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 0
y[1] (numeric) = 1.9677831197569086710672634524606
absolute error = 1.9677831197569086710672634524606
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.37
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.934
Order of pole (six term test) = 7.432
TOP MAIN SOLVE Loop
bytes used=140043100, alloc=4652204, time=4.75
x[1] = 2.9
y[1] (analytic) = 0
y[1] (numeric) = 1.9774731898126240715732324815317
absolute error = 1.9774731898126240715732324815317
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.738
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.936
Order of pole (six term test) = 7.454
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 0
y[1] (numeric) = 1.9871805715056582362448707865095
absolute error = 1.9871805715056582362448707865095
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.963
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.939
Order of pole (six term test) = 7.478
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = 0
y[1] (numeric) = 1.9969048836851811535897502379871
absolute error = 1.9969048836851811535897502379871
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.608
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.941
Order of pole (six term test) = 7.501
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 0
y[1] (numeric) = 2.0066457419027486964655825718129
absolute error = 2.0066457419027486964655825718129
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.291
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.944
Order of pole (six term test) = 7.524
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = 0
y[1] (numeric) = 2.016402758530474481907290502422
absolute error = 2.016402758530474481907290502422
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.946
Order of pole (six term test) = 7.546
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 0
y[1] (numeric) = 2.0261755428806603779870695479384
absolute error = 2.0261755428806603779870695479384
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.949
Order of pole (six term test) = 7.566
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 0
y[1] (numeric) = 2.0359637013268228149694437528335
absolute error = 2.0359637013268228149694437528335
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.951
Order of pole (six term test) = 7.584
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = 0
y[1] (numeric) = 2.0457668374260508886637195982653
absolute error = 2.0457668374260508886637195982653
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.953
Order of pole (six term test) = 7.599
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 0
y[1] (numeric) = 2.0555845520426311352440226917361
absolute error = 2.0555845520426311352440226917361
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.954
Order of pole (six term test) = 7.611
bytes used=144045156, alloc=4652204, time=4.88
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 0
y[1] (numeric) = 2.065416443472872810219606170714
absolute error = 2.065416443472872810219606170714
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.955
Order of pole (six term test) = 7.619
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = 0
y[1] (numeric) = 2.0752621075710665209284705275146
absolute error = 2.0752621075710665209284705275146
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.956
Order of pole (six term test) = 7.624
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = 0
y[1] (numeric) = 2.0851211378765081430423772402391
absolute error = 2.0851211378765081430423772402391
relative error = -1 %
Correct digits = -1
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 = 0.004571
Order of pole (three term test) = -0.9291
Radius of convergence (six term test) for eq 1 = 3.957
Order of pole (six term test) = 7.625
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = 0
y[1] (numeric) = 2.0949931257415190981697490827824
absolute error = 2.0949931257415190981697490827824
relative error = -1 %
Correct digits = -1
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 = 0.01413
Order of pole (three term test) = -1.242
Radius of convergence (six term test) for eq 1 = 3.957
Order of pole (six term test) = 7.622
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = 0
y[1] (numeric) = 2.1048776604603932826935077849557
absolute error = 2.1048776604603932826935077849557
relative error = -1 %
Correct digits = -1
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 = 0.02337
Order of pole (three term test) = -1.869
Radius of convergence (six term test) for eq 1 = 3.957
Order of pole (six term test) = 7.616
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = 0
y[1] (numeric) = 2.1147743293992002183609305116416
absolute error = 2.1147743293992002183609305116416
relative error = -1 %
Correct digits = -1
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 = 0.03207
Order of pole (three term test) = -2.795
Radius of convergence (six term test) for eq 1 = 3.956
Order of pole (six term test) = 7.606
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = 0
y[1] (numeric) = 2.1246827181263733436365975458893
absolute error = 2.1246827181263733436365975458893
relative error = -1 %
Correct digits = -1
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 = 0.04
Order of pole (three term test) = -3.994
Radius of convergence (six term test) for eq 1 = 3.955
Order of pole (six term test) = 7.592
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = 0
y[1] (numeric) = 2.134602410544011782127893802732
absolute error = 2.134602410544011782127893802732
relative error = -1 %
Correct digits = -1
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 = 0.04697
Order of pole (three term test) = -5.438
Radius of convergence (six term test) for eq 1 = 3.954
Order of pole (six term test) = 7.575
TOP MAIN SOLVE Loop
bytes used=148046060, alloc=4652204, time=5.02
x[1] = 3.07
y[1] (analytic) = 0
y[1] (numeric) = 2.1445329890198234110906761079973
absolute error = 2.1445329890198234110906761079973
relative error = -1 %
Correct digits = -1
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 = 0.05278
Order of pole (three term test) = -7.088
Radius of convergence (six term test) for eq 1 = 3.952
Order of pole (six term test) = 7.556
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = 0
y[1] (numeric) = 2.1544740345196366096200549692893
absolute error = 2.1544740345196366096200549692893
relative error = -1 %
Correct digits = -1
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 = 0.05728
Order of pole (three term test) = -8.902
Radius of convergence (six term test) for eq 1 = 3.951
Order of pole (six term test) = 7.534
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = 0
y[1] (numeric) = 2.1644251267404076930305902856233
absolute error = 2.1644251267404076930305902856233
relative error = -1 %
Correct digits = -1
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 = 0.06036
Order of pole (three term test) = -10.83
Radius of convergence (six term test) for eq 1 = 3.949
Order of pole (six term test) = 7.511
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = 0
y[1] (numeric) = 2.1743858442436507374373011310674
absolute error = 2.1743858442436507374373011310674
relative error = -1 %
Correct digits = -1
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 = 0.06192
Order of pole (three term test) = -12.83
Radius of convergence (six term test) for eq 1 = 3.947
Order of pole (six term test) = 7.487
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = 0
y[1] (numeric) = 2.1843557645892162668720804776772
absolute error = 2.1843557645892162668720804776772
relative error = -1 %
Correct digits = -1
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 = 0.06192
Order of pole (three term test) = -14.83
Radius of convergence (six term test) for eq 1 = 3.945
Order of pole (six term test) = 7.462
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = 0
y[1] (numeric) = 2.1943344644693451145202080275453
absolute error = 2.1943344644693451145202080275453
relative error = -1 %
Correct digits = -1
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 = 0.06035
Order of pole (three term test) = -16.79
Radius of convergence (six term test) for eq 1 = 3.943
Order of pole (six term test) = 7.437
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = 0
y[1] (numeric) = 2.2043215198429236798520313612191
absolute error = 2.2043215198429236798520313612191
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.166
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.05724
Order of pole (three term test) = -18.65
Radius of convergence (six term test) for eq 1 = 3.941
Order of pole (six term test) = 7.412
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = 0
y[1] (numeric) = 2.2143165060698667844716843367042
absolute error = 2.2143165060698667844716843367042
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.486
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.05267
Order of pole (three term test) = -20.36
Radius of convergence (six term test) for eq 1 = 3.939
Order of pole (six term test) = 7.389
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = 0
y[1] (numeric) = 2.224318998045554381227285875657
absolute error = 2.224318998045554381227285875657
relative error = -1 %
Correct digits = -1
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 = 0.04676
Order of pole (three term test) = -21.86
Radius of convergence (six term test) for eq 1 = 3.938
Order of pole (six term test) = 7.367
TOP MAIN SOLVE Loop
bytes used=152047168, alloc=4652204, time=5.16
x[1] = 3.16
y[1] (analytic) = 0
y[1] (numeric) = 2.2343285703352484932485748701939
absolute error = 2.2343285703352484932485748701939
relative error = -1 %
Correct digits = -1
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 = 0.03967
Order of pole (three term test) = -23.13
Radius of convergence (six term test) for eq 1 = 3.937
Order of pole (six term test) = 7.348
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = 0
y[1] (numeric) = 2.2443447973084169517261395549006
absolute error = 2.2443447973084169517261395549006
relative error = -1 %
Correct digits = -1
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 = 0.03159
Order of pole (three term test) = -24.11
Radius of convergence (six term test) for eq 1 = 3.936
Order of pole (six term test) = 7.332
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = 0
y[1] (numeric) = 2.2543672532728907629545870403173
absolute error = 2.2543672532728907629545870403173
relative error = -1 %
Correct digits = -1
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 = 0.02275
Order of pole (three term test) = -24.78
Radius of convergence (six term test) for eq 1 = 3.935
Order of pole (six term test) = 7.318
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = 0
y[1] (numeric) = 2.264395512608782265870135036991
absolute error = 2.264395512608782265870135036991
relative error = -1 %
Correct digits = -1
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 = 0.01339
Order of pole (three term test) = -25.12
Radius of convergence (six term test) for eq 1 = 3.935
Order of pole (six term test) = 7.308
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = 0
y[1] (numeric) = 2.274429149902091640369122044976
absolute error = 2.274429149902091640369122044976
relative error = -1 %
Correct digits = -1
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 = 0.003772
Order of pole (three term test) = -25.13
Radius of convergence (six term test) for eq 1 = 3.935
Order of pole (six term test) = 7.301
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = 0
y[1] (numeric) = 2.284467740077929793355178389324
absolute error = 2.284467740077929793355178389324
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.935
Order of pole (six term test) = 7.298
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = 0
y[1] (numeric) = 2.2945108585332861828976788823632
absolute error = 2.2945108585332861828976788823632
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.936
Order of pole (six term test) = 7.298
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = 0
y[1] (numeric) = 2.3045580812692707401738337719129
absolute error = 2.3045580812692707401738337719129
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.937
Order of pole (six term test) = 7.302
TOP MAIN SOLVE Loop
bytes used=156048160, alloc=4652204, time=5.30
x[1] = 3.24
y[1] (analytic) = 0
y[1] (numeric) = 2.3146089850227597130073482625657
absolute error = 2.3146089850227597130073482625657
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.939
Order of pole (six term test) = 7.309
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = 0
y[1] (numeric) = 2.32466314739737598272080500834
absolute error = 2.32466314739737598272080500834
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.941
Order of pole (six term test) = 7.32
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = 0
y[1] (numeric) = 2.334720146993735196518662811795
absolute error = 2.334720146993735196518662811795
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.943
Order of pole (six term test) = 7.333
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 0
y[1] (numeric) = 2.3447795635388899094662891350898
absolute error = 2.3447795635388899094662891350898
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.946
Order of pole (six term test) = 7.349
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = 0
y[1] (numeric) = 2.3548409780149048420049164255718
absolute error = 2.3548409780149048420049164255718
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.949
Order of pole (six term test) = 7.366
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = 0
y[1] (numeric) = 2.3649039727864973294464958303659
absolute error = 2.3649039727864973294464958303659
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.951
Order of pole (six term test) = 7.385
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = 0
y[1] (numeric) = 2.3749681317276780675590067846964
absolute error = 2.3749681317276780675590067846964
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.954
Order of pole (six term test) = 7.405
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = 0
y[1] (numeric) = 2.3850330403473283416468214507927
absolute error = 2.3850330403473283416468214507927
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.958
Order of pole (six term test) = 7.425
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = 0
y[1] (numeric) = 2.3950982859136510638521782551634
absolute error = 2.3950982859136510638521782551634
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.961
Order of pole (six term test) = 7.445
TOP MAIN SOLVE Loop
bytes used=160049240, alloc=4652204, time=5.44
x[1] = 3.33
y[1] (analytic) = 0
y[1] (numeric) = 2.4051634575774341330906905731181
absolute error = 2.4051634575774341330906905731181
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.964
Order of pole (six term test) = 7.464
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = 0
y[1] (numeric) = 2.4152281464940658723652763262666
absolute error = 2.4152281464940658723652763262666
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.967
Order of pole (six term test) = 7.482
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = 0
y[1] (numeric) = 2.4252919459442435874024920757836
absolute error = 2.4252919459442435874024920757836
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.969
Order of pole (six term test) = 7.498
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = 0
y[1] (numeric) = 2.4353544514533176267942038256635
absolute error = 2.4353544514533176267942038256635
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.972
Order of pole (six term test) = 7.511
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = 0
y[1] (numeric) = 2.4454152609092147052280521152468
absolute error = 2.4454152609092147052280521152468
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.974
Order of pole (six term test) = 7.521
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = 0
y[1] (numeric) = 2.4554739746788856760289201196201
absolute error = 2.4554739746788856760289201196201
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.976
Order of pole (six term test) = 7.528
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = 0
y[1] (numeric) = 2.4655301957232244051451239456812
absolute error = 2.4655301957232244051451239456812
relative error = -1 %
Correct digits = -1
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 = 0.004045
Order of pole (three term test) = -0.9207
Radius of convergence (six term test) for eq 1 = 3.977
Order of pole (six term test) = 7.532
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = 0
y[1] (numeric) = 2.4755835297104059038932372490682
absolute error = 2.4755835297104059038932372490682
relative error = -1 %
Correct digits = -1
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 = 0.01376
Order of pole (three term test) = -1.212
Radius of convergence (six term test) for eq 1 = 3.978
Order of pole (six term test) = 7.532
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = 0
y[1] (numeric) = 2.4856335851275934201851913452249
absolute error = 2.4856335851275934201851913452249
relative error = -1 %
Correct digits = -1
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 = 0.02334
Order of pole (three term test) = -1.813
Radius of convergence (six term test) for eq 1 = 3.979
Order of pole (six term test) = 7.529
TOP MAIN SOLVE Loop
bytes used=164050144, alloc=4652204, time=5.59
x[1] = 3.42
y[1] (analytic) = 0
y[1] (numeric) = 2.4956799733909657655299102504859
absolute error = 2.4956799733909657655299102504859
relative error = -1 %
Correct digits = -1
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 = 0.03255
Order of pole (three term test) = -2.71
Radius of convergence (six term test) for eq 1 = 3.98
Order of pole (six term test) = 7.521
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = 0
y[1] (numeric) = 2.5057223089540177657306893309397
absolute error = 2.5057223089540177657306893309397
relative error = -1 %
Correct digits = -1
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 = 0.04116
Order of pole (three term test) = -3.88
Radius of convergence (six term test) for eq 1 = 3.98
Order of pole (six term test) = 7.511
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = 0
y[1] (numeric) = 2.5157602094140883647659385757219
absolute error = 2.5157602094140883647659385757219
relative error = -1 %
Correct digits = -1
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 = 0.04897
Order of pole (three term test) = -5.295
Radius of convergence (six term test) for eq 1 = 3.98
Order of pole (six term test) = 7.496
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = 0
y[1] (numeric) = 2.5257932956170725817012159174452
absolute error = 2.5257932956170725817012159174452
relative error = -1 %
Correct digits = -1
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 = 0.05578
Order of pole (three term test) = -6.919
Radius of convergence (six term test) for eq 1 = 3.979
Order of pole (six term test) = 7.479
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = 0
y[1] (numeric) = 2.5358211917602752174740020233627
absolute error = 2.5358211917602752174740020233627
relative error = -1 %
Correct digits = -1
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 = 0.06141
Order of pole (three term test) = -8.713
Radius of convergence (six term test) for eq 1 = 3.978
Order of pole (six term test) = 7.458
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = 0
y[1] (numeric) = 2.545843525493365929845239073634
absolute error = 2.545843525493365929845239073634
relative error = -1 %
Correct digits = -1
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 = 0.06572
Order of pole (three term test) = -10.63
Radius of convergence (six term test) for eq 1 = 3.977
Order of pole (six term test) = 7.435
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = 0
y[1] (numeric) = 2.5558599280173970385391654351451
absolute error = 2.5558599280173970385391654351451
relative error = -1 %
Correct digits = -1
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) = -12.62
Radius of convergence (six term test) for eq 1 = 3.976
Order of pole (six term test) = 7.41
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = 0
y[1] (numeric) = 2.5658700341818471864049395798494
absolute error = 2.5658700341818471864049395798494
relative error = -1 %
Correct digits = -1
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 = 0.06996
Order of pole (three term test) = -14.64
Radius of convergence (six term test) for eq 1 = 3.975
Order of pole (six term test) = 7.384
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = 0
y[1] (numeric) = 2.5758734825796557641366132155711
absolute error = 2.5758734825796557641366132155711
relative error = -1 %
Correct digits = -1
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 = 0.06976
Order of pole (three term test) = -16.62
Radius of convergence (six term test) for eq 1 = 3.973
Order of pole (six term test) = 7.357
TOP MAIN SOLVE Loop
bytes used=168051096, alloc=4652204, time=5.73
x[1] = 3.51
y[1] (analytic) = 0
y[1] (numeric) = 2.5858699156402148034894578425802
absolute error = 2.5858699156402148034894578425802
relative error = -1 %
Correct digits = -1
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 = 0.06801
Order of pole (three term test) = -18.52
Radius of convergence (six term test) for eq 1 = 3.972
Order of pole (six term test) = 7.329
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = 0
y[1] (numeric) = 2.5958589797202868548417969001357
absolute error = 2.5958589797202868548417969001357
relative error = -1 %
Correct digits = -1
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 = 0.06473
Order of pole (three term test) = -20.29
Radius of convergence (six term test) for eq 1 = 3.97
Order of pole (six term test) = 7.301
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = 0
y[1] (numeric) = 2.6058403251928191871911092048687
absolute error = 2.6058403251928191871911092048687
relative error = -1 %
Correct digits = -1
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 = 0.06001
Order of pole (three term test) = -21.87
Radius of convergence (six term test) for eq 1 = 3.969
Order of pole (six term test) = 7.274
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = 0
y[1] (numeric) = 2.6158136065336264800707699181866
absolute error = 2.6158136065336264800707699181866
relative error = -1 %
Correct digits = -1
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 = 0.05397
Order of pole (three term test) = -23.23
Radius of convergence (six term test) for eq 1 = 3.968
Order of pole (six term test) = 7.249
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = 0
y[1] (numeric) = 2.625778482405916015272922966399
absolute error = 2.625778482405916015272922966399
relative error = -1 %
Correct digits = -1
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 = 0.04677
Order of pole (three term test) = -24.33
Radius of convergence (six term test) for eq 1 = 3.967
Order of pole (six term test) = 7.225
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = 0
y[1] (numeric) = 2.6357346157426312195243814420235
absolute error = 2.6357346157426312195243814420235
relative error = -1 %
Correct digits = -1
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 = 0.03859
Order of pole (three term test) = -25.13
Radius of convergence (six term test) for eq 1 = 3.966
Order of pole (six term test) = 7.203
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = 0
y[1] (numeric) = 2.6456816738265912552671983728082
absolute error = 2.6456816738265912552671983728082
relative error = -1 %
Correct digits = -1
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 = 0.02964
Order of pole (three term test) = -25.61
Radius of convergence (six term test) for eq 1 = 3.965
Order of pole (six term test) = 7.184
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = 0
y[1] (numeric) = 2.6556193283684062033480599885809
absolute error = 2.6556193283684062033480599885809
relative error = -1 %
Correct digits = -1
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 = 0.02018
Order of pole (three term test) = -25.77
Radius of convergence (six term test) for eq 1 = 3.965
Order of pole (six term test) = 7.167
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = 0
y[1] (numeric) = 2.6655472555821492266516456429385
absolute error = 2.6655472555821492266516456429385
relative error = -1 %
Correct digits = -1
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 = 0.01045
Order of pole (three term test) = -25.59
Radius of convergence (six term test) for eq 1 = 3.965
Order of pole (six term test) = 7.154
bytes used=172054636, alloc=4652204, time=5.87
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = 0
y[1] (numeric) = 2.6754651362587689454824434760971
absolute error = 2.6754651362587689454824434760971
relative error = -1 %
Correct digits = -1
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 = 0.0007207
Order of pole (three term test) = -25.09
Radius of convergence (six term test) for eq 1 = 3.966
Order of pole (six term test) = 7.144
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = 0
y[1] (numeric) = 2.6853726558372270917989905577791
absolute error = 2.6853726558372270917989905577791
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.967
Order of pole (six term test) = 7.137
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = 0
y[1] (numeric) = 2.6952695044733483382604729876585
absolute error = 2.6952695044733483382604729876585
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.968
Order of pole (six term test) = 7.134
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = 0
y[1] (numeric) = 2.7051553771063710175215539976197
absolute error = 2.7051553771063710175215539976197
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.97
Order of pole (six term test) = 7.134
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = 0
y[1] (numeric) = 2.7150299735231892554102503945334
absolute error = 2.7150299735231892554102503945334
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.972
Order of pole (six term test) = 7.137
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = 0
y[1] (numeric) = 2.7248929984202788366906172365478
absolute error = 2.7248929984202788366906172365478
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.974
Order of pole (six term test) = 7.143
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = 0
y[1] (numeric) = 2.7347441614633009022360338546192
absolute error = 2.7347441614633009022360338546192
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.977
Order of pole (six term test) = 7.152
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = 0
y[1] (numeric) = 2.7445831773443793398553658799213
absolute error = 2.7445831773443793398553658799213
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.979
Order of pole (six term test) = 7.162
TOP MAIN SOLVE Loop
bytes used=176055284, alloc=4652204, time=6.01
x[1] = 3.68
y[1] (analytic) = 0
y[1] (numeric) = 2.7544097658370494760068019811118
absolute error = 2.7544097658370494760068019811118
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.983
Order of pole (six term test) = 7.175
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = 0
y[1] (numeric) = 2.764223651848877400536435317336
absolute error = 2.764223651848877400536435317336
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.986
Order of pole (six term test) = 7.189
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = 0
y[1] (numeric) = 2.7740245654717509597762429332512
absolute error = 2.7740245654717509597762429332512
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.989
Order of pole (six term test) = 7.204
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = 0
y[1] (numeric) = 2.7838122420298451332680621505595
absolute error = 2.7838122420298451332680621505595
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.992
Order of pole (six term test) = 7.219
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = 0
y[1] (numeric) = 2.7935864221252661645405100895995
absolute error = 2.7935864221252661645405100895995
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.996
Order of pole (six term test) = 7.234
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = 0
y[1] (numeric) = 2.803346851681380445304944356203
absolute error = 2.803346851681380445304944356203
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.999
Order of pole (six term test) = 7.248
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = 0
y[1] (numeric) = 2.8130932819838357537625397406676
absolute error = 2.8130932819838357537625397406676
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.002
Order of pole (six term test) = 7.261
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = 0
y[1] (numeric) = 2.8228254697192840200941201578551
absolute error = 2.8228254697192840200941201578551
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.005
Order of pole (six term test) = 7.273
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = 0
y[1] (numeric) = 2.8325431770118163343640429209726
absolute error = 2.8325431770118163343640429209726
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.008
Order of pole (six term test) = 7.282
TOP MAIN SOLVE Loop
bytes used=180056776, alloc=4652204, time=6.16
x[1] = 3.77
y[1] (analytic) = 0
y[1] (numeric) = 2.8422461714571224227963086780989
absolute error = 2.8422461714571224227963086780989
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.011
Order of pole (six term test) = 7.288
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = 0
y[1] (numeric) = 2.8519342261543882965236603161984
absolute error = 2.8519342261543882965236603161984
relative error = -1 %
Correct digits = -1
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 = 0.004636
Order of pole (three term test) = -0.928
Radius of convergence (six term test) for eq 1 = 4.013
Order of pole (six term test) = 7.291
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = 0
y[1] (numeric) = 2.8616071197359472213792319299586
absolute error = 2.8616071197359472213792319299586
relative error = -1 %
Correct digits = -1
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 = 0.01451
Order of pole (three term test) = -1.229
Radius of convergence (six term test) for eq 1 = 4.015
Order of pole (six term test) = 7.292
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = 0
y[1] (numeric) = 2.8712646363947005670683135712574
absolute error = 2.8712646363947005670683135712574
relative error = -1 %
Correct digits = -1
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 = 0.02439
Order of pole (three term test) = -1.83
Radius of convergence (six term test) for eq 1 = 4.017
Order of pole (six term test) = 7.289
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = 0
y[1] (numeric) = 2.8809065659093264681608985734976
absolute error = 2.8809065659093264681608985734976
relative error = -1 %
Correct digits = -1
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 = 0.03408
Order of pole (three term test) = -2.719
Radius of convergence (six term test) for eq 1 = 4.018
Order of pole (six term test) = 7.282
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = 0
y[1] (numeric) = 2.8905327036672955668829249439814
absolute error = 2.8905327036672955668829249439814
relative error = -1 %
Correct digits = -1
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 = 0.04334
Order of pole (three term test) = -3.875
Radius of convergence (six term test) for eq 1 = 4.019
Order of pole (six term test) = 7.272
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = 0
y[1] (numeric) = 2.9001428506857144078178653979022
absolute error = 2.9001428506857144078178653979022
relative error = -1 %
Correct digits = -1
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 = 0.05196
Order of pole (three term test) = -5.272
Radius of convergence (six term test) for eq 1 = 4.02
Order of pole (six term test) = 7.258
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = 0
y[1] (numeric) = 2.9097368136300183165862598640307
absolute error = 2.9097368136300183165862598640307
relative error = -1 %
Correct digits = -1
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 = 0.05975
Order of pole (three term test) = -6.877
Radius of convergence (six term test) for eq 1 = 4.02
Order of pole (six term test) = 7.242
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = 0
y[1] (numeric) = 2.9193144048305368176378837429936
absolute error = 2.9193144048305368176378837429936
relative error = -1 %
Correct digits = -1
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 = 0.06652
Order of pole (three term test) = -8.653
Radius of convergence (six term test) for eq 1 = 4.02
Order of pole (six term test) = 7.222
TOP MAIN SOLVE Loop
bytes used=184058004, alloc=4652204, time=6.30
x[1] = 3.86
y[1] (analytic) = 0
y[1] (numeric) = 2.9288754422969558298215486295326
absolute error = 2.9288754422969558298215486295326
relative error = -1 %
Correct digits = -1
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 = 0.07211
Order of pole (three term test) = -10.56
Radius of convergence (six term test) for eq 1 = 4.019
Order of pole (six term test) = 7.199
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = 0
y[1] (numeric) = 2.9384197497307020218058698550895
absolute error = 2.9384197497307020218058698550895
relative error = -1 %
Correct digits = -1
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 = 0.07639
Order of pole (three term test) = -12.55
Radius of convergence (six term test) for eq 1 = 4.019
Order of pole (six term test) = 7.174
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = 0
y[1] (numeric) = 2.9479471565352758121879265334511
absolute error = 2.9479471565352758121879265334511
relative error = -1 %
Correct digits = -1
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 = 0.07924
Order of pole (three term test) = -14.58
Radius of convergence (six term test) for eq 1 = 4.018
Order of pole (six term test) = 7.146
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = 0
y[1] (numeric) = 2.9574574978245605607846955086887
absolute error = 2.9574574978245605607846955086887
relative error = -1 %
Correct digits = -1
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 = 0.0806
Order of pole (three term test) = -16.59
Radius of convergence (six term test) for eq 1 = 4.017
Order of pole (six term test) = 7.117
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = 0
y[1] (numeric) = 2.9669506144291365177548671769841
absolute error = 2.9669506144291365177548671769841
relative error = -1 %
Correct digits = -1
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 = 0.08042
Order of pole (three term test) = -18.54
Radius of convergence (six term test) for eq 1 = 4.016
Order of pole (six term test) = 7.087
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = 0
y[1] (numeric) = 2.9764263529006290755071612457407
absolute error = 2.9764263529006290755071612457407
relative error = -1 %
Correct digits = -1
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 = 0.0787
Order of pole (three term test) = -20.38
Radius of convergence (six term test) for eq 1 = 4.015
Order of pole (six term test) = 7.056
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = 0
y[1] (numeric) = 2.9858845655141218045363928802629
absolute error = 2.9858845655141218045363928802629
relative error = -1 %
Correct digits = -1
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 = 0.07548
Order of pole (three term test) = -22.07
Radius of convergence (six term test) for eq 1 = 4.014
Order of pole (six term test) = 7.025
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = 0
y[1] (numeric) = 2.9953251102686656481700923096042
absolute error = 2.9953251102686656481700923096042
relative error = -1 %
Correct digits = -1
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 = 0.07082
Order of pole (three term test) = -23.56
Radius of convergence (six term test) for eq 1 = 4.013
Order of pole (six term test) = 6.995
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = 0
y[1] (numeric) = 3.004747850885916502544260879202
absolute error = 3.004747850885916502544260879202
relative error = -1 %
Correct digits = -1
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 = 0.06484
Order of pole (three term test) = -24.81
Radius of convergence (six term test) for eq 1 = 4.012
Order of pole (six term test) = 6.965
TOP MAIN SOLVE Loop
bytes used=188058968, alloc=4652204, time=6.44
x[1] = 3.95
y[1] (analytic) = 0
y[1] (numeric) = 3.0141526568069342168516406523108
absolute error = 3.0141526568069342168516406523108
relative error = -1 %
Correct digits = -1
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 = 0.05769
Order of pole (three term test) = -25.79
Radius of convergence (six term test) for eq 1 = 4.011
Order of pole (six term test) = 6.936
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = 0
y[1] (numeric) = 3.0235394031871768149703451491951
absolute error = 3.0235394031871768149703451491951
relative error = -1 %
Correct digits = -1
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 = 0.04953
Order of pole (three term test) = -26.47
Radius of convergence (six term test) for eq 1 = 4.01
Order of pole (six term test) = 6.909
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = 0
y[1] (numeric) = 3.0329079708897244629902072559608
absolute error = 3.0329079708897244629902072559608
relative error = -1 %
Correct digits = -1
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 = 0.04057
Order of pole (three term test) = -26.85
Radius of convergence (six term test) for eq 1 = 4.01
Order of pole (six term test) = 6.885
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = 0
y[1] (numeric) = 3.0422582464767683879675646396235
absolute error = 3.0422582464767683879675646396235
relative error = -1 %
Correct digits = -1
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 = 0.03102
Order of pole (three term test) = -26.9
Radius of convergence (six term test) for eq 1 = 4.01
Order of pole (six term test) = 6.862
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = 0
y[1] (numeric) = 3.051590122199400591567391195229
absolute error = 3.051590122199400591567391195229
relative error = -1 %
Correct digits = -1
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 = 0.02114
Order of pole (three term test) = -26.64
Radius of convergence (six term test) for eq 1 = 4.01
Order of pole (six term test) = 6.843
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = 0
y[1] (numeric) = 3.0609034959857407982564480794867
absolute error = 3.0609034959857407982564480794867
relative error = -1 %
Correct digits = -1
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) = -26.06
Radius of convergence (six term test) for eq 1 = 4.011
Order of pole (six term test) = 6.826
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = 0
y[1] (numeric) = 3.0701982714274376316035876378726
absolute error = 3.0701982714274376316035876378726
relative error = -1 %
Correct digits = -1
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 = 0.001311
Order of pole (three term test) = -25.18
Radius of convergence (six term test) for eq 1 = 4.012
Order of pole (six term test) = 6.812
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = 0
y[1] (numeric) = 3.0794743577645815242825101730191
absolute error = 3.0794743577645815242825101730191
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.013
Order of pole (six term test) = 6.802
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = 0
y[1] (numeric) = 3.0887316698690673378635363514423
absolute error = 3.0887316698690673378635363514423
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.015
Order of pole (six term test) = 6.795
TOP MAIN SOLVE Loop
bytes used=192059884, alloc=4652204, time=6.58
x[1] = 4.04
y[1] (analytic) = 0
y[1] (numeric) = 3.09797012822644509777452413963
absolute error = 3.09797012822644509777452413963
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.017
Order of pole (six term test) = 6.79
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = 0
y[1] (numeric) = 3.1071896589162976373003556387345
absolute error = 3.1071896589162976373003556387345
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.019
Order of pole (six term test) = 6.788
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = 0
y[1] (numeric) = 3.1163901935911842926104616149444
absolute error = 3.1163901935911842926104616149444
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.022
Order of pole (six term test) = 6.789
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = 0
y[1] (numeric) = 3.125571669454190099029582220695
absolute error = 3.125571669454190099029582220695
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.024
Order of pole (six term test) = 6.792
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = 0
y[1] (numeric) = 3.1347340292351202076115628045639
absolute error = 3.1347340292351202076115628045639
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.027
Order of pole (six term test) = 6.797
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = 0
y[1] (numeric) = 3.1438772211653794710891647160874
absolute error = 3.1438772211653794710891647160874
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.031
Order of pole (six term test) = 6.803
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = 0
y[1] (numeric) = 3.1530011989515773400391452419972
absolute error = 3.1530011989515773400391452419972
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.034
Order of pole (six term test) = 6.809
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = 0
y[1] (numeric) = 3.1621059217478983642388005655753
absolute error = 3.1621059217478983642388005655753
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.037
Order of pole (six term test) = 6.815
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = 0
y[1] (numeric) = 3.171191354127278711346650354769
absolute error = 3.171191354127278711346650354769
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.04
Order of pole (six term test) = 6.821
bytes used=196061472, alloc=4652204, time=6.72
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = 0
y[1] (numeric) = 3.180257466051429195894399399935
absolute error = 3.180257466051429195894399399935
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.043
Order of pole (six term test) = 6.826
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = 0
y[1] (numeric) = 3.1893042328397453568359527713959
absolute error = 3.1893042328397453568359527713959
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.046
Order of pole (six term test) = 6.828
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = 0
y[1] (numeric) = 3.1983316351371451322943208293686
absolute error = 3.1983316351371451322943208293686
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.049
Order of pole (six term test) = 6.828
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = 0
y[1] (numeric) = 3.2073396588808746564352271166614
absolute error = 3.2073396588808746564352271166614
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.051
Order of pole (six term test) = 6.824
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = 0
y[1] (numeric) = 3.2163282952663226463561349602988
absolute error = 3.2163282952663226463561349602988
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.053
Order of pole (six term test) = 6.816
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = 0
y[1] (numeric) = 3.2252975407118837573110157453127
absolute error = 3.2252975407118837573110157453127
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.054
Order of pole (six term test) = 6.803
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = 0
y[1] (numeric) = 3.2342473968229111633133112391792
absolute error = 3.2342473968229111633133112391792
relative error = -1 %
Correct digits = -1
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 = 0.009017
Order of pole (three term test) = -1.017
Radius of convergence (six term test) for eq 1 = 4.055
Order of pole (six term test) = 6.785
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = 0
y[1] (numeric) = 3.2431778703547984680083382599344
absolute error = 3.2431778703547984680083382599344
relative error = -1 %
Correct digits = -1
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 = 0.01915
Order of pole (three term test) = -1.432
Radius of convergence (six term test) for eq 1 = 4.055
Order of pole (six term test) = 6.76
TOP MAIN SOLVE Loop
bytes used=200062544, alloc=4652204, time=6.87
x[1] = 4.21
y[1] (analytic) = 0
y[1] (numeric) = 3.2520889731752308685336221521127
absolute error = 3.2520889731752308685336221521127
relative error = -1 %
Correct digits = -1
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 = 0.02938
Order of pole (three term test) = -2.131
Radius of convergence (six term test) for eq 1 = 4.054
Order of pole (six term test) = 6.73
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = 0
y[1] (numeric) = 3.260980722225645283757059824455
absolute error = 3.260980722225645283757059824455
relative error = -1 %
Correct digits = -1
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 = 0.0395
Order of pole (three term test) = -3.099
Radius of convergence (six term test) for eq 1 = 4.053
Order of pole (six term test) = 6.692
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = 0
y[1] (numeric) = 3.2698531394819389186764458917599
absolute error = 3.2698531394819389186764458917599
relative error = -1 %
Correct digits = -1
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 = 0.04931
Order of pole (three term test) = -4.317
Radius of convergence (six term test) for eq 1 = 4.051
Order of pole (six term test) = 6.647
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = 0
y[1] (numeric) = 3.278706251914465469768474301575
absolute error = 3.278706251914465469768474301575
relative error = -1 %
Correct digits = -1
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 = 0.0586
Order of pole (three term test) = -5.76
Radius of convergence (six term test) for eq 1 = 4.048
Order of pole (six term test) = 6.595
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = 0
y[1] (numeric) = 3.2875400914473578825886705957889
absolute error = 3.2875400914473578825886705957889
relative error = -1 %
Correct digits = -1
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 = 0.0672
Order of pole (three term test) = -7.399
Radius of convergence (six term test) for eq 1 = 4.044
Order of pole (six term test) = 6.536
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = 0
y[1] (numeric) = 3.2963546949172162538511606635093
absolute error = 3.2963546949172162538511606635093
relative error = -1 %
Correct digits = -1
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 = 0.0749
Order of pole (three term test) = -9.198
Radius of convergence (six term test) for eq 1 = 4.039
Order of pole (six term test) = 6.468
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = 0
y[1] (numeric) = 3.3051501040311991264700790444814
absolute error = 3.3051501040311991264700790444814
relative error = -1 %
Correct digits = -1
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 = 0.08156
Order of pole (three term test) = -11.12
Radius of convergence (six term test) for eq 1 = 4.034
Order of pole (six term test) = 6.394
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = 0
y[1] (numeric) = 3.3139263653245560585385995816658
absolute error = 3.3139263653245560585385995816658
relative error = -1 %
Correct digits = -1
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 = 0.08702
Order of pole (three term test) = -13.13
Radius of convergence (six term test) for eq 1 = 4.027
Order of pole (six term test) = 6.312
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = 0
y[1] (numeric) = 3.3226835301176389568759061722493
absolute error = 3.3226835301176389568759061722493
relative error = -1 %
Correct digits = -1
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 = 0.09117
Order of pole (three term test) = -15.17
Radius of convergence (six term test) for eq 1 = 4.02
Order of pole (six term test) = 6.223
TOP MAIN SOLVE Loop
bytes used=204063240, alloc=4652204, time=7.00
x[1] = 4.3
y[1] (analytic) = 0
y[1] (numeric) = 3.3314216544724292535073978170495
absolute error = 3.3314216544724292535073978170495
relative error = -1 %
Correct digits = -1
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 = 0.09392
Order of pole (three term test) = -17.22
Radius of convergence (six term test) for eq 1 = 4.013
Order of pole (six term test) = 6.128
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = 0
y[1] (numeric) = 3.340140799148617570179756289686
absolute error = 3.340140799148617570179756289686
relative error = -1 %
Correct digits = -1
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 = 0.09519
Order of pole (three term test) = -19.21
Radius of convergence (six term test) for eq 1 = 4.004
Order of pole (six term test) = 6.027
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = 0
y[1] (numeric) = 3.3488410295592720626697994817339
absolute error = 3.3488410295592720626697994817339
relative error = -1 %
Correct digits = -1
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 = 0.09496
Order of pole (three term test) = -21.11
Radius of convergence (six term test) for eq 1 = 3.995
Order of pole (six term test) = 5.92
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = 0
y[1] (numeric) = 3.3575224157261311641414872584263
absolute error = 3.3575224157261311641414872584263
relative error = -1 %
Correct digits = -1
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 = 0.09322
Order of pole (three term test) = -22.88
Radius of convergence (six term test) for eq 1 = 3.985
Order of pole (six term test) = 5.81
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = 0
y[1] (numeric) = 3.3661850322345559560525550147305
absolute error = 3.3661850322345559560525550147305
relative error = -1 %
Correct digits = -1
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 = 0.09001
Order of pole (three term test) = -24.47
Radius of convergence (six term test) for eq 1 = 3.975
Order of pole (six term test) = 5.695
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = 0
y[1] (numeric) = 3.3748289581881768870196511561954
absolute error = 3.3748289581881768870196511561954
relative error = -1 %
Correct digits = -1
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 = 0.08538
Order of pole (three term test) = -25.85
Radius of convergence (six term test) for eq 1 = 3.965
Order of pole (six term test) = 5.579
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = 0
y[1] (numeric) = 3.383454277163269035521119255283
absolute error = 3.383454277163269035521119255283
relative error = -1 %
Correct digits = -1
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 = 0.07944
Order of pole (three term test) = -26.99
Radius of convergence (six term test) for eq 1 = 3.954
Order of pole (six term test) = 5.46
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = 0
y[1] (numeric) = 3.3920610771628895722450826949183
absolute error = 3.3920610771628895722450826949183
relative error = -1 %
Correct digits = -1
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 = 0.07232
Order of pole (three term test) = -27.86
Radius of convergence (six term test) for eq 1 = 3.944
Order of pole (six term test) = 5.341
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = 0
y[1] (numeric) = 3.4006494505708105231643879661541
absolute error = 3.4006494505708105231643879661541
relative error = -1 %
Correct digits = -1
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 = 0.06416
Order of pole (three term test) = -28.44
Radius of convergence (six term test) for eq 1 = 3.933
Order of pole (six term test) = 5.222
TOP MAIN SOLVE Loop
bytes used=208064336, alloc=4652204, time=7.15
x[1] = 4.39
y[1] (analytic) = 0
y[1] (numeric) = 3.4092194941052793659170788336914
absolute error = 3.4092194941052793659170788336914
relative error = -1 %
Correct digits = -1
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 = 0.05515
Order of pole (three term test) = -28.73
Radius of convergence (six term test) for eq 1 = 3.922
Order of pole (six term test) = 5.106
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = 0
y[1] (numeric) = 3.4177713087726394106589660725607
absolute error = 3.4177713087726394106589660725607
relative error = -1 %
Correct digits = -1
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 = 0.04549
Order of pole (three term test) = -28.7
Radius of convergence (six term test) for eq 1 = 3.912
Order of pole (six term test) = 4.992
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = 0
y[1] (numeric) = 3.4263049998208413230898692741847
absolute error = 3.4263049998208413230898692741847
relative error = -1 %
Correct digits = -1
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 = 0.0354
Order of pole (three term test) = -28.38
Radius of convergence (six term test) for eq 1 = 3.902
Order of pole (six term test) = 4.882
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = 0
y[1] (numeric) = 3.4348206766928765426814742388649
absolute error = 3.4348206766928765426814742388649
relative error = -1 %
Correct digits = -1
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 = 0.02509
Order of pole (three term test) = -27.75
Radius of convergence (six term test) for eq 1 = 3.893
Order of pole (six term test) = 4.778
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = 0
y[1] (numeric) = 3.4433184529801627340837568610336
absolute error = 3.4433184529801627340837568610336
relative error = -1 %
Correct digits = -1
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 = 0.01478
Order of pole (three term test) = -26.85
Radius of convergence (six term test) for eq 1 = 3.885
Order of pole (six term test) = 4.681
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = 0
y[1] (numeric) = 3.4517984463759107850761098913641
absolute error = 3.4517984463759107850761098913641
relative error = -1 %
Correct digits = -1
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 = 0.004719
Order of pole (three term test) = -25.69
Radius of convergence (six term test) for eq 1 = 3.877
Order of pole (six term test) = 4.592
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = 0
y[1] (numeric) = 3.4602607786285022310617131791805
absolute error = 3.4602607786285022310617131791805
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.871
Order of pole (six term test) = 4.512
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = 0
y[1] (numeric) = 3.4687055754949053447671516909957
absolute error = 3.4687055754949053447671516909957
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.866
Order of pole (six term test) = 4.443
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = 0
y[1] (numeric) = 3.4771329666941574812757931711742
absolute error = 3.4771329666941574812757931711742
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.862
Order of pole (six term test) = 4.385
TOP MAIN SOLVE Loop
bytes used=212065276, alloc=4652204, time=7.29
x[1] = 4.48
y[1] (analytic) = 0
y[1] (numeric) = 3.4855430858609406135485064740989
absolute error = 3.4855430858609406135485064740989
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.86
Order of pole (six term test) = 4.34
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = 0
y[1] (numeric) = 3.4939360704992763329074185721172
absolute error = 3.4939360704992763329074185721172
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.86
Order of pole (six term test) = 4.31
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = 0
y[1] (numeric) = 3.5023120619363659232985079367339
absolute error = 3.5023120619363659232985079367339
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.861
Order of pole (six term test) = 4.294
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = 0
y[1] (numeric) = 3.5106712052766004482098225453267
absolute error = 3.5106712052766004482098225453267
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.864
Order of pole (six term test) = 4.295
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = 0
y[1] (numeric) = 3.5190136493557651155884417761066
absolute error = 3.5190136493557651155884417761066
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.87
Order of pole (six term test) = 4.314
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = 0
y[1] (numeric) = 3.5273395466954615096365750876427
absolute error = 3.5273395466954615096365750876427
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.877
Order of pole (six term test) = 4.351
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = 0
y[1] (numeric) = 3.5356490534577705996218145939834
absolute error = 3.5356490534577705996218145939834
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.887
Order of pole (six term test) = 4.407
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = 0
y[1] (numeric) = 3.5439423294001787554354416346164
absolute error = 3.5439423294001787554354416346164
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.9
Order of pole (six term test) = 4.483
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = 0
y[1] (numeric) = 3.5522195378307883181829723822163
absolute error = 3.5522195378307883181829723822163
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.914
Order of pole (six term test) = 4.58
TOP MAIN SOLVE Loop
bytes used=216066400, alloc=4652204, time=7.43
x[1] = 4.57
y[1] (analytic) = 0
y[1] (numeric) = 3.560480845563833592179966708075
absolute error = 3.560480845563833592179966708075
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.932
Order of pole (six term test) = 4.698
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = 0
y[1] (numeric) = 3.5687264228755224429204917651392
absolute error = 3.5687264228755224429204917651392
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.952
Order of pole (six term test) = 4.837
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = 0
y[1] (numeric) = 3.5769564434602230044321722030096
absolute error = 3.5769564434602230044321722030096
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.974
Order of pole (six term test) = 4.997
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = 0
y[1] (numeric) = 3.5851710843870143194566750835597
absolute error = 3.5851710843870143194566750835597
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 3.998
Order of pole (six term test) = 5.176
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = 0
y[1] (numeric) = 3.5933705260566190576034503971137
absolute error = 3.5933705260566190576034503971137
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 4.024
Order of pole (six term test) = 5.374
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = 0
y[1] (numeric) = 3.601554952158735780502692235033
absolute error = 3.601554952158735780502692235033
relative error = -1 %
Correct digits = -1
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 = 0.008323
Order of pole (three term test) = -0.9912
Radius of convergence (six term test) for eq 1 = 4.052
Order of pole (six term test) = 5.588
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = 0
y[1] (numeric) = 3.6097245496297875494953375288379
absolute error = 3.6097245496297875494953375288379
relative error = -1 %
Correct digits = -1
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 = 0.01863
Order of pole (three term test) = -1.361
Radius of convergence (six term test) for eq 1 = 4.082
Order of pole (six term test) = 5.814
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = 0
y[1] (numeric) = 3.6178795086111030009874566880882
absolute error = 3.6178795086111030009874566880882
relative error = -1 %
Correct digits = -1
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 = 0.02922
Order of pole (three term test) = -2
Radius of convergence (six term test) for eq 1 = 4.112
Order of pole (six term test) = 6.049
TOP MAIN SOLVE Loop
bytes used=220067444, alloc=4652204, time=7.57
x[1] = 4.65
y[1] (analytic) = 0
y[1] (numeric) = 3.6260200224075453476870831313138
absolute error = 3.6260200224075453476870831313138
relative error = -1 %
Correct digits = -1
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 = 0.03992
Order of pole (three term test) = -2.897
Radius of convergence (six term test) for eq 1 = 4.142
Order of pole (six term test) = 6.285
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = 0
y[1] (numeric) = 3.634146287446604100936417737462
absolute error = 3.634146287446604100936417737462
relative error = -1 %
Correct digits = -1
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 = 0.05052
Order of pole (three term test) = -4.035
Radius of convergence (six term test) for eq 1 = 4.171
Order of pole (six term test) = 6.516
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = 0
y[1] (numeric) = 3.6422585032379636506341500499501
absolute error = 3.6422585032379636506341500499501
relative error = -1 %
Correct digits = -1
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 = 0.06086
Order of pole (three term test) = -5.394
Radius of convergence (six term test) for eq 1 = 4.198
Order of pole (six term test) = 6.731
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = 0
y[1] (numeric) = 3.6503568723335621851738950747163
absolute error = 3.6503568723335621851738950747163
relative error = -1 %
Correct digits = -1
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 = 0.07073
Order of pole (three term test) = -6.951
Radius of convergence (six term test) for eq 1 = 4.222
Order of pole (six term test) = 6.917
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = 0
y[1] (numeric) = 3.6584416002881537847479617090693
absolute error = 3.6584416002881537847479617090693
relative error = -1 %
Correct digits = -1
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 = 0.07997
Order of pole (three term test) = -8.677
Radius of convergence (six term test) for eq 1 = 4.241
Order of pole (six term test) = 7.062
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = 0
y[1] (numeric) = 3.6665128956203858776035148153796
absolute error = 3.6665128956203858776035148153796
relative error = -1 %
Correct digits = -1
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 = 0.0884
Order of pole (three term test) = -10.54
Radius of convergence (six term test) for eq 1 = 4.253
Order of pole (six term test) = 7.149
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = 0
y[1] (numeric) = 3.6745709697744036106937043427891
absolute error = 3.6745709697744036106937043427891
relative error = -1 %
Correct digits = -1
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 = 0.09587
Order of pole (three term test) = -12.51
Radius of convergence (six term test) for eq 1 = 4.257
Order of pole (six term test) = 7.162
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = 0
y[1] (numeric) = 3.6826160370819920539231469491415
absolute error = 3.6826160370819920539231469491415
relative error = -1 %
Correct digits = -1
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 = 0.1022
Order of pole (three term test) = -14.55
Radius of convergence (six term test) for eq 1 = 4.25
Order of pole (six term test) = 7.084
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = 0
y[1] (numeric) = 3.6906483147252665311097437159894
absolute error = 3.6906483147252665311097437159894
relative error = -1 %
Correct digits = -1
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 = 0.1074
Order of pole (three term test) = -16.61
Radius of convergence (six term test) for eq 1 = 4.231
Order of pole (six term test) = 6.901
TOP MAIN SOLVE Loop
bytes used=224068644, alloc=4717728, time=7.71
x[1] = 4.74
y[1] (analytic) = 0
y[1] (numeric) = 3.6986680226999207511188087752528
absolute error = 3.6986680226999207511188087752528
relative error = -1 %
Correct digits = -1
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 = 0.1112
Order of pole (three term test) = -18.67
Radius of convergence (six term test) for eq 1 = 4.199
Order of pole (six term test) = 6.601
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = 0
y[1] (numeric) = 3.7066753837790417995978865656103
absolute error = 3.7066753837790417995978865656103
relative error = -1 %
Correct digits = -1
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 = 0.1136
Order of pole (three term test) = -20.68
Radius of convergence (six term test) for eq 1 = 4.152
Order of pole (six term test) = 6.179
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = 0
y[1] (numeric) = 3.7146706234775004455601877424281
absolute error = 3.7146706234775004455601877424281
relative error = -1 %
Correct digits = -1
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 = 0.1146
Order of pole (three term test) = -22.61
Radius of convergence (six term test) for eq 1 = 4.09
Order of pole (six term test) = 5.634
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = 0
y[1] (numeric) = 3.7226539700169246179220562929847
absolute error = 3.7226539700169246179220562929847
relative error = -1 %
Correct digits = -1
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 = 0.1141
Order of pole (three term test) = -24.41
Radius of convergence (six term test) for eq 1 = 4.013
Order of pole (six term test) = 4.975
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = 0
y[1] (numeric) = 3.7306256542912633151684562860562
absolute error = 3.7306256542912633151684562860562
relative error = -1 %
Correct digits = -1
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 = 0.1121
Order of pole (three term test) = -26.06
Radius of convergence (six term test) for eq 1 = 3.922
Order of pole (six term test) = 4.215
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = 0
y[1] (numeric) = 3.7385859098329476267560347822042
absolute error = 3.7385859098329476267560347822042
relative error = -1 %
Correct digits = -1
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 = 0.1087
Order of pole (three term test) = -27.51
Radius of convergence (six term test) for eq 1 = 3.819
Order of pole (six term test) = 3.375
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = 0
y[1] (numeric) = 3.746534972779654967804878939605
absolute error = 3.746534972779654967804878939605
relative error = -1 %
Correct digits = -1
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 = 0.1039
Order of pole (three term test) = -28.75
Radius of convergence (six term test) for eq 1 = 3.705
Order of pole (six term test) = 2.48
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = 0
y[1] (numeric) = 3.7544730818416820592001224677477
absolute error = 3.7544730818416820592001224677477
relative error = -1 %
Correct digits = -1
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 = 0.09786
Order of pole (three term test) = -29.74
Radius of convergence (six term test) for eq 1 = 3.584
Order of pole (six term test) = 1.554
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = 0
y[1] (numeric) = 3.7624004782699316235294222962666
absolute error = 3.7624004782699316235294222962666
relative error = -1 %
Correct digits = -1
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 = 0.09062
Order of pole (three term test) = -30.48
Radius of convergence (six term test) for eq 1 = 3.457
Order of pole (six term test) = 0.6222
TOP MAIN SOLVE Loop
bytes used=228070068, alloc=4717728, time=7.85
x[1] = 4.83
y[1] (analytic) = 0
y[1] (numeric) = 3.7703174058245172134126443161396
absolute error = 3.7703174058245172134126443161396
relative error = -1 %
Correct digits = -1
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 = 0.08235
Order of pole (three term test) = -30.95
Radius of convergence (six term test) for eq 1 = 3.328
Order of pole (six term test) = -0.2933
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = 0
y[1] (numeric) = 3.7782241107439900428111707387691
absolute error = 3.7782241107439900428111707387691
relative error = -1 %
Correct digits = -1
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 = 0.0732
Order of pole (three term test) = -31.13
Radius of convergence (six term test) for eq 1 = 3.199
Order of pole (six term test) = -1.175
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = 0
y[1] (numeric) = 3.7861208417151911538964714612598
absolute error = 3.7861208417151911538964714612598
relative error = -1 %
Correct digits = -1
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 = 0.06336
Order of pole (three term test) = -31.03
Radius of convergence (six term test) for eq 1 = 3.071
Order of pole (six term test) = -2.008
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = 0
y[1] (numeric) = 3.7940078498437317220568899324187
absolute error = 3.7940078498437317220568899324187
relative error = -1 %
Correct digits = -1
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 = 0.05301
Order of pole (three term test) = -30.66
Radius of convergence (six term test) for eq 1 = 2.948
Order of pole (six term test) = -2.785
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = 0
y[1] (numeric) = 3.8018853886251037796598552299724
absolute error = 3.8018853886251037796598552299724
relative error = -1 %
Correct digits = -1
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 = 0.04235
Order of pole (three term test) = -30.01
Radius of convergence (six term test) for eq 1 = 2.83
Order of pole (six term test) = -3.499
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = 0
y[1] (numeric) = 3.8097537139164231252822106818229
absolute error = 3.8097537139164231252822106818229
relative error = -1 %
Correct digits = -1
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 = 0.03158
Order of pole (three term test) = -29.12
Radius of convergence (six term test) for eq 1 = 2.719
Order of pole (six term test) = -4.149
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = 0
y[1] (numeric) = 3.8176130839088056792791406752232
absolute error = 3.8176130839088056792791406752232
relative error = -1 %
Correct digits = -1
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 = 0.02089
Order of pole (three term test) = -27.99
Radius of convergence (six term test) for eq 1 = 2.614
Order of pole (six term test) = -4.734
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = 0
y[1] (numeric) = 3.8254637591003780487746531504347
absolute error = 3.8254637591003780487746531504347
relative error = -1 %
Correct digits = -1
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 = 0.01047
Order of pole (three term test) = -26.65
Radius of convergence (six term test) for eq 1 = 2.518
Order of pole (six term test) = -5.257
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = 0
y[1] (numeric) = 3.833306002269922575403832985671
absolute error = 3.833306002269922575403832985671
relative error = -1 %
Correct digits = -1
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 = 0.0005216
Order of pole (three term test) = -25.12
Radius of convergence (six term test) for eq 1 = 2.43
Order of pole (six term test) = -5.719
TOP MAIN SOLVE Loop
bytes used=232070908, alloc=4717728, time=7.99
x[1] = 4.92
y[1] (analytic) = 0
y[1] (numeric) = 3.8411400784511566573873953184612
absolute error = 3.8411400784511566573873953184612
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.35
Order of pole (six term test) = -6.125
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = 0
y[1] (numeric) = 3.8489662549076456637293424541721
absolute error = 3.8489662549076456637293424541721
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.279
Order of pole (six term test) = -6.478
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = 0
y[1] (numeric) = 3.8567848011083482924447530861896
absolute error = 3.8567848011083482924447530861896
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.218
Order of pole (six term test) = -6.782
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = 0
y[1] (numeric) = 3.8645959887037927666824382175395
absolute error = 3.8645959887037927666824382175395
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.165
Order of pole (six term test) = -7.038
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = 0
y[1] (numeric) = 3.8724000915028818123319104263783
absolute error = 3.8724000915028818123319104263783
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.121
Order of pole (six term test) = -7.25
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = 0
y[1] (numeric) = 3.8801973854503239181118088191589
absolute error = 3.8801973854503239181118088191589
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.087
Order of pole (six term test) = -7.419
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = 0
y[1] (numeric) = 3.8879881486046879441344829139755
absolute error = 3.8879881486046879441344829139755
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.064
Order of pole (six term test) = -7.545
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = 0
y[1] (numeric) = 3.8957726611170777174271039966579
absolute error = 3.8957726611170777174271039966579
relative error = -1 %
Correct digits = -1
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
Radius of convergence (six term test) for eq 1 = 2.051
Order of pole (six term test) = -7.627
Finished!
diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(x));
Iterations = 490
Total Elapsed Time = 8 Seconds
Elapsed Time(since restart) = 7 Seconds
Time to Timeout = 2 Minutes 51 Seconds
Percent Done = 100.2 %
> quit
bytes used=235662308, alloc=4717728, time=8.10